Hortense Duboureau

Mariette Renaud-Petel

MD Céline Klein

MD Elodie Haraux
email: haraux.elodie@chu-amiens.fr

DEVELOPMENT AND EVALUATION OF A LOW-COST PART-TASK TRAINER FOR LAPAROSCOPIC REPAIR OF INGUINAL HERNIA IN BOYS AND THE ACQUISITION OF BASIC LAPAROSCOPY SKILLS

INTRODUCTION

Laparoscopy is an essential surgical tool that is now supplanting open surgery in many indications, included those in pediatric surgery [START_REF] Velde | Minimally invasive pediatric surgery: Increasing implementation in daily practice and resident's training[END_REF]. Although surgical skills have traditionally been taught and learnt through companionship in the operating room, this paradigm has recently been challenged by legal and ethical concerns for patient safety, work hour restrictions, the cost of operating room time, and the risk of complications. Simulation offers a potential solution to two conflicting demands: residents want to be trained in surgery but parents want their children to be operated on by experienced surgeons. This has become especially true since the advent of minimally invasive pediatric surgery; a counter-intuitive visuospatial interface and greatly reduced proprioceptive feedback create specific training issues [START_REF] Bidarkar | Role of simulation for paediatric proceduralists: practice makes perfect or trial and error?[END_REF]. It has been shown that simulations improve the operating room performance of surgical residents -especially for laparoscopy, a technically demanding procedure that requires regular practice [START_REF] Roberts | Evolution of surgical skills training[END_REF].

Low-cost models enable laparoscopic skills to be practiced more freely [START_REF] Li | A systematic review of low-cost laparoscopic simulators[END_REF]. We therefore developed a novel, lowcost model of laparoscopic inguinal hernia repair (LIHR) in boys. Congenital inguinal hernias are caused by the persistence of the vaginal process. As described by Becmeur et al. [START_REF] Becmeur | A continuous series of 96 laparoscopic inguinal hernia repairs in children by a new technique[END_REF], the laparoscopic technique reproduces each of the steps in conventional surgery: dissection, division, and suture of the vaginal process at the internal inguinal ring. In boys specifically, the vaginal process is freed from the vas deferens and the testicular artery and then fully divided. Lastly, the peritoneum is closed with an intracorporeal knot. The objectives of the present study were to evaluate this part-task trainer in LIHR and assess its value in resident training programs and, more generally, in the learning of basic laparoscopy skills.

MATERIALS AND METHODS

We have conceived and designed an LIHR simulation model that can be assembled easily from low-cost, readily available equipment and implemented with a user manual (Appendix 1 online and Video 1 (Video)). Firstly, a plastic bottle (volume: >1 L) was cut 7 cm below the neck and 7 cm from the bottom. The intermediate part was discarded. The plastic ring under the bottle cap is removed from the neck of the bottle before assembly, and kept for later. The bottom part was kept for the end of the assembly. The top part of the bottle (the "funnel") was turned upside down and inclined, in order to mimic the inguinal canal. A colored non-sterile surgical glove (size L or XL) was applied to the funnel; the fingers were passed through the neck and cut off a few centimeters below. The glove mimicked the inguinal wall; at the end of the procedure, the surgeon could check whether or not the wall had been accidentally perforated. Two elastic loops (e.g. Ethiloops® or "scoubidou" lanyards) of different colors were placed in the bottle neck; these respectively represented the vas deferens and the testicular artery. The threads were fixed with adhesive tape (e.g. Leukoplast® S LF from BSN Medical, Hamburg, end of the second glove's fingers were also cut off a few centimeters below the neck of the bottle. The plastic ring present around the neck of the bottle can be used to hold the distal part of the folded gloves and the loops.

The gloves must be tight. The bottom of the bottle was then used. A small hole was made in the center of the bottom, using a pair of scissors. A resistant elastic loop or an elongated balloon was knotted around the neck of the bottle and then passed through the hole in the bottom of the bottle, in order to attach the two parts together. It is important to place the neck of the bottle at an angle and to tape it tightly to the laparoscopic trainer.

We mailed an user manual and an evaluation questionnaire to all of the university medical center performing pediatric surgery in France (32), to one university medical center in Belgium, and to all the other surgical units in our university medical center (urology, visceral surgery, and gynecology) that used laparoscopy (Appendix 1, online only). We proposed to all the surgical teams to test and to evaluate this model in order to have various level of laparoscopic practitioners. We collected participant's characteristics (status (resident, expert), surgical specialty), time for model construction and for the procedure (min). The evaluation questionnaire featured 11 items rated on a 5-point Likert scale (Table 2). The item scores were described as the median [interquartile range (IQR)] and compared as a function of the level of expertise (residents vs. experts) using Student's t test. The threshold for statistical significance was set to p<0.01. We calculated an overall score by summing the median scores for all but three of the items. Two of the excluded items concerned the ease of the procedure (the ease of glove resection and the ease of suturing); in retrospect, we considered that they were not directly related to the model's quality and were very dependent on the participant's level of expertise. The third item was the quality of the view; in retrospect, we considered that this item was imprecise. We considered the model had been of value when the median overall score was 4 or over.

RESULTS

From April 2018 to April 2019, 55 practitioners from 10 university medical centers (34 departments, including 31 pediatric surgery departments and 3 general surgery departments) participated in the study. The participants' characteristics are summarized in Table 1. Forty-one of the 55 participants (74.6%) were pediatric surgeons. The scores given by the participants are detailed in Table 2. In both groups, all the participants managed to assemble the model and perform the training procedure.

The time needed to assemble the model was relatively short: 15.0 ± 6.2 minutes overall, 12.0 for the residents and 15.0 minutes for the experts (p=0.07). The mean duration of the laparoscopy procedure was significantly longer for the residents (30.0 ± 16.8 min) than for the experts (26.5 ± 11.7 min; p=0.01).

The participants had a good overall impression of the model (4.0 ± 1.0) and had no difficulty in obtaining the required equipment (76.3% of the participants gave a score of 5 out of 5 for this item).

The participants considered that the user manual was very easy to understand (score: (5.0 ± 0.6) and that the model was very easy to assemble (25.4 % of the participants gave a score of 4, and 49% gave a score of 5); there were no significant intergroup differences for these scores. Furthermore, the participants considered that the model was moderately easy to use (3.0 ± 0.9) and quite realistic (4.0 ± 0.9).

The model was considered to be very easy to use by 7% of the participants, easy to use by 12.8%, moderately easy to use by 49%, difficult to use by 23.6%, and very difficult to use by 5.4%. Middling scores were given for the quality of the view (3.0), resection of the glove (3.0) and suturing (3.0). Suturing was reported more difficult for the residents (with a mean score of 4.0, vs. 3.0 for the experts; p=0.01). The model's value in learning basic laparoscopy skills was rated at 5.0 (5.0 for the residents vs. 4.0 for the experts; p=0.004). Although both groups awarded a high score for this item, the score was significantly higher among the residents than among the experts. The median overall score was 4.0 (4.1 for the residents vs. 4.0 for the experts; p=0.36); according to our criterion, the evaluation was therefore positive.

DISCUSSION

Simulators are educational tools that enable physicians to repeatedly practice medical procedures in complete safety. The use of a simulator avoids the stress induced by real operating conditions [START_REF] Roberts | Evolution of surgical skills training[END_REF]. Moreover, laparoscopic surgery training for residents is a major need [START_REF] Fiard | The role of simulation in the curriculum of French urologists-in-training: a study by the French Association of Urologists-in-Training (AFUF)][END_REF][START_REF] Philippe | Interest of a structured laparoscopy training in a simulation center: survey of resident's point of view[END_REF]. Training on animals, human cadavers and high or low fidelity simulators is possible, but these models are not always widely available. The cost of simulation systems, the large number of residents (relative to the number of simulators) and the shortcomings of this type of training restrict continuing medical education for residents [START_REF] Fiard | The role of simulation in the curriculum of French urologists-in-training: a study by the French Association of Urologists-in-Training (AFUF)][END_REF].

Low-cost simulation models constitute a very interesting option for surgical education, since they offer unlimited access to training. However, it is essential to find an appropriate model that meets the surgeon's training needs.

A number of low-cost models have been described in the literature [START_REF] Rod | Low-cost training simulator for open dismembered pyeloplasty: development and face validation[END_REF][START_REF] Nazari | Validity of a Low-Cost Lichtenstein Open Inguinal Hernia Repair Simulation Model for Surgical Training[END_REF]. The main objective of the present study was to evaluate a low-cost model of LIHR. Even though the majority of pediatric inguinal hernias are repaired through open surgery, laparoscopic surgery is a minimally invasive treatment option. Although this operation is often performed laparoscopically, we chose to model this particular procedure because it involves a variety of basic laparoscopy skills. Indeed, we focused more on the precise performance of laparoscopic procedures than on LIHR per se. Our trainees used the model to learn to grip, resect, suture and knot in different directions.

Our part-task trainer is easily assembled from material that is cheap and readily available. We also designed a questionnaire so that surgeons could evaluate our model. Firstly, we achieved our main objective; the model was evaluated by our participants as a tool for learning LIHR and basic laparoscopy skills. The participants had a good opinion of our manual and our model, regardless of their level of expertise and their surgical specialty. In this study, we recorded data concerning our creation of the model, the performance of the procedure and the users' level of satisfaction. Despite the apparent common-sense validity, our study design prevented us from formally validating the model or confirming its ability to train surgeons effectively.

