Bruno Perez
email: bruno.perez@univ-fcomte.fr

Christophe Lang
email: christophe.lang@univ-fcomte.fr

Julien Henriet
email: julien.henriet@univ-fcomte.fr

Laurent Philippe
email: laurent.philippe@univ-fcomte.fr

Frédéric Auber
email: fauber@chu-besancon.fr

Fr éd

éric Auber

Risk prediction in surgery using case-based reasoning and agent-based modelization

Keywords: Case-based reasoning, multi-agent system, simulation, risk prediction, adverse events in surgery

Introduction

In hospitals, surgery is performed in increasingly innovative and high-performance settings. Instruments are connected and maintained with all the rigor required by health and safety standards. All parameters are checked before and after the surgery (patient identity and condition, surgical equipment, surgical instruments, etc.) in order to leave as little space as possible for unforeseen events. However, even in this secure environment, minimizing the risk of serious adverse events, incidents, remains one of the main concerns of practitioners [?]. As an example, despite all the implemented protocols, J. W. Suliburk recorded 188 adverse events out of the 5365 operations included in their study: 56,4% were due to human error and 51,6% were due to human performance deficiencies [?]. Among many other incidents, we can note dosage errors, gestural clumsiness and human fatigue. In this context, we aim at model the operating room environment and resources in order to predict and quantify the patient's exposure to risk.

Our proposal is to create a simulator able to reproduce the system evolution, where the system state depends on a set of values, each of which corresponds to the value of attributes such as the vital signs of a patient (temperature, capnia, etc.), the rate of infectious particles or the fatigue of a person. For each attribute, individual alert and incident thresholds are defined by experts. With the simulator, we aim to generate a large number of varied situations and determine their evolution towards incidents. Depending on the risk exposure level, the system state is then classified as normal, alert or incident. The issue we face is to aggregate the values of the attributes in order to identify alert states and thus anticipate incidents. Our study is oriented towards predictive models composed of non-deterministic entities raises, among other things. Our ambition consists of determining alert states which characterize a system evolving toward an incident state. Our objective therefore consists in bringing out risky situations that are a priori unpredictable. In this case, a situation can be considered risky when no alert threshold (individual alert) is reached. A combination of thresholds must then be considered. Consequently, the difficulty resides in the determination of these combined and non-predefined thresholds. despite no individual alert is raised. Basic alert states are triggered when the value of one of our system attributes reaches its associated single threshold. Nevertheless, more complex alert states must also be triggered when values of a set of different attributes are reached. In this partical case, a combination of thresholds must be considered, with combined thresholds values different from single thresholds values. Consequently, the difficulty resides in the determination of these combined and non-predefined thresholds. In this context, our contribution consists in identifying these complex alert states on the basis of acquired knowledge (past experiences). This knowledge is then analysed using decision support tools. Consequently, the multi-agent system is the paradigm we have chosen to generate a large number of situations, some of which are initially unpredictable.

However, this model shows weaknesses in terms of the acquisition of knowledge based on experience. We therefore propose the coupling between a multi-agents system (MAS) where agents interact in a given environment, and a case-based reasoning (CBR) system that allows solving a target problem by analogy with stored knowledge. In response to these issues, our contribution consists, on the one hand, in bringing out situations with risks that are a priori unforeseeable, and on the other hand in capitalizing on all the simulations (experience base).

To achieve these two objectives, we have chosen to couple a multi-agents system with a case-based reasoning, knowing that :

the SMA paradigm is characterized by agents that interact with each other and produce emerging phenomena;

the CBR paradigm allows us to solve problems by analogy with past experiences.

In addition to the presentation of this architecture, this paper exposes our work on the classification of different methods of similarity calculations that we consider essential. Indeed, the operating room environment requires a great rigor in terms of the veracity of the information processed.

In this paper, we therefore explore conceptual approaches in relation to the problematic: "risk prediction in a non-deterministic context". The specific literature on predictive modeling (Prognostics and Health Management, Multi-Agents System, Case-Based Reasoning) is the subject of Section 2. We then expose our MAS and CBR architectures in Section 3. Section 4 materializes this architecture with a description of our simulator. Section 5 describes analysis of data management (discrimination between distance calculations). In particular, we present our positioning in response to the determination of aggregated thresholds. We then present our first results in Section 6 and comment them in the next one.

"Predictive systems" aim to deliver new information from past observations, from simulations or from learning. They mainly depend on the environment and on available data. The era of big data is a major current track in the production of the last ones, which we hope will be both exhaustive and reliable.

Several paradigms exist and coexist, either independently or in a complementary manner. Among them, the literature gives great importance to Prognostics and Health Management (PHM). PHM is a major paradigm in the detection of failures for industry, since the impact of an incident is often far-reaching. PHM is a five-step process [?] that starts with data acquisition from sensors (monitoring), proceeds with data manipulation (or processing), then assesses conditions, establishes a diagnosis and finishes with prognostics and decision support.

With this in mind, integrity measures for machining tools, such as cutting machines, prevent the deterioration of work pieces (often expensive) through the anticipation of tools replacement [?]. In [?], the authors show the effectiveness of PHM modeling in identifying risks that are specific to the oil and gas industry in terms of reliability, availability, and maintainability of equipment while achieving cost savings. More and more committees apply the principles of the PHM in the context of human health prognosis [?] with the aim of empowering technologies to provide care. The focus is on biofeedback control of these intelligent technologies for health [?], in a context where a hardware failure can have serious consequences on the diagnosis of human pathologies. However, we did not find any study on risk prediction of complex interactive systems operating in non-determinist contexts such as surgery and the operating room environment.

The multi-agent systems described in the following section are built according to the interaction principle and overcome this disadvantage.

Definitions taken from the literature characterize MAS as systems composed of autonomous entities that interact with each other according to certain rules in a specific environment. In [?], Ferber defines agents as autonomous software entities able to perceive (by messages, by data capture...) in an environment.

In this context, cognitive agents act with reflection and awareness of their environment composed of other entities, unlike reactive agents that only react to stimuli. Thus, in the case of complex problems such as the epidemiological and ecological analysis of infectious diseases, standard models based on differential equations become unsuitable due to too many parameters and are supplanted by MAS [?]. There is also an increasing integration of the agent paradigm in strengthening collaborative automatic learning that cannot be dissociated from knowledge acquisition. It characterizes the autonomy of the agents and can be implemented beforehand (innate knowledge) or acquired through experience.

This second case concerns the entity's ability to explore a knowledge base [?].

Its performance depends mainly on the collection of information that enriches its learning. The CBR architecture designed according to this principle can be a solution to this requirement.

The notion of knowledge acquisition is at the heart of dynamic models enriched by experience. Our modelling of non-deterministic entities is part of this framework and values of the solutions are not necessarily known. It is therefore essential to have a memory of previous cases and an ontology to structure them.

Case-based reasoning is an artificial intelligence paradigm based on the development of solutions by analogy with prior experience and general knowledge in the field of application. It is widely used in medicine [?], in industrial maintenance [?] or in stock market analysis [?]. To find a solution, the CBR needs a database of solved cases, the characterization of similarities and finally the knowledge of adaptation processes. Several articles deal with knowledge acquisition, similarity or decision-making with MAS [?]. The different predictive approaches structure their modeling based on the analysis of past experiences. The nature of the data and the analysis tools distinguish these predictive concepts. Two main approaches are considered in the literature for the use of CBR in an MAS. In the first approach, the CBR coupling with MAS integrates, in the agent, the capacity to solve problems from experiments extracted from a case database. In [?] problems are solved locally with sometimes a collaborative approach [?]. In [?],

case-based reasoning gives to the multi-agents system the access to a structured database that accelerates data mining. This case search mode, built for a specific problem, however, shows its limitations on non-similar cases. In addition, the CBR/MAS coupling brings a dynamic aspect since it produces a dynamic model enriched by experiments. Indeed, multi-agents simulation remains at the heart of our work, whose challenge is to "predict in a non-deterministic context".

The CBR is therefore integrated as a source of active knowledge acquisition and proposes a decision support system in a multi-agent environment. One of the main objectives is to suggest possible answers in different contexts constrained by many parameters. Once again, the value of a case-by-case approach lies in its ability to find solutions by analogy. These can be ordered according to a hierarchy (bargaining agent (BA), expert agent (EA)) [?] or organized into collaborative committees. The system can explore its own case database [?], several merged databases [?], or independent databases. The search for similar cases can integrate different principles of initiation and learning such as artificial neural networks [?]. These decision support tools, which integrate greater adaptability in the acquisition of knowledge, are one of the possibilities we have explored.

However, this is limited to case bases, while other types of data such as traces are interesting sources of information. This type of coupling meets our need in terms of knowledge acquisition, but remains incomplete in response to our predictability problem. Indeed, our model must also integrate the anticipation of non-deterministic situations through an analytical approach of past experiences. As we mentioned in the introduction, our contribution to the integration of this type of analysis uses the MAS/CBR coupling presented in the following section.

3 Architecture of the model This section highlights our originality in relation to the determination of alert thresholds that are not defined a priori. We describe the architecture of our model that integrates the MAS/CBR coupling as a response to our predictive approach. Figure ?? describes the architecture of our decision path.

Our research work, which aims to prevent risks in a non-deterministic environment, is materialized (among others) by the implementation of an alert generator. This supposes the possibility of producing a large number of situations as close as possible to those of the studied context (operating room in our case). The MAS paradigm that we have chosen meets this expectation thanks to its ability to highlight unexpected situations. Concerning the acquisition of knowledge, it can either be implemented beforehand (innate knowledge) or acquired through experience. The second case supposes the capacity to explore a knowledge base by the entity. This is why we have integrated a CBR in our architecture whose principle consists in solving a problem by analogy with a problem resulting from past experience. This method also allows to capitalize on experiences. In a schematic way, the coupling between our multi-agent system and a case-based reasoning can thus be defined as a collaboration operated by exchanges. Figure 1 summarizes these. The SMA generates situations (at risk or without risk) which are transmitted to the CBR to be compared with past experiences. The result of this comparison can lead to a modification of the system data (MAS and/or CBR) and generate, for example, an alert (modification of the status of the alert agent).

Fig. 1: MAS/CBR exchanges

At each cycle (interval between two times t i and t i+1 i ∈ 1, n equal here to 60 seconds) a new case which takes again the value of each attribute (specific to each agent a1, a2, ..., a7) is generated. Each of them enriches a knowledge base (CBR Base) which is then exploited following the CBR steps described in section 3.3. The following section details the architecture of our MAS and CBR.The next three paragraphs describe respectively: the formalism used, our multi-agent system, our case-based reasoning, and finally the MAS/CBR coupling (global vision).

Formalism

All simulations are sequenced in identical time periods called cycles. Each of them corresponds to a period of time going from t i to t i+1 i ∈ 1; n which can be parameterized (for example 60s). The state variables (named attributes) define the behavior of each agent that is essential to achieve the simulation objectives. Their values are modified at each simulation cycle. They give us the state of the system which thus corresponds to the value of the attribute(s) of each agent (the patient's temperature for example) at a given moment (at a given cycle).

All these values give a state to the system (global state of the system): normal, alert or f ailure. The state normal precedes the state alert i which is succeeded by the state f ailure. There are three increasing levels of alert (i ranging from 1 to 3) whose intensity is inversely proportional to the time that separates an alert from an incident (f ailure). As far as data acquisition is concerned, we distinguish two modes within our architecture: offline mode and online mode also called 'real-time mode". In the offline mode, the data results from a function or statistical data and is assigned to each cycle. In the connected mode, the data are issued from a dynamic capture: the connected sensors (bracelet for fatigue, electrochemical sensors for infection rate...) and the monitoring devices.. Whatever the mode considered, these sources of information are considered as resources "at the disposal" of the agents. Thus an agent can request one or more instances of a resource (for example the sound level of a sensor) according to his rights.

In this article, we only deal with the unconnected mode, which corresponds to the one currently implemented. This formalism being posed, we now approach the description of our two paradigms.