The participants considered that the procedure was moderately difficult to perform, and the suturing was a little more difficult. The residents took significantly longer to perform the simulated procedure. This disparity can be explained by the fact that suturing is the most technically difficult procedure and by the difference in the level of expertise between the two groups. This may also be why the residents gave a higher score than the experts did for the model's value in learning basic laparoscopy skills.

Judging from the scores given by the participants, easy access to the material required to build the model is an asset of our design. Moreover, the time taken to assemble the model was acceptably short. It noteworthy that once the model had been built, it can be used to perform another procedure by fitting new gloves. Robert et al.

have described a low-cost laparoscopy home training model [START_REF] Robert | Development and validation of a model of training at home to the laparoscopy[END_REF] that could be combined with our model for training purposes. Building a low-cost model from easy-to-source material may enable a resident to progress by training at hospital or at home.

The study participants judged that the model was realistic. Although this plastic model clearly does not simulate human tissue, it does schematically represent the main anatomical features needed to understand and learn the surgical procedure. When designing the model, we tested various types of equipment. The neck of the bottle was selected because it mimicked the internal inguinal ring. We also wanted to make the model smaller, and so tried to build it with a smaller bottle. Unfortunately, this test was not satisfactory. Firstly, the glove was not fully stretched over a smaller bottle, and the remaining folds would have hindered the procedure. Secondly, the mouth of the smaller bottle was the same size as in the bigger bottle, and so did not resemble the baby's anatomy. The study participants' main criticism concerned the view, with a mean score of 3.3 out of 5. In retrospect, we admit that this item was too imprecise to be useful in evaluating the model, since it concerned both the model and the laparoscopic trainer. Hence, we decided to exclude this item from the mean overall score. In fact, the view in a conventional laparoscopic trainer is not optimal, since the fixed tablet camera provides a view along a single axis; in contrast, the coelioscopy camera held by the surgical assistant can track the surgeon's movement. In our experience, repeated training with simple, nonrealistic model is more beneficial than the occasional use of a high-fidelity model.

It has been proven that simulation improves the operating room performance of surgical residents [START_REF] Derossis | The effect of practice on performance in laparoscopic simulator[END_REF].

Development of standardized training curricula is an absolutely necessity -particularly for minimally invasive surgery [START_REF] Velde | Minimally invasive pediatric surgery: Increasing implementation in daily practice and resident's training[END_REF]). The French National Pediatric Surgery Simulation Program was initiated in 2015 [START_REF] Breaud | The National Pediatric Surgery Simulation Program in France: A tool to develop resident training in pediatric surgery[END_REF].

Following the present study, our model was used as a training tool in this national program. We now would like to validate this model as an educational tool -mainly for the acquisition of basic laparoscopic surgical skills. By collating data from the French national program's annual evaluation, we also intend to study the model's potential for translation into clinical practice and the retention of the learned skills over time. Repeated practice with our model might accelerate the learning curve, as has been described in the literature for other models [START_REF] Velde | Minimally invasive pediatric surgery: Increasing implementation in daily practice and resident's training[END_REF][START_REF] Seymour | Virtual Reality Training Improves Operating Room Performance[END_REF][START_REF] Lynagh | A systematic review of medical skills laboratory training: where to from here[END_REF].

It might be possible to extrapolate our model to other methods of congenital inguinal hernia repair (such as nondismembered repair, where the whole vaginal process is left in place) or to adult inguinal hernia repair (by placing the inferior epigastric vessel either medial or lateral to the defect, so that the surgeon can also open up the preperitoneal space).

Lastly, we hope that this model will be disseminated and will improve the surgical skills of surgical residents, including those in developing countries where access to practical training may be more limited.

CONCLUSION

Declaration of Interest: None

  We developed a low-cost simulation model of LIHR for surgical training and skills acquisition. This low-cost model was evaluated positively and as an effective teaching and training tool for LIHR and basic laparoscopy skills. This type of practical work should be integrated into resident training programs. Our model has already been used in the French National Pediatric Surgery Simulation Program and might be of value in many other countries -especially developing countries.

Table 1 : Characteristics of the participants

 1

	Surgical specialty UROLOGY PEDIATRICS	VISCERAL SURGERY	GYNECOLOGY	TOTAL n (%)
	EXPERTS (SENIORS/ ASSISTANTS)	4 (1/3)	25 (15/10)	0	0	29 (52.7%) (29.1/ 23.6)
	RESIDENTS	7	16	2	1	26 (47.3)
	TOTAL n (%)	11 (20.0)	41 (74.6)	2 (3.6)	1 (1.8)	55 (100)

Table 2 : Results of the evaluation Median duration [IQR] (min)

 2

		All participants (n=55)	Residents (n=29)	Experts (n=26)	p
	Assembly	15.0 [10.0-16.0] 12.0 [10.0-22.7] 15.0 [10.0-15.0]	0.07
	Procedure	26.5 [15.0-33.2] 30.0 [20.0-42.2] 20.0 [13.2-30.0]	0.01*
	Total


David Laharie
email: david.laharie@chu-bordeaux.fr

Arnaud Bourreille

Julien Branche

Matthieu Allez

Yoram Bouhnik

Jerome Filippi

Frank Zerbib

Guillaume Savoye

Lucine Vuitton

Jacques Moreau

A Amiot

L Beaugerie

O Dewit

A Lopez-Sanroman

M Fumery

A Buisson

B Coffin

G Van Assche

M Farkkila

J P Gisbert

S Nahon

JB, MA, YB, JF, FZ, GS, LV, JM, AA, JC, ER, OD, ALS, JLD Ab

Ipsen. G Savoye declares boards, transports Spindler

Coloplast Vifor Benckiser

Pharma

Alfasigma, Janssen, Biocodex Mayoli Takeda

MSD Ferring

Mayoli Janssen

Biocodex Janssen

E Ricart

Takeda Roche

X Roblin

Pfizer, Janssen, Takeda Abbvie

Evolution of endoscopic lesions in steroid-refractory acute severe ulcerative colitis responding to infliximab or cyclosporine

Keywords: ulcerative colitis, cyclosporine, infliximab, mucosal healing, UCEIS

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

What You Need to Know

Background:

-Endoscopic remission has become a therapeutic goal in ulcerative colitis -Few data are available on the evolution of endoscopic lesions of patients admitted for acute severe ulcerative colitis

Findings:

-Endoscopic remission of acute severe ulcerative colitis takes approximately three months -It starts with bleeding remission, followed by ulceration/erosion healing and then by restoration of the vascular pattern.

-Infliximab provides higher rate of patients in endoscopic remission than cyclosporine in patients who experienced intravenous steroid failure.

Implications for patient care:

-Patients should not be assessed too early by flexible sigmoidoscopy.

-Infliximab provides a higher endoscopic remission rate than cyclosporine at three months.

Introduction

Ulcerative colitis is a chronic and disabling inflammatory bowel disease affecting the rectum and the colon [START_REF] Ungaro | A treat-to-target update in ulcerative colitis: a systematic review[END_REF], characterized by unpredictable inflammatory flares that can be in 25% of patients a life-threatening severe attack (2).

Identification of patients having an acute severe ulcerative colitis is still based on the historical clinico-biological Truelove-Witts criteria [START_REF] Truelove | Cortisone in ulcerative colitis; final report on a therapeutic trial[END_REF][START_REF] Harbord | Third European Evidence-based Consensus on Diagnosis and Management of Ulcerative Colitis. Part 2: Current Management[END_REF]. These patients should be emergently admitted in a dedicated unit to receive speed-acting parenteral drugs according to a standardized protocol with the aim to avoid salvage colectomy [START_REF] Harbord | Third European Evidence-based Consensus on Diagnosis and Management of Ulcerative Colitis. Part 2: Current Management[END_REF]. The medical regimen starts with intravenous steroids, followed by infliximab or cyclosporine in case of failure.

Despite an optimal management, even in experienced centers, acute severe ulcerative colitis death rate remains 1% in Western countries [START_REF] Dong | Systematic review with meta-analysis: mortality in acute severe ulcerative colitis[END_REF].

The ultimate therapeutic objective in ulcerative colitis is to achieve sustained steroid-free clinical remission together with healing of endoscopic inflammatory lesions (4). Consequently, repeated endoscopic assessments have been implemented in practice to score the severity of endoscopic lesions to adjust the therapeutic strategy. The two more frequently used endoscopic ulcerative colitis scoring systems are the Mayo endoscopic subscore and the more recent ulcerative colitis endoscopic index of severity (UCEIS) that has been built and validated on the most reproducible inflammatory items that are vascular pattern, bleeding and erosions/ulcerations [START_REF] Schroeder | Coated oral5-aminosalicylic acid therapy for mildly to moderately activeulcerative colitis. A randomized study[END_REF](7)[START_REF] Travis | Reliability and initial validation of the ulcerative colitis endoscopic index of severity[END_REF][START_REF] Vuitton | Defining endoscopic response and remission in ulcerative colitis clinical trials: an international consensus[END_REF]. Interestingly, UCEIS can be used for assessing patients with acute severe ulcerative colitis as shown by two retrospective cohorts [START_REF] Corte | Association between the ulcerative colitis endoscopic index of severity (UCEIS) and outcomes in acute severe ulcerative colitis[END_REF][START_REF] Xie | Ulcerative Colitis Endoscopic Index of Severity (UCEIS) versus Mayo Endoscopic Score (MES) in guiding the need for colectomy in patients with acute severe colitis[END_REF] Few data are available on the evolution of acute severe ulcerative colitis endoscopic lesions.

Therefore, the aim of the present study was to describe the evolution of endoscopic lesions in a prospective cohort of patients admitted for a steroid-refractory acute severe ulcerative colitis and included in the CYSIF trial [START_REF] Laharie | Ciclosporine versus infliximab in acute severe colitis refractory to intravenous steroids: a randomized study[END_REF], if they responded to a second-line medical therapy. published in extenso showing that treatment failure occurred in 60% patients given cyclosporine and 54% given infliximab [START_REF] Laharie | Ciclosporine versus infliximab in acute severe colitis refractory to intravenous steroids: a randomized study[END_REF].

Methods

Study design and patients

CYSIF was a

The institutional review board at each center approved the protocol, and all patients provided written informed consent.

For assessment of endoscopic disease activity, four flexible sigmoidoscopies planed in the study protocol were performed at baseline and at days 7, 42 and 98 in patients still in the study. Examinations were locally read and not recorded.

All patients enrolled into the CYSIF trial were included in the endoscopic post-hoc analysis if they achieved steroid-free clinical remission at day 98, defined as total Mayo score at 2 or less with a Mayo endoscopic sub-score at 1 or less, or if they had steroid-free Mayo endoscopic sub-score at 2 and all other sub-scores at 1 or less at day 98 without new treatment initiated at day 98. Patients who experienced a relapse or any severe adverse event leading to treatment modification or interruption between day 7 and day 98 have been excluded.

Endoscopic findings

For each endoscopic assessment, the following pre-specified endoscopic lesions were recorded per segment (rectum and sigmoid colon) on a standardized form: erythema (absent/mild/moderate/frank), friability (absent/mild/moderate/marked), granularity (absent/ present), erosion (absent/rare/intermediate/numerous), superficial ulceration (absent/rare/ intermediate/numerous), deep ulceration (absent/rare/intermediate/numerous), including welllike ulceration, mucosal detachment and mucosal abrasion (absent/present), pseudopolyp (absent/present). Mayo endoscopic sub-score was reported from the standardized form. As UCEIS is available since 2012, total score and its sub-scores -vascular pattern, bleeding and erosions/ulcerations -were post-hoc calculated in each segment from endoscopic reports as follows: vascular pattern was scored 0 when erythema was normal, 1 when it was mild and 2 when it was moderate or frank; bleeding was scored as friability; erosions/ulcerations was scored 0 when erosion and ulceration were absent, 1 in presence of erosion but no ulceration, 2 in presence of superficial ulceration but not deep ulceration and 3 in presence of deep ulceration. Global UCEIS and, vascular pattern, bleeding and erosions/ulcerations sub-scores were calculated for the whole examination, as maximal values across rectum and sigmoid segments.

Global endoscopic remission was defined as UCEIS at 0 and partial endoscopic remission as vascular pattern sub-score at 0 for vascular pattern, as bleeding sub-score at 0 for bleeding, as erosions/ulcerations sub-score at 0 for ulceration/erosion.

Objectives

Objectives of the study were the following: i) to describe the time course of Mayo endoscopic sub-score, UCEIS and UCEIS sub-scores globally and per treatment group; ii) to compare endoscopic remission between the three UCEIS sub-scores at each time point globally and per treatment group; iii) to compare the evolution of the UCEIS erosions/ulcerations sub-score between patients having a sub-score of 3 and those having a sub-score of 2 at inclusion at each time point; iv) to compare global and partial endoscopic remission between rectum and sigmoid at each time point; v) to compare global and partial endoscopic remission between patients treated with infliximab and those receiving cyclosporine and at each time point.

Statistics

Patient characteristics were described through n, proportion, median, inter-quartile range (IQR) for qualitative and quantitative items, respectively. To describe Mayo endoscopic subscore, UCEIS and its sub-scores, n, mean ± standard deviation, proportions of each sub-score value were used since median (IQR) were not enough informative due to too numerous ties. Partial endoscopic remission rates were compared between UCEIS sub-scores at each time points through paired chi-square test. Global and partial endoscopic remission rates were compared similarly between rectum and sigmoid segments. UCEIS and its sub-scores were compared at each time point between both treatment groups, as endoscopic remission rates through chi-square test or as absolute levels through Mann-Whitney test.

According to the numerous tests performed, significance was achieved for a p-value less than 0.005.

Results

Study population

From the 115 patients randomized in the CYSIF trial, 55 have been included into the present endoscopic analysis (29 received infliximab and 26 cyclosporine) because they achieved steroid-free clinical remission at day 98. Characteristics of these 55 patients were similar regarding age, gender, disease extension, median Lichtiger score and median CRP level with those of the 60 randomized patients who were excluded from the present analysis.

Main patients' characteristics and endoscopic findings at baseline are presented per treatment arm in table 1. Briefly, 30 (55%) were women with a median age of 35 (IQR: 27-48) years and a median disease duration since diagnosis of 2.1 (0.2-7.0) years; 14 (25%) patients were admitted for first attack of ulcerative colitis. At inclusion, patients had received intravenous steroids during 8 (6-9) days; they had median Lichtiger score of 12 [START_REF] Xie | Ulcerative Colitis Endoscopic Index of Severity (UCEIS) versus Mayo Endoscopic Score (MES) in guiding the need for colectomy in patients with acute severe colitis[END_REF][START_REF] Laharie | Ciclosporine versus infliximab in acute severe colitis refractory to intravenous steroids: a randomized study[END_REF](13).

Regarding endoscopic findings at baseline, all except two patients had Mayo endoscopic subscore of 3 and 49 (89%) patients had UCEIS of 6 or more. Regarding UCEIS sub-scores at baseline, 55 (100%) patients had vascular pattern sub-score of 2, 41 (75%) bleeding subscore of 2-3 and 53 (96%) erosions/ulcerations subscore of 2-3.

Evolution of endoscopic lesions

UCEIS and Mayo endoscopic sub-scores are described in figures 1, UCEIS sub-scores in figure 2.

In the whole cohort, endoscopic remission defined by UCEIS of 0 was achieved in 1 (n=55, 2%) patient at day 7, 13 (n=54, 24%) at day 42 and in 25 (n=50, 50%) at day 98. The endoscopic remission rate for vascular pattern was lower than the endoscopic remission rates for bleeding, but not for erosions/ulcerations, at day 7 (20% and 5%, n=55, p=0.004 and p=1.00). The endoscopic remission rate for vascular pattern was lower than the endoscopic remission rates for bleeding and for erosions/ulcerations at day 42 (62% and 65%, n=54, p<0.001 for both) and at day 98 (78% and 92%, n=50, p=0.007 and p<0.001) (Figure 3). As described in figures S1 (supplementary appendix), these results were mainly observed among cyclosporine treated patients, whereas the sub-score remission rates appeared to evolve in a more parallel way in patients on infliximab.

When comparing patients having erosions/ulcerations sub-score of 3 to patients having a erosions/ulcerations sub-score of 2 at inclusion, proportions of patients achieving erosions/ulcerations sub-score of 0 were 0% and 22% (n=44 and 9) at day 7 (p=0.03), 58% and 89% (n=43 and 9) at day 42 (p=0.13) and 90% and 100% (n=39 and 9) at day 98 (p=1.00).

Evolution of endoscopic lesions according to bowel segment

There was no observed difference in endoscopic remission rates between sigmoid and rectum at each time-point whatever the assessment used, UCEIS or UCEIS sub-scores (table S1 in supplementary appendix).

Evolution of endoscopic lesions according to medication

UCEIS, Mayo endoscopic sub-score and UCEIS sub-scores are described according to treatment in figure S2 and S3 in supplementary appendix.

Endoscopic remission rates with infliximab and cyclosporine were 3% and 0% (n=29 and 26, p=0.34) at day 7, 28% and 20 % (n=29 and 25, p=0.52) at day 42 and, 73% and 25% (n=26 and 24, p<0.001) at day 98, respectively (Figure 4). Median UCEIS was significantly lower in patients treated with infliximab than in those who received cyclosporine only at day 98 (p=0.002; p=0.45 at day 7 and p=0.64 at day 42).

Regarding UCEIS sub-scores in patients treated by infliximab and cyclosporine, endoscopic remission rates at day 98 were 81% and 29% for vascular pattern (p=0.002), 88% and 67% for bleeding (p=0.06), 88%% and 96% for erosions/ulcerations (p=0.34), suggesting that the observed difference on UCEIS between infliximab and cyclosporine treated patients was mainly due to a difference in vascular pattern sub-score (Figure S4 in the supplementary appendix).

Discussion

In a prospective cohort of patients admitted for steroid-refractory acute severe ulcerative colitis responding to a second-line medical therapy, we observed that the process of endoscopic response in patients started from day 7 with absence of bleeding, and then followed by ulceration healing and by restoration of the vascular pattern, without discrepancies between sigmoid and rectum. We also observed that endoscopic remission rate at day 98 was higher in patients treated with infliximab than with cyclosporine.