MAS model for the operating room

In this non-deterministic context, and in order to achieve our objective (predicting operating room incidents), we model the operating room as a multi-agent system. Thus, the operating room is designed as a multi-agent system where each entity is represented by one agent. Each of them, belongs to a group called species (the agent surgeon belongs to the species P ersonal). Note that a species can be composed of only one agent (agent alert belongs to the species Supervisor).

This type of model allows to create different scenarios and to simulate the possible evolutions of the state of the system. Moreover, these models, in which agents interact with each other, make it possible to incorporate risks that have been minimized or ignored to date and thus contribute to the optimization of safety in the operating room. For example, simulating the movement of persons (personal agent) allows to determine the level of suspended particles [?] which in turn allows to calculate the level of risk. The architecture of our model, which integrates the BDI (Belief, Desire, Intention) paradigm, has five species of entities: P ersonal, M aterial, Inf ection, P atient, Supervisor. Table 2 gives a description of the attributes of these agents. On an experimental basis, we simulated the evolution of infection sites in parallel with human fatigue and patient's vitals over a period of time divided into cycles.

We chose to model the evolution of the values of the most significant attributes in an operating room according to experts in the field (surgeons and anaesthetists of the Besancon University Hospital). The following paragraphs therefore explain the modelling of human fatigue, that of patient's vitals and that of infection. The major role of the agent alert will also be described.

Modeling fatigue. Fatigue can be modelled using several data acquisition methods. In offline mode, data is extracted from statistical files or from a function. If it is a dynamic capture, the connected sensors (bracelet for fatigue) and moni- because it can be applied to continuous phenomena and highlights the non-linear nature of fatigue. It is given by the following relationship: f (t) = ae (k×t) where a is the initial value, k the growth constant, and t the time. It should be noted that in our case we treated the fatigue level of a single agent knowing that each participant may have its own risk threshold.

Modeling patient's vitals. As for the fatigue, Patient characteristics and constants can be extracted from statistical data. However, there are no adapted monotonous functions for this type of variation. For this reason, the data evolve randomly according to a step set by the experts. We choose dynamic data captured from sensors or monitoring in a connected context.

Modeling the infection. The two main types of contamination which can be observed are, on the one hand, exogenous agents in the operating room and, on the other hand, endogenous agents (belonging to the patient). Our system is able to simulate the evolution of the infection rate of exogenous hosts according to decontaminating agents and time. The progression or regression of infection is related to the overlap between contaminated or healthy particles over time.

alert agent The alert cognitive agent is central to our architecture and plays the role of:

central control (gathers the different alert thresholds);

adapter (manages a collective alert level);

regulator (proposes possible solutions).

Its preventive role, characterized by the possibility of alerting or adjusting its alert thresholds, requires prior access to the past experiences which characterize the case base in CBR.

Other key points of our predictive model include the interactions between different entities (agents). An alert does not only depend on an single threshold but also on the aggregation of different levels depending on each attribute of the system. It implies to think about the definition, the representation and the measure of these collective thresholds. To overcome these two necessities related to alerts and interactions between agents, we suggest coupling our MAS with case-based reasoning. In the introduction of this paper, we have notified the importance of knowledge acquisition in our system. More precisely, it is a question of choosing a paradigm that integrates on the one hand the enrichment of its database from experiences, and on the other hand the search for the solution of a problem by analogy with other problems already solved. Case-based reasoning, adapted to this type of learning, is presented in the following section.

Knowledge acquisition: case-based reasoning

In the following paragraph, we propose a brief description of the five specific steps of the case-based reasoning cycle.

Elaborate. The monitoring of our system and the resulting decision aids are formalised as follows: U → R with U characterizing a sequence of quadruplets (E, A, V, c) and R the couple (attribute value,recommendation). We have assigned the attribute A of value V at cycle c to each entity E. In the example : (nurse,fatigue,1.5,1200) → (normal,no preco), the value 1.5 is assigned to the attribute "fatigue" of the agent "nurse" at cycle 1200. In our CBR system, a case is composed of two parts: the problem part corresponds to the quadruplet U and the solution part corresponds to the couple R.

Retrieve. The retrieve step is usually based on finding the source case (stored in the case base) the most similar to the target case (case to be retrieved). In our context, we will compare a set of target cases with a set of source cases. Indeed, the system state (MAS) that we record in our CBR database at each cycle, or that we compare, is composed of an identifiable set of cases (for example {((surgeon, f atigue, 1, 10),(normal, no preco)), ((patient, temperature, 38, 10), (normal, no preco))}).

Since quadruplets are not necessarily homologous (different attributes), we have chosen to compare each quadruplet of the set of target cases with all sets of quadruplets of the source case. The calculation of the distance of the selected vector is defined according to the relation :

sim( -→ C , -→ S ) = 1 n 2 n i=1 n j=1 4 k=1 (1 -I) 2
(1)

I = x ki y kj if x ki ≤ y kj . Otherwise (y kj ≤ x ki ) I = y kj x ki .
x ki and y kj are respectively the values associated with each element of the target quadruplet ( -→ C ) and the source quadruplet ( -→ S ) among n quadruplets.

The comparison of quotients exonerates us from the scale problems specific to the different attributes. We consider this distance calculation as canonical and complementary to other approaches defined in Section 5.

Reuse. This step is used to define the target case solution. In the case of automatic processing, the inheritance of the source case solution modifies the target case one. When an adaptation is necessary, (for example with a sufficient but imperfect similarity), we apply the following decomposition:

path(srce,target) = (p 0 r1 → p 1 r2 → p 2 ...p n-1 rn → p n )
p i : system state, r i : transition between two states (p i and pi + 1)

As an example, let us consider the following case:

target p 0 = (nurse fatigue limit∧nurse dexterity threshold), srce p n = (surgeon fatigue limit∧surgeon dexterity limit).

Figure 3 summarizes this request: the agent nurse does not belong to the case base, but it belongs to a parental (personal ) class with which it is possible to compare the degree of similarity of an agent of the same nature (from the same group). It is therefore possible to associate the collective thresholds inherited from the surgeon class to this new class.