Controlled trials assessing the efficacy of biologic agents in refractory ulcerative colitis, evaluated endoscopic remission -defined as Mayo endoscopic sub-score of 0-1 -at the end of the induction period (13)(14)[START_REF] Sandborn | Subcutaneous golimumab induces clinical response and remission in patients with moderate-to severe ulcerative colitis[END_REF][START_REF] Feagan | Vedolizumab as induction and maintenance therapy for ulcerative colitis[END_REF][START_REF] Sandborn | Tofacitinib as induction and maintenance therapy for ulcerative colitis[END_REF][START_REF] Sands | Ustekinumab as induction and maintenance therapy for ulcerative colitis[END_REF][START_REF] Sands | Vedolizumab versus adalimumab in moderate-to-severe ulcerative colitis[END_REF]. However, data on the evolution of endoscopic lesions from baseline to this endpoint is scarce. Drug-related factors, such as its mode of action or speed of onset, and disease-related factors, like endoscopic severity at baseline and segmental location between colon and rectum, may influence the evolution of endoscopic healing in ulcerative colitis. This granularity of data cannot be captured by sequential fecal calprotectin measurements and requires repeated endoscopic assessments. We present here one of the first study conducted in ulcerative colitis that closely monitored endoscopic response by four flexible sigmoidoscopies within 14 weeks. The optimal time point for assessing mucosal healing in ulcerative colitis remains arbitrary, from 6 to 12 weeks in controlled trials and depends on medication given. Our data suggest leaving sufficient time for healing to occur and to do not look at it too early in patients who started anti-TNF or cyclosporine.

We observed that bleeding and ulcerations improved within 6 weeks in two third of patients, while the recovery of normal vascular pattern took longer and was only achieved in half of patients at day 98. It could be speculated that histological remission would be the next step.

Unfortunately, no biopsy samples were collected in our cohort.

Two randomized controlled trials have compared infliximab to cyclosporine in acute severe ulcerative colitis showing no difference on short and long-term outcomes between both drugs [START_REF] Laharie | Ciclosporine versus infliximab in acute severe colitis refractory to intravenous steroids: a randomized study[END_REF][START_REF] Laharie | Long-term outcome of patients with steroidrefractory acute severe UC treated with ciclosporin or infliximab[END_REF][START_REF] Williams | Comparison Of iNfliximab and ciclosporin in STeroid Resistant Ulcerative Colitis: pragmatic randomised Trial and economic evaluation (CONSTRUCT)[END_REF]. However, in this ancillary study from the CYSIF trial, infliximab induced a significantly higher proportion of endoscopic remission, i.e. Mayo endoscopic subscore or UCEIS 0, than cyclosporine. This result was confirmed when comparing median UCEIS at day 98 while responders to infliximab had higher median Lichtiger score and CRP level at baseline than responders to cyclosporine. Such a finding may have an impact on subsequent disease course as several studies have shown that patients with a remnant mild endoscopic inflammation experience more relapse and surgery than those who achieved mucosal healing [START_REF] Colombel | Early mucosal healing with infliximab is associated with improved long-term clinical outcomes in ulcerative colitis[END_REF][START_REF] Ardizzone | Mucosal healing predicts late outcomes after the first course of corticosteroids for newly diagnosed ulcerative colitis[END_REF][START_REF] Barreiro-De Acosta | Evaluation of the Risk of Relapse in Ulcerative Colitis According to the Degree of Mucosal Healing (Mayo 0 vs 1): A Longitudinal Cohort Study[END_REF]. Indeed, 46 % of patients initially treated with cyclosporine subsequently received infliximab during the first year of follow-up in our cohort [START_REF] Laharie | Long-term outcome of patients with steroidrefractory acute severe UC treated with ciclosporin or infliximab[END_REF].

Beyond traditional features observed in active ulcerative colitis, acute severe attacks may be associated in 33-72% to more severe endoscopic lesions, consisting in deep ulcerations, welllike ulcerations or mucosal detachment mostly found in the rectum or the sigmoid colon [START_REF] Carbonnel | Colonoscopy of acute colitis. A safe and reliable tool for assessment of severity[END_REF][START_REF] Jarnerot | Infliximab as rescue therapy in severe to moderately severe ulcerative colitis: a randomized, placebo-controlled study[END_REF][START_REF] Cacheux | Predictive factors of response to cyclosporine in steroid-refractory ulcerative colitis[END_REF][START_REF] Monterubbianesi | Infliximab three-dose induction regimen in severe corticosteroid-refractory ulcerative colitis: early and late outcome and predictors of colectomy[END_REF][START_REF] Poullenot | Severe endoscopic lesions are not associated with more infliximab fecal loss in acute severe ulcerative colitis[END_REF]. Conversely to prior endoscopic scores, severe endoscopic lesions have been implemented into the UCEIS corresponding to the erosions/ulcerations sub-score at 3 defined as 'deeper excavated defects in the mucosa, with a slightly raised edge' (7). Some retrospectives series have observed an association between these lesions and higher colectomy rates or infliximab fecal excretion [START_REF] Cacheux | Predictive factors of response to cyclosporine in steroid-refractory ulcerative colitis[END_REF][START_REF] Monterubbianesi | Infliximab three-dose induction regimen in severe corticosteroid-refractory ulcerative colitis: early and late outcome and predictors of colectomy[END_REF]30). However, prospective studies have not yet confirmed this relationship. Similar to Jarnerot et al. who reported the first placebo-controlled trial conducted with infliximab in acute severe ulcerative colitis [START_REF] Jarnerot | Infliximab as rescue therapy in severe to moderately severe ulcerative colitis: a randomized, placebo-controlled study[END_REF], baseline severe endoscopic lesions were not predictive of treatment failure in multivariate analysis in our trial [START_REF] Laharie | Ciclosporine versus infliximab in acute severe colitis refractory to intravenous steroids: a randomized study[END_REF]. Moreover, we observed in the present study that patients with the UCEIS erosions/ulcerations sub-score of 2 and 3 at inclusion have the same evolution for ulceration healing after day 7, even if these results had to be taken with caution due to the evident lack of power. Overall, the significance of severe endoscopic lesions remains poorly understood and requires further studies.

The present study acknowledges some limitations such as UCEIS post-hoc calculation, endoscopic assessments not centrally read and lack of histologic assessment. Last, as in most exploratory studies, numerous tests were performed. Nevertheless, we defined statistical significance when p-value was less than 0.005.

In order to describe evolution of endoscopic lesions in patients responding to a second-line medical therapy, patients included into the present analysis were prospectively followed within a randomized clinical trial and closely monitored by four repeated flexible sigmoidoscopies using a standardized form describing pre-specified endoscopic lesions per segment with few missing data.

In conclusion, endoscopic remission of acute severe ulcerative colitis takes approximately three months. It starts with bleeding remission at day 7, followed by ulceration/erosion healing and then by restoration of the vascular pattern that is coming back to normal in half of patients at three months. In clinical practice, patients should not be assessed too early by flexible sigmoidoscopy. The higher rate of patients in endoscopic remission after induction with infliximab than cyclosporine may be associated with less subsequent disease flare, suggesting deep remission would be a desirable goal in acute severe ulcerative colitis.

Funding: this survey is an investigator-initiated study. No pharmaceutical company had any role in study design, data collection, analysis, interpretation, or writing of this report.

  European randomized, open-label, controlled trial conducted in 23 French and Belgian GETAID (Groupe d'Etude sur les Affections Inflammatoires Digestives) and 6 European ECCO (European Crohn and Colitis Organisation) centers, comparing cyclosporine to infliximab in 115 patients admitted for steroid-refractory acute severe ulcerative colitis (EudraCT: 2006-005299-42; ClinicalTrials.gov number: NCT00542152). Patients have been included from June 2007 to August 2010. Briefly, eligible patients were adults having an acute severe ulcerative colitis defined by a Lichtiger score >10, who were refractory to at least 0.8 mg/kg/d of intravenous methylprednisolone or equivalent given for at least 5 days and who were naive for cyclosporine, infliximab and thiopurine except if it was started less than four weeks before inclusion. Patients with indication for emergent colectomy or having proctitis, Crohn's disease, active infection or usual contra-indication to cyclosporine, infliximab and thiopurine were excluded. Results of the initial study have been previously

Figure legends : Figure 1 :

 :1 Figure legends:

Figure 2 :

 2 Figure 2: Description of the UCEIS sub-scores at days 7 (n=55), 42 (n=54) and 98 (n=50) in

Figure 3 :

 3 Figure 3: Evolution of vascular pattern (VP), bleeding (B) and erosions/ulcerations (U)

Figure 4 :

 4 Figure 4: Rates of endoscopic remission (UCEIS at 0) in patients admitted for a steroid-

Table 1 :

 1 Main patients' characteristics and endoscopic findings at baseline

	Characteristic	All	Infliximab	Cyclosporine
		(n=55)	(n=29)	(n=26)
	Female gender, n (%)	30 (55)	15 (52)	15 (58)

M Esteve declares lecture fees and consultant fees from AbbVie, MSD, Janssen, Takeda, Pfizer and Tillots and has received research funding from MSD and Abbvie. M Farkkila declares lecture or consultation fees from AbbVie, Tillotts Pharma, DelSiTech, Pfizer.

JP Gisbert has served as a speaker, a consultant and advisory member for or has received research funding from MSD, Abbvie, Hospira, Pfizer, Kern Pharma, Biogen, Takeda, Janssen, Roche, Sandoz, Celgene, Ferring, Faes Farma, Shire Pharmaceuticals, Dr. Falk Pharma, Tillotts Pharma, Chiesi, Casen Fleet, Gebro Pharma, Otsuka Pharmaceutical, Vifor Pharma. P Marteau declares fees from Biocodex, Ferring, Janssen, Mayoli Spndler. S Nahon declares lectures or advisory board fees from AbbVie, MSD, Vifor Pharma, Pfizer, Janssen and Ferring. M de Vos declares no conflict of interest.