Review and retain. Once experts in the field have corrected it if possible, each new target case, is added to the case base with in order to optimize further searches of similar events.

In this section, we have shown that integrating case-based reasoning into an MAS improves automatic knowledge acquisition. Beyond this coupling, data The global vision of the two paradigms we have just discussed is the subject of the following paragraph.

Global vision of the MAS/CBR coupling

The diagram 4 provides a global vision of the MAS/CBR coupling. It distinguishes the MAS and CBR paradigms. The multi-agent system is composed of agents belonging to different species such as: P ersonal, Inf ectious and P atient.

The state variables described in Section 3.2 characterize the behaviors, actions and objectives of each agent. CBR is represented according to the five cycles (Recall, Reuse, Review, Memorize) described in Section 3.3. MAS and CBR interact in the form of cooperation. This is because the determination of the system status and its updating depends on the reasoning by analogy specific to CBR. In the same way, the enrichment of the case base results from the state of the system exhibited at each cycle by the MAS. Beyond a classical representation, our architecture integrates a holistic organization to our SMA (agent aa interacts with all species), and the possibility for our case based reasoning to interact with several data acquisition sources (data sensors, monotoring ...).

These two specificities are not discussed in more detail in this paper.

Fig. 4: Global architecture

The following section presents the interface of the simulator, the form used for each type of data by R Ã PC and our first simulations.

A similator for risk prediction

We have described in the Section 3 of this paper, our architecture built according to the coupling of a multi-agent system with a case-based reasoning. Our different choices and contributions in terms of structure have been explained.

The present section is rather devoted to the exploitation of the model and thus to the generated simulations. We distinguish a visual aspect through the MAS, unlike the CBR which is rather similar to the hidden side of the simulator. The two following paragraphs present respectively our simulator built from the Gama platform and the structuring of the data of CBR.

Gama platform: a tool to implement the simulator

As shown in Figure 5 the user interface is split into two blocks. The first one is reserved for parameterization and the second one for visualization of the current simulations. In this example, this last one is subdivided into several windows in which evolve (among others): operating room agents, patient constants, infectious agents and system status (visualization of alerts). creasing, decreasing, random). In addition to these parameters, there are also the following possibilities: neutralization of one or more attributes and deletion of one or more agents that you wish to exclude from the simulation. Figure 6 illustrates the possibilities offered by the "Actions" tool of the Gama platform. Each attribute of an agent can be disabled (alert f atigue in our example) and each agent can be excluded from the simulation by a simple deletion ("Kil" option).

These features are useful among others to evaluate the interactions between agents. It is a detailed view of all the agents and attributes of the system for a given cycle. The state of the system that we recall is driven by the agent alert, is a synthesis of all the states of all the attributes observed at a given cycle. Any serious undesirable event resulting from the evolution of one or more attributes, then modifies the state of the system whose value becomes f ailure for the current cycle. The previous states browsed in an antechronological order take respectively the values: alert0, alert1 and alert2.

Figure 8 shows a f ailure state at cycle 65, then respectively alert0, alert1

and alert2 for the previous cycles. We observe that the state f ailure of the system, results in our example from the failure of only one attribute (cf Figure 7 status f ailure of the attribute pressure increase). The levels of alerts preceding this state, are those which will be proposed by the system during the search for Fig. 7: System Status Detail analogy between the target case and the source case. The SMA/R Ã PC coupling is an architecture intended to observe the virtual dynamics of a possible representation of reality but also allows the emergence of unpredictable phenomena.

In this section, we have shown that integrating case-based reasoning into an MAS improves automatic knowledge acquisition. Beyond this coupling, data analysis and the quality of data selection are key elements developed in the Fig. 8: Focus on system status following section. We did not find any architecture coupling MAS and CBR in the context of risk predictability within an operating room. However, the (multi-player) game "3D Virtual Operating Room" [?] is an interesting tool for risk prevention in an operating room that we compared to our simulator. This comparison is presented in the following section.

Comparison of our simulator with 3D Virtual Room

"3D Virtual Operation Room" is a role-playing game for medical and nursing students. It consists for each player to take the professional role he intends to play. Each of them then finds himself in a virtual operating room with a patient ready to be operated on. This tool allows the player to be confronted with professional situations resulting from real cases of adverse events. A balance sheet established for each player allows to analyze their behaviors. Table 9 summarizes the comparison according to the objectives to be achieved, the targeted personnel, and the operational mode.

On reading Table 9, we can see differences for each of the elements compared.

In terms of objectives, the "3D Virtual Room" platform aims to train students while our architecture is designed to simulate the world of the operating room to produce undesirable events that are a priori unpredictable. Next, in the case of the game "3D Virtual Room", it is the students who are targeted while in the case of our simulator, it is the health professionals already trained or in training. A simulator produces a large number Role-playing game where players of scenarios for the emergence react to serious adverse events and analysis of serious adverse events that cannot be predicted a priori Fig. 9: MAS/CBR Comparison with "3D Virtual Room" Finally, the operational mode differs between the two tools, knowing that "3D Virtual Room" involves players in the form of a role-playing game, whereas our simulator makes virtual agents evolve in the operating room environment. In conclusion, our architecture, which makes it possible to alert and prevent new risks, is more of an operational tool, whereas the "3D Virtual Room" platform is more of an educational tool.

The next section is devoted to comparing different similarity calculations. We believe that the quality of the data selection is a key element of our MAS/CBRcoupled predictive system.

Evaluation of different similarity calculations

The notion of event has been linked to cases. The CBR cycle followed allows our system to identify alert states based on the combination of attributes values.

As explained in Section 3, alerts are weighted according to their proximity to the preceding f ailure, which threshold is determined by the expert (e.g. 40 for temperature). We thus obtain a base containing 3 types of cases:

normal: without alert; f ailure: incident; alert: alert0 weight 0 (case n -1 ) > alert1 weight 1 (case n -2 ) >,...,> alertk weight k (case n -k + 1). f ailure = case n.

An alert is therefore linked to the exceeding of the threshold of a case attribute observed in our case base. Knowing that a case always belongs to a set (cf 3.3), we have a global approach of the alert. It is no longer only attached to a value, but corresponds to an aggregation of values. This overcomes the difficulty of manual and empirical determination of these alerts. In parallel to this case classification, we propose to open the "retrieve" step to main similarity calculations we have evaluated:

-Euclidian distances calculations (see Formula 1); -Confidence interval calculations; -Complexity Invariance Distance [?] (CID) calculations;

-Cosine similarity calculations.

In order to simplify the reading of this article the expression similarity calculation includes the calculations we have just listed. These calculations are described in the following formula with the exemption of the Euclidean distances already described in Section 3.3 (see Formula 1). Confidence interval calculations. Using the state application previously defined in the "elaborate" step of CBR (see 3.3), the formula of the calculation of the confidence value p, for instance for three attributes X = (x 1 , x 2 , ..., x n ), Y = (y 1 , y 2 , ..., y n ), Z = (z 1 , z 2 , ..., z n ) , is:

p =      α β , β = 0 (cf f igure 10a ) 0 , β = 0 (2)
with α and β defined by: Knowing that several modalities are possible (calculates: C0, C1, C2, C3) the prioritization rule must be consistent and explicit. In our study, it is related to the strongest representation of modality. The example presented in Table 1 shows the results obtained when applying the 4 calculations which return the state of the source case the most similar to the target case: We applied this hierarchical ranking to five attributes (hypothermia, hypoxia, capnia, infection, human tiredness) and obtained the following result: only on Euclidean distance. Thus, we have added to the system the ability to discriminate between calculation choices such as CID, cosine distance or confidence interval calculation. This learning optimizes the choice of calculations.

α = card{xi ≥ yi ∀ i ∈ 1, n , state(X) = state(Y )} β = card{Z / ∃ z k ∈ [xi, yi]} (
∀i ∈ 0, 2 , 2 i=0 C3i > 2 i=0 C0i > 2 i=0 C2i > 2 i=0 C1i C1 = {(normal,
C3 > C0 > C2 > C1

Results

We have chosen GAMA [?] as the development framework. GAMA allows to build agent models in an integrated development environment (IDE) including the GAML language (GAMA Modeling Language). The determination of thresholds, which results from a retroactive analysis of an incident (f ailure), can generate an alert when a complex and dangerous situation is reached (proximity detection with a set of thresholds) before reaching each single threshold.

Figure 11 illustrates this type of case. Indeed, we can see from the "Infection"

and "Personal Tiredness" graphs that their individual f ailure threshold is not exceeded while a collective alert is triggered (determined based on the similarity calculations that we evaluated and explained in the Section 5).

Fig. 11: Fatigue and infection aggregation

In addition to this operational aspect, we compare both of the threshold types (predefined single thresholds, calculated thresholds). In each case, the validity of the status (alert i " i ∈ N, normal) is dynamically affected and verified. In the example of Alert detection is determined according to the threshold levels (individual and collective) set during the simulator initialization phase. The curve "Predefined thresholds" in Figure 12 shows that there is no linear relationship between the number of validated cases and time. In addition, the relatively small number of cases validated even after 500 cycles is explained by the difficulty of pre-defining aggregated thresholds in a context where the influences are both multiple and time-dependent.

The determination of the alert depends on distance calculations chosen by screening according to the the evaluation of several similarity calculations described in Section 5. The curve "Calculated" in Figure 12 shows results which are quite close to the reference values. We applied this same comparison protocol to 1000 simulations and obtained a coefficient of variation equal to 7.1% for the predefined thresholds and equal to 5.3% for the calculated thresholds.

As these results show, the measurement of the coefficient of variation of the standard deviations of each type of threshold (single and predefined versus aggregated and not predefined) for the entire test set (1000 simulations) is low (<15%: the values are homogeneous). This confirms the effectiveness of our results and therefore our position in relation to the MAS/CBR coupling, which allows us to effectively determine the threshold combinations.

Discussion

This study shows the effectiveness of the MAS/CBR coupling which allows analytical management of thresholds and avoids contexts where each global threshold is predetermined. For example, the number of possible thresholds for 7 variables would be 127 (2 7 -{∅} combinations). In addition, a module for prioritizing similarity calculations (decision tree) has been integrated in order to optimize the selection of source cases. We evaluated four distance calculations (Euclidian distances, confidence interval calculations, cosine distance and CID) knowing that the decision support tool (decision tree) allows us to extend this number to n (n ∈ N) calculations. This architecture, which allows cases to be generated and then analyzed, is efficient in determining alerts before an incident (f ailure) occurs.

Similarly, this system, which is able to listen to the generated data by a MAS, can be coupled with monitoring systems which evaluate in real time the state of the various entities of the simulator (patient constants, human fatigue, equipment efficiency, etc.). It can therefore be enriched by real situations rather than data from arbitrarily chosen functions (e.g. human fatigue). This new source of values for each attribute will make the case base more reliable. Consequently, the validation by experts of the thresholds determined by the system (aggregated thresholds) increases its efficiency.

One of this MAS/CBR system limitations concerns the anticipation of these alerts and therefore the possibility of making assumptions about the evolution of the system at a given time. Indeed, beyond the automatic determination of alert thresholds, we consider in our perspectives their anticipation by extrapolating the state of the system at time t.

Conclusion

This paper presents the MAS/CBR system we have designed and implemented in order to predict the risks in surgery blocks.

The results show that our model can manage data in an environment where the data are as disparate as infectious agents or human fatigue. We have also described our positioning in determining thresholds that are not predictable a priori and therefore difficult to configure since based on combinations of factors.

We consider that, in its current form, our simulator is an effective alert generator.

Nevertheless, in a medium term, we plan to integrate our system in a dynamic mode (connection to sensors, monitoring, etc.). We hope that the surgery room environment will benefit from a system where entities are not only reactive but also interactive. Finally, we believe that beyond alert detection (which we have optimized), we could plan a set of possible trajectories from the first cycles based on the state of the system. This is a retroactive study of the drift zones.