L Peyrin-Biroulet reports personal fees from AbbVie, Janssen, Genentech, Ferring, Tillots, Pharmacosmos, Celltrion, Takeda, Boerhinger Ingelheim, Pfizer, Index Pharmaceuticals , Sandoz, Celgene, Biogen, Samsung Bioepis, Alma, Sterna, Nestle, Enterome, Allergan, MSD, Roche, Arena, Gilead, Hikma, Amgen, BMS, Vifor, Norgine ; Mylan, Lilly, Fresenius Kabi, Oppilan Pharma, Sublimity Therapeutics, Applied Molecular Transport, OSE Immunotherapeutics, Enthera, Theravance; grants from Abbvie, MSD, Takeda ; stock options : CTMA. JY Mary declares no conflict of interest.

This study was funded by the Association Francois Aupetit.


Maâmar El

Amine Hamri
email: amine.hamri@lsis.org

Norbert Giambiasi
email: norbert.giambiasi@lsis.org

Claudia Frydman
email: claudia.frydman@lsis.org

Min-Max DEVS Modeling and Simulation

The representation of timing, a key element in modeling hardware behavior, is realized in hardware description languages including ADLIB-SABLE, Verilog, and VHDL, through delay constructs. The use of delays in the literature may be organized into four classes. Under the first category, the mean values are utilized as precise delay elements in the simulators. VHDL adopts this view to characterize transport delays, where a single value is utilized, rise and fall delays, and inertial delays. In describing the lifetime of a state, also termed time advance function, DEVS proposes to use precise delay elements. Under the second category, termed min-max delay, a delay is represented through an interval, implying that the value of the delay is not known precisely and that any of the values in the interval represents a possible value for the actual delay. In the third category, a delay is expressed in the form of a stochastic distribution. The use of fuzzy models of delays constitutes the fourth category. In the real world, however, precise values for delays are very difficult, if not impossible, to obtain with certainty. The reasons include variations in the manufacturing process, temperature, voltage, and other environmental parameters. Consequently, simulations that employ precise delay values are susceptible to inaccurate results. This paper proposes an extension to the classical DEVS by introducing min-max delays for use in both internal and external transition functions. In the augmented formalism, termed Min-Max-DEVS, the state of a hardware model may, in some time interval, become unknown and is represented by the symbol, φ. The occurrence of φ implies greater accuracy of the results, not lack of information. Min-Max-DEVS offers a unique advantage, namely, the execution of a single simulation pass utilizing min-max delays is equivalent to multiple simulation passes, each corresponding to a set of precise delay values selected from the interval. This, in turn, poses a key challenge efficient execution of the Min-Max-DEVS simulator.

INTRODUCTION

Hardware Description Languages (VHDL, Verilog, ADLIB, etc.) and logic gate simulators use the concept of delay [START_REF] Breuer | Diagnosis and reliable design of digital systems[END_REF][START_REF] Giambiasi | Silog: A practical tool for digital logic circuit simulation[END_REF] to represent timed behaviors. Different classes of delay models have been introduced [START_REF] Breuer | Diagnosis and reliable design of digital systems[END_REF][START_REF] Giambiasi | Silog: A practical tool for logic digital network simulation[END_REF][START_REF] Ghosh | On the need for consistency between the VHDL language constructs and the underlying hardware design[END_REF][START_REF] Walker | On the nature and inadequacies of transport timing delay constructs in VHDL[END_REF][START_REF] Smaili | Discrete event simulation with fuzzy dates[END_REF] to allow different kinds of temporal analysis. Delay models can be regrouped into four categories. Models of the first categories are characterized by the fact that values associated with the delay are mean values considered in the model as a precise value [START_REF]Introduction to VHDL[END_REF][START_REF] Navabi | VHDL: analysis and modeling of digital systems[END_REF][START_REF] Friedman | Logical design of digital systems[END_REF]. Theses delay can be preprint SIMPAT 2006 pure transport delays (characterized by only one value) [START_REF]Introduction to VHDL[END_REF][START_REF] Navabi | VHDL: analysis and modeling of digital systems[END_REF], rise-fall delays (characterized by two values in Boolean models) [START_REF] Calma | [END_REF][START_REF] Abromovici | Digital systems testing and testable design[END_REF], or inertial delays (with one or two values) [START_REF] Brzowzowski | Advances in asynchronous circuit theory. Part II: Bounded inertial delay model[END_REF]. The second category regroups models that represent the delay by a time interval in which all points correspond to a possible value of the real delay, these models are called min-max models [START_REF] Breuer | Diagnosis and reliable design of digital systems[END_REF][START_REF] Giambiasi | Silog: A practical tool for logic digital network simulation[END_REF]. The third category corresponds to probabilistic models; the delay is represented by a stochastic variable with a distribution of probability [START_REF] Magnhagen | Probability based verification of time margins in digital design[END_REF]. The fuzzy models of delays [START_REF] Smaili | Discrete event simulation with fuzzy dates[END_REF][START_REF] Dubois | Processing fuzzy temporal knowledge[END_REF] constitute the fourth category; the imprecision knowledge on delay values is represented by a distribution of probability.

In the DEVS formalis m [START_REF] Zeigler | Theory of modeling and simulation[END_REF], Zeigler introduced the concept of the lifetime of a state (called time advance function) which corresponds to the concept of precise delay values in digital circuits. This life time is defined by a function giving a precise value corresponding to the concept of precise delay value in the digital circuit simulation field. For the simulation of system models during a design process, the delay values can not be knwon with precision (the scatterng of parameters due to the manufacturing process, for example). For a classical simulation with precise delay values the user must choice a precise value into the distribution of possible delay values (for example, in databooks of integrated circuits, the manufacturer gives one delay value corresponding to the mean value of possible delays). In an analysis process of a real system several measurements are realized in order to obtain a mean value for different delays.

For theses reasons, in order to obtain more realistic simulation models, we propose the Min-Max DEVS formalism which generalizes the concept of min-max delays, coming from the field of digital circuits. The aim of Min-Max-DEVS is to model and simulate real systems for which the delays values are not known with accuracy and not as in [START_REF] Seong | Real time DEVS simulation: Concurrent time-selective execution of combined RT-DEVS model and interactive environment[END_REF] to do real-time simulations. The interpretation of Min-Max-DEVS is also very different from that of Timed Automata (T.A.) [START_REF] Alur | A theory of timed automata[END_REF][START_REF] Paillet | Discrete event calculus models a high level specification for discrete event systems[END_REF][START_REF] Giambiasi | From timed automata to DEVS models[END_REF]. T.A. has been introduced for high level specifications of discrete event systems and for accurate temporal simulations. In T.A. the concept of temporal window allows us intervals, in which some events can be taken into account, to be defined. For a best understanding of the meaning attach to Min-Max-DEVS, we recall the meaning of ambiguous delay in the domain of digital circuits, the minimum delay corresponds to the faster circuit and the maximum delay corresponds to the slower one. All the transitions of states, in the possible real circuits, are between these two limits. It is for that the state of a gate model in the min-max interval is an unknown state, noted φ. The interpretation of φ is:

-Some circuits have already had a state change, -Some circuits don't have even a state change. In fact, the s imulation of a model with min-max delays corresponds to the simulation of all the possible circuits with only one stage of simulation. The simulation results can give large time periods with the unknown state, someone can think that this kind of results gives less information than a Boolean model. It is wrong because an unknown state gives us the information that with the knowledge that we have on the delays it is impossible to predict the behavior of the real systems in these time periods. A Boolean simulation, using mean values of delays, gives for these states a Boolean value which is false in some time intervals.

After a brief recall of classical delay models and of the DEVS formalism, we present the Min-Max-DEVS formalism and its operational semantics. The most difficult problem to solve is to obtain a fast simulation technique, knowing that with min-max delays, all the possible precise models are to be simulated during only one stage of simulation.

Recall

Delay Models

The simp lest type of delay used in the digital circuit field is the pure transport delay. A gate model is composed of an ideal logic gate followed by a transport delay (Fig. 1). This delay is defined by one value, which represents a mean value of real delays for the considered category of gates. This delay has an anticipatory semantics, every input event will be realized on the output, so events are only delayed.

Fig. 1. A gate model

Let us consider a transport delay with a value of 12 time units (t.u.) and the following input sequence of events (0�1 at t=60), (1�0 at t=65), (0�1 at t=70) and (1�0 at t=74). All these events are delayed of 12 t.u. as we can see on the Fig. A rise-fall delay is defined by two precise values corresponding to a mean value for each possible state change (0�1 and 1�0), the delay depends on the state change. In [START_REF] Giambiasi | Silog: A practical tool for logic digital network simulation[END_REF]20,[START_REF] Ghosh | A preemptive scheduling mechanism for accurate behavioral simulation of digital designs[END_REF] the s imulation algorithm of this delay gives us its semantics that is a preemptive semantics. Some inputs events will be canceled.

As an example, for a rise-fall delay defined by the following values (R-rise=20 t.u. and R-fall=10 t.u.). On the Fig. 3, we can see that the input pulse between 60 and 65 corresponding to two input events is cancelled on the delay output. There is preemption of these two events because the time interval between them is short. The problem with these delays (transport or rise-fall delay) is that we assume we know a precise value of the delays of the real gates, which is evidently impossible because it depends on the environment and on the manufacturing process. In fact, the delay values are the mean values of real delays.