Fig. 2 :

 2 Fig. 2: State variables of simulated agents

Fig. 3 :

 3 Fig. 3: Adaptation

Fig. 5 :

 5 Fig. 5: Global vision of the simulator

Fig. 6 :

 6 Fig. 6: Control of attributes and agents

3 )

 3 Figure10illustrates the measure of confidence interval membership. The xaxis shows the attributes and the y-axis shows their values from the source and target cases. Thus, x i , y i , z i , which belong to X, Y , Z respectively, correspond to the y-axis coordinates in Figure10a. When p ind (ind: confidence index initialized or calculated from the evaluation results of the model) any vector belonging to this interval inherits the value of state system (normal, f ailure) common to both of the vectors surrounding it. Figure10awhich represents nonsecant curves illustrates this type of interval. Otherwise (secant curve as shown in Figure10b), the system will enrich its learning with distance calculations (euclidian distances d ED , cosinus similarity, CID).

  normal), (alertj, normal), (alertj, alertj)} with j ∈ N C0 = C2 = C3 = {normal, alertj} Input : R: no targeted attribute set, C: targeted attribute, S: learning data Output : decision tree 1 Function ID3(RCS) node with as value the most frequent of the values of the categorical attribute that are found in records of S 10 end 11 D ← the attribute that has the largest gain (D, S) among all the attributes of R 12 {d j with j == 1, 2, ..., m} ← the attribute values of D 13 {s j with j == 1, 2, ..., m} ← the subsets of S respectively constituting of records of values d j for the attribute D 14 return a tree whose root is D and the arcs are labeled by d1, d2, ..., dm and going to subtrees ID3 (R-D, C,s 1 ), ID3 (R-D, C , s 2 ), ..., ID3 (R-D, C, s m ) 15 end Algorithme 1 : Decision tree ID3

  Fig. 12: Prediction zone: secant curves

  This example shows that we have extended the similarity calculation based

	Case Cycle state	C0	C1	C2	C3
	122 150 normal normal (normal,normal) normal normal
	123 155 normal normal (normal,alert2) normal normal
	124 160 alert2 alert2 (normal,alert1) normal alert2
	125 165 alert1 alert0 (alert0,alert1) alert2 alert1
	Table 1: Learning test for the best similarity calculation

Table 2

 2

	we observe that among the 3 cases (case 2049, case 2050, case

Acknowledgements

The authors would like to thank the European Regional Development Fund (UFC SACD/920/2303/MASSAI-OPE-2019-109) for their financial support.

Declaration of competing interest

The authors have no conflicts to declare.


Elie Geagea

Judicaël Jeannoutot

Michel Feron

Frank Palmino

Frédéric Cherioux

Christophe M Thomas

Alain Rochefort

Michel Féron

Frédéric Chérioux

Collective radical oligomerisation induced by an STM tip on a silicon surface

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

Introduction

On-surface synthesis under ultrahigh-vacuum (UHV) conditions has attracted considerable attention as a means to generate new and stable molecular structures, as it offers an alternative and highly efficient strategy for controlling chemical reactions and allows direct observation or induction of reaction pathways by scanning tunnelling microscopy (STM). [1,2] However, so far, the number of C-C bond-forming chemical reactions reported on surfaces remains very limited and have mainly developed on coinage metal surface [2] or insulators [3] but never on a silicon-semiconductor. The development of on-surface chemistry on a silicon surface is still a major scientific and economic challenge because silicon wafers are commonly used in electronic devices. In particular, onsurface radical polymerisations have rarely been investigated despite their efficiency in the absence of any catalytic role of the surface, while radical species have been observed as intermediates in cross-coupling reactions on surfaces. Most of the reported results are based on a single tip-induced reaction which causes an intramolecular reorganization or initiation step to result in a single 1D-polymer chain. [1g, 2, 3a] The relative absence of on-surface radical polymerisation is quite surprising, as free radical polymerisation is the main industrial method for obtaining polymeric systems and composite materials. The relatively non-specific nature of free radicals with respect to monomers makes it one of the most versatile polymerisation methods, but at the same time renders their reactions difficult to control. [4] Indeed, 'living' radical polymerisation, where irreversible terminations and transfers are absent while all chains are initiated and grow simultaneously, was considered impossible for many years owing to fast propagation and inevitable radical termination reactions. [5] In the mid-1990s, new methodologies were developed to exploit equilibria between growing radicals and dormant species. [START_REF]These methods include atom-transfer radical polymerization (ATRP) and stable free-radical polymerization (SFRP), which proceed with reversible termination, and reversible addition-fragmentation transfer (RAFT), which proceeds with reversible chain transfer. See for instance[END_REF] These approaches differ in the method of radical generation but all involve the use of a persistent (metallo)radical that reduces the steady-state concentration of the propagating radicals and minimizes the normal termination of living polymers. The simplicity of adding these reagents to a polymerisation reaction has resulted in the ability to synthesize well-defined functionalized (co)polymers. [7,8] However, for a range of applications such as microelectronics, coating technologies and biotechnology, contamination of the final polymer/oligomer by the reagents/additives has become a significant problem and a key limiting factor in their use. Another approach to polymer/oligomer synthesis is that of tandem reactions, which produce macromolecules with new structures and functions. [9] In particular, since radical reactions are ideal for sequencing, for the very fundamental reason that the product of every radical reaction is a radical, tandem radical chemistry may serve as a versatile method in radical oligomerisation. These reactions take place in two or more consecutive steps mediated by the radical's unpaired electron, and have significant advantages over conventional multistep syntheses such as timeand cost-savings, atom economy, waste reduction and energy consumption. [10] However, they are limited by the reactivity of the active sites, which must be well matched so that the product of one chemical transformation does not interfere with the overall tandem sequence. Here, we propose to use the ability of a STM-tip to generate an organic radical with the free radical polymerization process, with both steps occurring on a semi-conductor surface. We report the first on-surface synthesis of alkyl oligomers on a model silicon surface, mediated by tunnelling electrons from a STM junction. We show, using STM imaging that the on-surface reaction is most likely initiated electronically and involves radical intermediates that preferentially form cross-reacted linear oligomeric products, even on semiconductor surfaces.