For a more precise representation of real gates, probabilistic and fuzzy models have been introduced [START_REF] Magnhagen | Probability based verification of time margins in digital design[END_REF][START_REF] Smaili | Discrete event simulation with fuzzy dates[END_REF][START_REF] Dubois | Processing fuzzy temporal knowledge[END_REF]. These categories of delays have not widely used because the simulation algorithms are complex and heavy and it is not easy to obtain a probability distribution function for the delay.

Another category of delay models uses a time interval to define possible values of the delay. In this time interval, each point corresponds to a possible value of a real delay. These models are widely used because they represent the imprecise knowledge about real delays and they have very fast simulation techniques. These delay models are called ambiguous delays or min-max delays [START_REF] Breuer | Diagnosis and reliable design of digital systems[END_REF][START_REF] Giambiasi | Silog: A practical tool for logic digital network simulation[END_REF].

Ambiguous delays

An ambiguous transport delay is defined by two values [t min , t max ] which represent the distribution of the possible real delays of the corresponding gate. In this case, the variables of a model have three possible values [0, 1, Φ]. Φ represents the unknown value due to the imprecision on delay values. In fact, when a gate model is in the state Φ, the interpretation is that some possible real gates are in the state 0 and some other are in the state 1 depending on the real value of the delay.

In fact, with this modeling we represent in one model all the possible behaviors for the different delay values. In other words, we simulate in one pass all the possible behaviors of the corresponding circuit. The simulation process consists in using 4 events: (0 to Φ), (Φ to 0), (Φ to 1) and (1 to Φ). The occurrence of the event (0 to Φ) represents the faster possible signal (faster circuit corresponding to a real circuit with the minimum delays for all its logic gates), and event (Φ to 0) represents the slower circuit. Let us consider a gate delay with the following values: d min = 3, d max = 8. On the Fig. 4 we have the output response for an input pulse (0 to 1 at 10) (1 to 0 at 50). The delay definition introduces two ambiguous intervals [START_REF] Magnhagen | Probability based verification of time margins in digital design[END_REF][START_REF] Paillet | Discrete event calculus models a high level specification for discrete event systems[END_REF] and (53, 58) in which the model is in an unknown state. The interpretation of the output signal is:

-Before 13, none possible real gate have commuted, -Between 13 and 18, some real gates are in the state 0, some others are in the state 1, -After 18, all the possible real gates are in the state 1. In the other words, the signal defined by the events (0 to Φ) and (1 to Φ) correspond to the faster possible gate; the events (Φ to 1) and (Φ to 0) correspond to the slower possible gate (see Fig. 5).

Review of the DEVS Formalism

According to the literature on DEVS [START_REF] Seong | Real time DEVS simulation: Concurrent time-selective execution of combined RT-DEVS model and interactive environment[END_REF][START_REF] Zeigler | Multifaceted modeling and discrete event simulation[END_REF][START_REF] Praehofer | System theoretic formalisms for combined discrete-continuous system simulation[END_REF][START_REF] Zeigler | Theory of modeling and simulation[END_REF] the specification of a discrete event model is a structure M, given by: M= <X, S, Y, δ δ δ δ int , δ δ δ δ ext , λ λ λ λ, D>, where X is the set of the external input events, S the set of the sequential states, Y the set of the output events, δ δ δ δ int is the internal transition function that defines the state changes caused by internal events, δ δ δ δ ext is the external transition function that specifies the state changes due to external events, λ λ λ λ is the output function, and the function D:

S�R +
∪∞ represents the maximum length or the lifetime of a state. Thus, for a given state s i , D(s i ) represents the time during which the model will remain in state s i if no external event is incurred.

Zeigler introduces the concept of total states, TS, of a system as: TS= {(s, e) s ∈ S, o < e < D (s)}, Where e represents the elapsed time in state s. The concept of total states is fundamental in that it permits one to specify a future state based on the elapsed time in the present state. Potential benefits may lie in its ability to implement event filtering, wherein a planned change of state will be realized by a model only when the time that separates two key events exceeds a predefined value, and to encapsulate otherwise the mechanical event filtering at the conceptual level.

The time life function D(s i ) gives a precise value that generally corresponds to a mean value of the corresponding duration of the transient state in the real system. It is obvious that in a design process this value is very approximate. For a more realistic modeling, we propose to define the lifetime of a state by a min-max value.

Min-Max-DEVS formalism

A Min-Max-DEVS formalism is proposed instead of DEVS formalism to model systems in which the lifetime of transient states is represented with time intervals and not with mean values. The first step is to define an external min-max specification, which corresponds to a user specification. An internal specification will be associated with this user specification. The internal specification defines the operational semantics of the formalism. The external specification of Min-Max-DEVS is identical to RT-DEVS [START_REF] Seong | Real time DEVS simulation: Concurrent time-selective execution of combined RT-DEVS model and interactive environment[END_REF], but the interpretation and the operational semantics defined by the internal specification are different.

A Min-Max Discrete EVent System specification is a structure: -dmax represents the maximum time the model remains in state si, dmax corresponds to the slower real system.

M= <X, S, Y, δ δ δ δ int , δ δ δ δ ext , λ λ λ λ,

Interpretation:

As in the field of digital circuits, we introduce a min-max definition for the lifetime of transitory states because in general:

-In an analysis process, the length of the state cannot be measured with precision, only a window of possible values can be defined.

-In a design process, there are several possible realizations of the designed system and the manufacturing process is never perfected (all the products have slightly different features). In other words, we consider that it is impossible to obtain a precise value for the length of the transitory states of a real system and then, we define these lengths with a minimum value and a maximum value. In fact, when a model uses precise values for delays, the hypothesis is that these values are mean values.

To illustrate this specification, let us consider a very simple model of a water pump (Fig. 6), controlled by start/stop switch [START_REF] Luh | Abstracting event-based control models for high autonomy systems[END_REF]. The pump model has an input port pw and an output port w. If the water pump is turned on (pw=start), it starts pumping water trough the water pipe after a delay defined by the min-max values. If it is turned off (pw=stop), it stops pumping and the flow of water will be off (w=stopliquid) after a min-max delay. As we see, the needed time to start and to stop pumping water is expressed with time intervals (min-max delays), this is due to the fact that is impossible to obtain precise values for the system in the real world.

Formally, the external min-max specification of its discrete event model is: S={pumping, off, on, stop} X={pw}, Y={w} pw={stop, start}, w={stopliquid, startliquid} Output function: λ(on)=w=startliquid, λ(off)= w=stopliquid Where:

-XI = X x {fast, slow} The event (xj, fast) is interpreted as an event with the value x j , this event represents (as we will see in the following) the faster signal in the real world, its occurrence time defines the beginning of a temporal window in which the event xj can occur at each time (depending on the real value of the delay).

The event (x j , slow) is interpreted as an event with the value x j , this event represents (as we will see in the following) the slower signal in the real world, ending the window.

-SI = (S U Φ) Φ) Φ) Φ) x (S U Φ) Φ) Φ) Φ) x A With:
-A = {fast, slow, autonomous, passive}, -Φ Φ Φ Φ is an unknown value, -The interpretation of a model state (s i , s j , A) is:

If s i = s j , the external model is in state s i and all the possible real systems are in state s i .

If s i ≠ s j , the external model is in an unknown state, because some fast real systems are in state s j and the slower systems are still in s i.

The interpretation of a state (Φ, Φ, Α) is that the model is in a completely unknown state, representing the fact that there is, at this time, more than two possible situations in the real world. -YI = Y x {fast, slow} where:

((y j , fast), t j ) is an output event with the occurrence date t j , representing the response of the faster real system, ((y j , slow), t k ) is an output event with the occurrence date t k , representing the response of the slower real system. In the temporal window [t j , t k ], the external model is in an unknown state, this window represents all possible occurrence times of the event y j . With these definitions, we can now define the functions of the internal model. Internal transition function δ δ δ δI int :

δI int : (S U Φ ) Φ ) Φ ) Φ ) x (S U Φ) Φ) Φ) Φ) x A � � � � (S U Φ) Φ) Φ) Φ) x (S U Φ) Φ) Φ) Φ)
x A with the following rules: δI int (s i , s i , autonomous)=(s i , δ int (s i ), autonomous) with: DI(s i , s i , autonomous) = Min(D(s i )), the second element of the triplet (s i , s i , autonomous) represents the faster real system, and we apply the internal transition function to this element after the minimum delay. The internal model is now in a state (s i , s j , autonomous) which is associated with an unknown state for the external model. The length of this unknown state is Max(D(s i ))-Min(D(s i)) t.u., after this time all the real systems have had the corresponding state change.

δIint(si, sj, autonomous)=(sj, sj, passive) if sj is a passive state =(s j , s j , autonomous) if s j is an active state with: DI(si, δint(si), autonomous)=Max(D(si))-Min(D(si)).

To understand these rules, we have to consider that we model simultaneously the state changes of all the possible real systems. To obtain the previous rule, we consider the faster and the slower real systems. The model state (s i , s j , autonomous) represents that some real systems (the fast systems) have had a state change and the other are still in the previous state (the slow systems).

Let us consider now, two active states s 1 and s 2 with min-max lifetimes (Fig. 8), the model being in s 1 at t=t 1 , we have: δI int (s 1 , s 1 , autonomous) =(s 1 , δ int (s 1 ), autonomous)=(s 1 , s 2 , autonomous) and: DI(s 1 , s 1 , autonomous)=Min(D(s 1 )) at t 2 =t 1 + Max(D(s 1 ))-Min(D(s 1 )), we have: -And if no input event occurs, the next output event will be emitted at the time of the state change for the slower system corresponding to the output event (λ λ λ λ(si), slow). That is to say that the faster event must be interpreted as defining the beginning of a temporal window in which a real system can send out the considered output event, the slower event defines the end of this window: at the occurrence time of the slower output event all the possible real systems have had the considered state change.