Results and discussion

Results

We chose the Si(111)√3x√3R30°-B surface as the model semiconductor surface because the subtle balance of molecule-surface and molecule-molecule interactions promotes the formation of extended supramolecular networks [11] . As one-electron reduction of aryl alkyl ethers (e.g., cyanoanisole) has already been shown to produce the corresponding phenoxide anion and the alkyl radical [12] , we decided to use the same type of compounds in this study. Having previously obtained bilayered networks of aryl alkyl ether derivatives on Si(111)√3x√3R30°-B surface [13] or ionic alkali halide surfaces [14] , we synthesized a pyridyl analog (1,4di(4',5-bis(decyloxy)benzene, PDB-OC10, Figure 1a) rather than a cyano derivative in order to reinforce molecule surface interactions to observe separate nanolines instead of a compact 2D supramolecular network on a Si(111)√3x√3R30°-B surface [15] . PDB-OC10 is based on a phenyl core terminating with two pyridyl moieties, distanced by 1.4 nm and further core-substituted with two lateral ether alkyl chains (Figure 1a) containing 10 atoms of carbon. The side chain lengths in PDB-OC10 is 3.6 nm. Figures 1b andS1 (for a larger scale) show a high resolution STM image, recorded at 110 K, after the deposition of PDB-OC10 by thermal sublimation under ultra-high vacuum conditions on a Si(111)√3x√3R30°-B substrate maintained at room temperature. Well-organized stripes consisting of aligned pair of bright protrusions (length: 1.6 ± 0.1 nm) surrounded by slightly darker rods (length: 2.0 ± 0.2 nm), are observed. The stripes follow the three principal directions rotated by 120° of the substrate, surrounding the empty free space where the silicon adatoms are visible (inset of the Figure 1b). Consistent with the features of PDB-OC10, the bright protrusions can be attributed to the triphenyl cores of PDB-OC10 and the darker paired rods correspond to the interdigitated C10 alkyl chains of two PDB-OC10 molecules involved in two adjacent lines (Figure 1b) [13,16] . Based on our STM observations and measurements, we obtain the adsorption model of the PDB/Si(111)√3x√3R30°-B interface (See insert in Figure 1b). With these results in hand, we were then interested in obtaining a better understanding of the reaction behaviour by scanning a large area of the PDB-OC10/Si(111)√3x√3R30°-B network at a lower bias voltage. This result is representative of those obtained in repeated experiments for the bias voltage between -4.5 V to 0 V. Due to the molecule-molecule and molecule-surface interactions, the alkyl chains of PDB-OC10 molecules are always well visible in the STM images. Notably, at the bias voltage of -4.5 V, we observed a remarkable modification of the PDB-OC10 molecules in the STM images (See Figure 2). The well-organized network is now disordered and the cross-shape of PDB-OC10 molecules disappeared. If the bias voltage is decreased beyond -4.5 V, the destruction of the original supramolecular network is still observed. A further study of the effect of the bias voltage on the PDB-OC10/Si(111)√3x√3R30°-B interface was then carried out. A 50x50nm 2 area was imaged by STM at Vs = -1.3 V, showing the typical STM image features of the PDB-OC10/Si(111)√3x√3R30°-B interface (Figure S2a). Then, the same area was scanned at -4.5 V. All the cross-shape corresponding to the PDB-OC10 molecules disappeared (Figure S2b), while Si(111)√3x√3R30°-B surface is unaffected as shown by the uncovered area surrounded by dashed lines in Figure S2b. The same procedure was performed along a line of molecules, leading to the destruction of only the scanned line (Figure S3). Since the cross-shape of PDB-OC10 molecules is not visible, we moved the tip to another area of the PDB-OC10/Si(111)√3x√3R30°-B interface, which have been previously scanned only at a voltage below -4.5 V, showing the ordered supramolecular network (Figure 3a) constituted by entire PDB-OC10 molecules. This intact area is then scanned again at -1.3 V. During the scan, rod-like features appeared and filled the uncovered zone until it was completely covered by strips of parallel continuous rods (Figure 3b). The rod-like features are arranged parallel in three different domains (see black dashed outlines on Figure 3b) following the three symmetry axes of the Si(111)√3x√3R30°-B surface. Based on the systematic analysis of more than 20 STM images, a statistical analysis of the size distribution of strips reveals a size repartition centered at a length of 2.1 nm (Figure S4). In addition, the length of these rod-like structures increases with time (Figure 3c). Three STM images of the same area have been recorded after 40 and 50 minutes. The length of a rod structure increases from 2.4 nm to 7.4 nm while the number of small initial rods decreases. Finally, we have compared the profile of a C10 lateral alkyl chain of an entire PDB-OC10 molecule with the profile of a nanorod on the same STM image (Figure S5). These two profiles the same shape and differ only by their length. On the basis of all these features, the rods are attributed to alkane oligomers adsorbed on the Si(111)√3x√3R30°-B surface. The number of carbon atoms in the most common adsorbed alkane was 20 for a rod length of 2.1 ± 0.2 nm, respectively. In addition, the rod corresponding to the decane (10 carbon atoms) and longer alkanes (like hexacontane, 60 carbon atoms 7.4 nm, Figure 3c) were very rarely observed. The observation, of the growth of long alkanes definitively indicates that a polymerization process occurs on the surface.