δI int (s 1 ,

External Transition function δ δ δ δI ext :

To define the external trans ition function of the internal model we have to analyze the different possible cases. However, due to the fact we represent all the possible real systems; for an internal state (s i , s j , A) the slow event must be applied to the slower system, that is to say to state s i, and the fast event must be applied to the faster system, that is to say to state s j . First case: For an input event xj, the present state s1 and the next state δext(s1, e, xj) are passive states (Fig. 9).

We apply the fast event to the faster system, that is to say to the second element of the triplet: (s 1 , s 1 , passive), and the slow event to the slower system, then, we have: δIext((s1, s1, passive), e, (xj, fast))=(s1, δext(s1, e, xj), fast) DI(s 1 , δ ext (s 1 , e, x j ), fast)=Infinity, δ ext (s 1 , e, x j ) is passive by hypothesis. After this transition, the external model is in an unknown state, because some real systems have not received the external event (x j ). Then: δI ext ((s 1 , s 2 , passive), e, (x j , slow))=(δ ext (s 1 ,e, x j ), s 2 , passive)=(s 2 , s 2 , passive), at this time, the internal model is in state (s 2, s2, passive), the external model is in state s 2 and the interpretation is that all the possible real systems have had the state change due to the external event (x j). Remark 2. In the temporal window [t i , t j ] the state is unknown of the external model due to the imprecision on the occurrence times of the input events and not due to a min-max definition of the lifetime of the considered state. Second case: s i is a passive state and δ ext (s i , e, x j ) is an active state: first, we consider the occurrence of an input event ((x j , fast), t i ) followed by the event ((x j , slow), t j ) (Fig. 10) such as: t j t i < Min(D(δ ext (s i , e, x j )).

The slow event occurs before the autonomous transition of the faster system. Now, we consider that t j t i >Min(D(s 1 )) (Fig. 11).

( we apply the fast event to the faster system, and DI(s 1, s2, fast)=Min(D(s2)) if s2 is an active state (infinity if s2 is passive, previous case), and δIint(s1, s2, fast)=(s1, δint(s2), A)= (s1, s3, fast), in this case when the internal model is in state  s1, s3, fast) there is more than two possible evolutions, for that we choose for the internal transition function the following rule:

δI int (s 1 , s 2 , fast)=(Φ, Φ, passive).
If the slow event occurs before the internal transition: δI ext ((s 1 , s 2 , fast), e, (x j , slow))=(δ ext (s 1 , e, x j ), s 2 , autonomous) =(s 2 , s 2 , autonomous) with DI(s 2 , s 2 , autonomous)=(Min(D(s 2 ))-e Third case: the present state is unknown when the fast event occurs; some real systems are in s 1, the others in s2.

We suppose first that (x j , slow) occurs after the internal transition s 1 to s 2 in the slower system. In this case, when the internal model is in state (s1, s3, A) there is a great number of possible evolutions (more than two), for that we choose, for the external transition function the following rules: δI ext ((s i , s j , autonomous), e, (x j , fast))=(Φ, Φ, passive) totally unknown passive state.

We introduce the totally unknown state (Φ, Φ, passive) because at this time, there is more than two possible evolutions depending on the different lifetimes of the states and the occurrence times of the input events. This state is passive, and:

δI ext ((Φ, Φ, passive), e, (x j , (fast or slow)))=(Φ, Φ, passive)

The model remains definitely in the totally unknown state. Fourth case: two successive fast events.

For a state (s i , s j , fast), if an input event (x k , fast) occurs, we are in an analogous situation than the previous one. In fact, the model receives two successive fast events before receiving the corresponding slow event.

δI ext ((s i , s j , fast), e, (x j , fast)) = (Φ, Φ, passive) totally unknown state. After this detailed interpretation, we describe the internal model IM for the previous example (the water pump) based on its external specification.

IM=<XI, SI, YI, δI The interpretation in the real world is: when the model is in the state (off, stop, autonomous), some real systems are in the state off and some other are in the state stop, so the external model is in the unknown state. After 4 t.u., all the real systems are in state stop.

For the trans ient state on we obtain: δI The output function is : λI(off, off, autonomous)=(stopliquid, fast) λI(off, stop, autonomous)=(stopliquid, slow) λI(on, on, autonomous)=(startliquid, fast) λI(on, pumping, autonomous)=(startliquid, slow). For the external transition, to be clear, we consider that the external input events (stop, ε) and (start, ε) are given with a precise occurrence time which is denoted by the symbol ε in the value of the event (on a practical point of view, this type of event can be decomposed into two events: one fast and one slow event, with the same occurrence time). δI In some situations, the information given by this model does not represent the real system. For example, when the current state of the model is pumping and the event stop occurs at date t = 5 t.u., the next state is off; the scheduled internal event is expected at date t = t + D(off) = 5+8 = 13 t.u.. In the real world it is wrong because some fast systems have had the corresponding state change before t = 13 t.u., and the slow systems are even in the state off.

Min-Max-DEVS simulator

An interpretation of the dynamics of a Min-Max-DEVS model is given by considering the Min-Max-DEVS-simulator based on the DEVS-simulator proposed by Zeigler [START_REF] Seong | Real time DEVS simulation: Concurrent time-selective execution of combined RT-DEVS model and interactive environment[END_REF]. The DEVS-simulator employs two variables, one to represent the sequential state s of the model and one to store the occurrence time of the last event. It has also three storage cells whose values are determined by the state variables and its inputs. The first holds the time of the next internal transition tn, where tn = tl + D(S), when it is given the global model time, the simulator can compute the elapsed time since the last event e, where e = t tl, and the left time to fire the next internal transition σ σ σ σ, where σ = tn t. (done, t) (X, t) Fig. 15. Simulator of an abstract DEVS [START_REF] Seong | Real time DEVS simulation: Concurrent time-selective execution of combined RT-DEVS model and interactive environment[END_REF] The difference between the Min-Max-DEVS-simulator and the previous simulator is that the first employs two time variables tf and ts besides tl and tn to hold the occurrence time of the fast and the slow events.

The elapsed time in a state of the internal model, since the last event and the left time to the next internal event e and σ σ σ σ, are computed in the same manner than in the DEVS-simulator when it is given the global current simulation time t. As shown in algorithm 1, for correct initialization of the simulator an initialization message (i, t) has to be received at the beginning of each simulation run. When a Min-Max-DEVS-simulator receives such an initialization message, it initializes its time of last event tl by the initial date of the simulation. The time of the next event tn, is computed by adding the minimum value of the time advance D(s) to the time of the last event tl. Time tn is sent to the parent coordinator to tell it when the fast internal event should be executed by this component simulator.

An internal state transition message (*, t) causes the execution of an internal event. When a *-message is received by a Min-Max-DEVS-s imulator, it computes the output and carries out the internal trans ition function of the internal model associated, so that the new state of the internal model can be deduced. The output is sent back to the parent coordinator in an output message ((y, fast), t) or ((y, slow), t) according to the current state of the internal model (s i = s j , s i ≠ s j respectively). Finally, the time of the last event is set to the current time and the time of the next event is set to the current time plus the minimum value of the time advance function D(s j ) if all systems are in the same state, or plus the difference between the maximum and minimun value of the time advance function D(s j ) plus the difference between the occurrence time of the slow and fast event if some systems are in the state s i and other are still in state s j .

An input message ((x, fast), t) or ((x, slow), t) informs the simulator of an arrival of an input event, (x, fast) or (x, slow), at simulation time t. This causes the simulator to execute the external transition function of the internal model given (x, fast) or (x, slow) and the elapsed time e. The time of the last event is set to t and the time of the next event is set to a value determined from rules of the internal model.

Example and Simulation

Now we will model a simple example of a filling system with Min-Max-DEVS formalism. This system, a filling system, is composed of a tank with a valve, a conveyor and barrels (Fig. 16). The filling system has two inputs:

-control of the valve: val = {open, close} -control of the conveyor: in = {roll, stop} and two sensor outputs :

-barrel level: bl = {capacity} -barrel position: bp = {good} The Min-Max-DEVS formalism was chosen instead of the DEVS formalism for the reason that some lifetimes of transient states can not be known with accuracy. As an example, the necessary time for adjusting the conveyor depends on:

-the speed of the conveyor, -the length between barrels. The Min-Max-DEVS model built (Fig. 17) is very simple and easy to specify by the users. It resembles to the classical DEVS model, but the unique difference consists in the duration of transient states Adcon0 and Filling0 expressed with time intervals [START_REF] Walker | On the nature and inadequacies of transport timing delay constructs in VHDL[END_REF][START_REF] Calma | [END_REF] and [START_REF] Calma | [END_REF]20] respectively and not with precise values.

Interpretation:

The transient states of the model are Adcon0 and Filling0, where their lifetimes are expressed with time intervals. Time intervals are used in place of precise values from the real world because, for example, the needed time to adjust the conveyor belt depends on its charge of barrels; and the length between barrels is not the same, there are always slight differences. The filling phase of a barrel is represented by the state Filling0, its duration is limited by two values 10 t.u. and 20 t.u. and can not be known with accuracy, because the liquid flow is unsteady and the valves are different from one system to another one. Now we suppose that the initial state of the internal model is (init, init, passive). Let us consider the following sequence of input events (in=(roll, fast), t=10), (in barrel is expressed with the interval [210, 225] and it can not be represented by an accurate value due to that concerns liquid flow and depends on the barrel volume to be filled. This example shows that it is impossible to obtain a precise value for the length of the transitory states of the real system and then, the unique realistic solution is to define these lengths with a minimum value and a maximum value.

Several simulations can be carried out to determine a set of values for every active state of the external model, until obtaining an optimal configuration of the system according to the speed of the conveyor, distance between barrels, etc. Remark 3. Someone can think that this ambiguous model that specifies the filling system is less accurate than a c lassical DEVS model because sometime the simulation results remain in the unknown value whereas the classical DEVS model will give an exact value. In fact, the information given by the Min-Max-DEVS model is more accurate because it indicates with the given values of delays (which are more realistic than a mean value) it is impossible to know the state of the real system.

Conclusion

In this paper we have introduced the concept of ambiguous delay in the DEVS formalism. This concept is well knwon and used in the field of digital circuits to represent the imprecise knowledge on real gate delays. In fact, in the past other approaches have been proposed in order to represent imprecise knowledge of the real world. One of them is based on probabilistic models [START_REF] Dubois | Processing fuzzy temporal knowledge[END_REF], another on fuzzy-logic models [START_REF] Smaili | Discrete event simulation with fuzzy dates[END_REF][START_REF] Zeigler | Theory of modeling and simulation[END_REF]. For example, in prerformance analysis of manufacturing systems, random generated values are used to define the duration of tasks in place of min max values. In this case, this kind of random approach is usefull because the probability distributions can be known and the basic models have a small number of states. For complex systems with a great number of transitory states, these approaches (probabilistic and fuzzy) bring expensive and complex simulations and do not necessary give more information than in the min-max approach (because the probability or possibility d istributions of delays are generally unknown). Moreover, the min-max approach can be considered as the best compromise between a precise model and a powerful simulation.

Due to the pratical orientantion of this papers, we have not presented all the analysis done to define the functions of the internal model and the formal demonstrations needed to validate the simulation algorithm. In this algorithm, the basic pratical rule is: fast events are applied to the faster model (minimum delay) and slow events are applied to the slower model (maximum delay). In order to avoid a combinatory explosion, we have chosen to introduce the totally unknown state, in which the model remains definitely. In this case the analysis of the simulation results concludes on the fact that the knowledge on the delay values is too imprecise to obtain exact information on the system behavior.

The Min-Max DEVS simulator carries out a single simulation which is equivalent to multiple simulation passes in which the lifetime of transitory states corresponds to all the possible values of the real system. Thanks to the semantics of the internal model which allows this feature.

Our current work concerns the development of a simulator of coupled Min-Max-DEVS models. On a conceptual level, we are studying the transformation for Timed-Automata in min-max models in order to validate high-level specification by simulation and to apply model-checking methods to Min-Max-DEVS models.

Fig. 3 .

 3 Fig. 3. Rise-Fall delay

Fig. 4 .

 4 Fig. 4. Ambiguous delay

  D>, where: -X, S and Y are the same sets than in classical DEVS -the state lifetime function D: i ) = (d min , d max ) where -d min is the minimum time the model remains in state s i , d min corresponds to the faster real system.

Fig. 6 .

 6 Fig. 6. Water pump Internal transition function: δ int (on)=pumping with D(on)=(6, 12) δ int (off)=stop with D(off)=(6, 10) External transition function:

Fig. 7 .

 7 Fig. 7. State graph of the water pump model using Min-Max-DEVS Now, we define the internal model with its operational semantics. Internal min-max Model and Operational Semantics: Given a user specification of a Min-Max-DEVS: EM= <X, S, Y, δ δ δ δ int , δ δ δ δ ext , λ λ λ λ , D>, We associate with this specification, an internal model as follows: IM= <XI, SI, YI, δ δ δ δI int , δ δ δ δI ext , λ λ λ λ I, DI>,

s 2 ,Fig. 8 .

 28 Fig. 8. Internal transition function of the internal modelOutput function λ λ λ λI:As in classical DEVS, an output event is emitted before the activation of the internal transition function:λ λ λ λI(s i , s i , A)=(λ λ λ λ(s i ), fast) λ λ λ λI(s i , s j , A)=(λ λ λ λ(s i ), slow)The interpretation of the output event (λ λ λ λ(s i ), fast) is: -This event occurs when the faster possible real system has a state change.-And if no input event occurs, the next output event will be emitted at the time of the state change for the slower system corresponding to the output event (λ λ λ λ(si), slow). That is to say that the faster event must be interpreted as defining the beginning of a temporal window in which a real system can send out the considered output event, the slower event defines the end of this window: at the occurrence time of the slower output event all the possible real systems have had the considered state change.External Transition function δ δ δ δI ext :To define the external trans ition function of the internal model we have to analyze the different possible cases. However, due to the fact we represent all the possible real systems; for an internal state (s i , s j , A) the slow event must be applied to the slower system, that is to say to state s i, and the fast event must be applied to the faster system, that is to say to state s j . First case: For an input event xj, the present state s1 and the next state δext(s1, e, xj) are passive states (Fig.9).We apply the fast event to the faster system, that is to say to the second element of the triplet: (s 1 , s 1 , passive), and the slow event to the slower system, then, we have: δIext((s1, s1, passive), e, (xj, fast))=(s1, δext(s1, e, xj), fast) DI(s 1 , δ ext (s 1 , e, x j ), fast)=Infinity, δ ext (s 1 , e, x j ) is passive by hypothesis. After this transition, the external model is in an unknown state, because some real systems have not received the external event (x j ).

Fig. 10 .

 10 Fig. 10. External transition function -transition from a passive state to an active state

Fig. 12 .

 12 Fig. 12. External transition function -transition from an active state to an active state

  , on, off}*{pumping, stop, on, off}*{fast, slow, passive, autonomous} XI={pw} and YI={w} with pw={stop, start}*{fast, slow} w={stopliquid, startliquid}*{fast, slow} We have in the external specification δ int (off)=stop with D(off)=(6,10) The corresponding internal transition function is : δI int (off, off, autonomous)=(off, stop, autonomous) with DI(off, off, autonomous)=Min(D(off))=6 δI int (off, stop, autonomous)=(stop, stop, passive) with DI(off, stop, autonomous)=Max(D(off))-Min(D(off))=4

  int (on, on, autonomous)=(on, pumping, autonomous) with DI(on, on, autonomous)=Min(D(on))=6 δI int (on, pumping, autonomous)=(pumping, pumping, passive) with DI(on, pumping, autonomous)=Max(D(off))-Min(D(off))=6

  ext ((pumping, pumping, passive), e, (stop, ε))=(off, off, autonomous) δI ext ((stop, stop, passive), e, (start, ε))=(on, on, autonomous) The internal state graph is given on the Fig. 13.

Fig. 13 .

 13 Fig. 13. State graph for the internal model of the water pump Unlike the Min-Max-DEVS model for the water pump, when we model this system with the DEVS formalism, the lifetime of transitory states on and off is expressed with a precise value which represents a mean value in the real world (Fig. 14). The formal specification of the water pump model using DEVS formalism is : S={pumping, off, on, stop} X={pw}, Y={w} pw={stop, start}, w={stopliquid, startliquid} Output function: λ(on)=startliquid, λ(off)=stopliquid Internal transition function: δ int (on)=pumping with D(on)=9, δ int (off)=stop with D(off)=8 External transition function: δ ext (pump ing, e, pw=stop)=off with D(pumping)= infinity, δ ext (stop, e, pw=start)=on with D(stop)=infinity

Fig. 14 .

 14 Fig. 14. State graph of the water pump model using DEVS

Fig. 16 .

 16 Fig. 16. A simple filling system

Fig. 17 .

 17 Fig. 17. The external model for the filling system using the Min-Max-DEVS

  2.

	D el ay inp ut D el ay inp ut
	6 0 6 0	65 65	70 70	7 4 7 4		t t
	D elay ou tput D elay ou tput
			7 2 7 2	77 77	82 82	8 6 t 8 6 t

Fig. 2. Input-output sequence of a transport delay

  External transition function -transition from a passive state to an active state From this analysis, for a present passive state s 1 of the external model and a next active state δ ext (s 1 , e, x j ), we define the following rules for the external transition function of the internal model:

	XI XI	xj, fast) (xj, fast)	(xj, slow) (xj, slow)
		t i t i	t j t j		t t
	faster real system faster real system	S1 S1	S2 S2	S3 S3
	slower real system slower real system	S1 S1	S2 S2	S3 S3
	external model external model	S1 S1	unknown state unknown state		S3 S3
	Fig. 11.

δIext((s1, s1, passive), e, (xj, fast))=(s1, δext(s1, e, xj), fast)=(s1, s2, fast)

The unknown state for intervals [START_REF] Calma | [END_REF][START_REF] Brzowzowski | Advances in asynchronous circuit theory. Part II: Bounded inertial delay model[END_REF] and [200,205] is due to the fact that it is not possible to know the precise date of events roll and open; in addition these time intervals start by fast events and finish by slow events.

For the interval [START_REF] Zeigler | Theory of modeling and simulation[END_REF][START_REF] Zeigler | Multifaceted modeling and discrete event simulation[END_REF], it is difficult to estimate the necessary duration to put barrels in the good place (estimate the lifetime of the state), because that depends on the conveyor speed and the distance between barrels. The end of the filling phase of a