Discussion

The formation of oligomeric alkanes from aromatic species containing only ether side chains as precursors has not yet been reported in the literature. The resulting mechanism should involve at least two steps: (i) activation of the C-O bonds of the aromatic precursors at a fixed bias voltage and then (ii) on-surface oligomerisation of the generated species. For instance, the activation mechanism of C-O bonds in alkyl aryl ether derivatives has been extensively investigated in solution [12] and most recently described by Yang et al. on noble metal surfaces [17] . In the latter case, the authors suggested that the dealkylation process is based on a thermally-induced intramolecular prototropy from a hydrogen atom of the alkyl chain to the oxygen atom of the ether function. In solution, the dealkylation of aryl alkyl ethers can originate from a reduction (through an electron transfer 12 ), or can be catalysed by a Lewis or Brønsted acid [18] or by organometallic complexes (oxidative addition [19] ). In our experiments, it is reasonable to rule out that the mechanism is based on a catalyst because no external catalytic species were introduced on the surface. Since the dealkylation reaction takes place even at low temperatures, a thermally-assisted mechanism is also unsuitable. As the transformation occurs at negative bias voltage, this involves electrons that tunnel from the substrate, through the adsorbed layer to the STM tip. Then, an electron originates from the valence band of the substate can be captured by low-lying energy empty states of PDB-OC10 molecule [20] to generate an anion that relax through a dissociative electron attachment (DEA) mechanism [1g, 21] . The relaxation of that anion on the Si(111)√3x√3R30°-B surface leads to the dissociation of PDB-OC10 into a phenoxide moiety and an alkyl radical. A similar reaction path was already demonstrated in the electrochemical reduction of cyanoanisole in solution [12] . From DFT calculations, the electronic structure of PDB-OC10/Si(111)-B system shown in Figure 4 supports such DEA mechanism for which the energy of empty states (mostly C-aromatic) above Fermi level (see Fig. 4(d)) are in the same energy range than the bias voltage used in STM experiments where the reaction occurs. Moreover, additional DFT calculations on gas phase species (see Figure S6) indicate that C-O bond breaking is easier on the aliphatic side than the aromatic side by around 1.8 eV/bond. 111))√3x√3R30°-B surface by DFT. Clearly in (a), the C10 chains of PDB-OC10 (92 atoms) are well-aligned along Si-adatom rows that we have identified within the substrate (582 atoms) through brighter color for clarity. The density of states (DOS) and the projection (PDOS) profiles of the system are reported in (d) where the PDOS of aromatic (CC) and aliphatic carbon atom (CH) are the summed contribution of each species around O moieties, all projections are multiplied by 40. The cleavage efficiency is 100%, leading to complete disorganization of the initial supramolecular network. It is worth noting that after C-O bond activation, the resulting phenoxide moieties were rarely observed on the STM images. This may be explained by their low adsorption energies on the Si(111)√3x√3R30°-B, leading to their desorption (Figure S7). A comparison of adsorption energy for both species on Si(111)-B obtained by DFT calculations also supports a weaker of phenoxide than PDB-OC10 on the surface (see SI, Figure S8). The alkane derivatives only reappear as a periodic supramolecular network by scanning the uncovered areas of the Si(111)√3x√3R30°-B surface (Figures 3 andS9). In addition, tip instabilities are observed during the scanning, indicated that molecules are adsorbed on the STM tip (Figure S10). These features indicate that (i) the STM tip can act as a reservoir of C10 alkyl radicals, which can be released on the surface and (ii) These C10 radicals are free to diffuse on the Si(111)√3x√3R30°-B surface.

From a mechanistic point of view, the combination of electron-attachment (reduction) and C-O bond cleavage can be considered as the initiation step of a radical oligomerisation (Figure 5). Since the procedure of DEA manipulation leads to the collective formation of radicals by scanning large areas of the starting supramolecular network of PBD-OC10 molecules, the resulting radicals can react with each other by radical oligomerisation. The chain growth step is regulated by the rate of radical formation, as is the propagation step of a radical oligomerisation (Figure 5). In contrast to oligomerisation in solution, alkyl radicals have to diffuse to react, limiting the possibilities of the substrates to react and explaining why only linear alkanes are observed. When alkanes are long, chain growth can be stopped by two main termination processes (Figure 5). Since residual hydrogen gas is present in very low amount in the UHV chamber, an additional termination step that would involve a reaction of radicals with H2 was safely ruled out. The occurrence of this type of side reactions could explain the fairly modest lengths observed for the final alkanes. However, in agreement with previous observations, we considered that the 2D confined geometry could also favour certain reactions that are not usually observed. Due to the unique space confinement, the formation of linear oligomers of similar molecular weights can be controlled. This finding is consistent with the statistical analysis of the size distribution of alkanes adsorbed on Si(111)√3x√3R30°-B surface and the step-by-step growth described in Figure 3c, which correspond to monitoring of the propagation step by STM images.

Conclusions

In summary, we have used STM under UHV conditions and with some voltage application to initiate the synthesis of alkyl oligomers on a semiconductor surface. We have shown that the lack of reactivity of semiconductors with respect to a metal surface can be circumvented by using the STM-tip as an active role-player. Indeed, all these experiments clearly demonstrate that the observed transformations are triggered by a local dissociative electron (tunnelling) attachment and do not require any another "catalytic" role of surfaces. This allows the collective formation of electron-induced radicals that are able to cross-react in a controlled manner without adding any additives to produce alkyl oligomers. The origin of the experimentally observed selectivity towards oligomer products has been attributed to the 1D restriction of the reactive species along the surface. This tunnelling electron-induced radical oligomerization is a major step towards the fabrication of molecular electronic devices and novel nanomaterials.

Figure 1 .

 1 Figure 1. a) Structural model of 1,4-bis(pyridyl)-2,5-bis(decyloxy)benzene PDB-OC10 molecule. Nitrogen atoms: blue, Oxygen atoms: red, Carbon atoms: grey, hydrogen atoms: white. b) Large scale STM image (60x60 nm 2 , Vs = -1.3 V, It = 7 pA, T = 110 K) representing the self-assembled structure of PDB-OC10 molecules on Si(111)√3x√3R30°-B substrate. The inset of the image corresponds to black dashed rectangular zoomed area (10x10 nm 2 , Vs = -1.3 V, It = 7 pA, T = 110 K) of supramolecular network on Si(111)√3x√3R30°-B surface.

Figure 2 .

 2 Figure 2. STM image captured while changing bias voltage during the scan shows significant modification of network at -4.5 V (60x60 nm 2 , Vs = variable values shown on image, It = 7 pA, T = 110 K).

Figure 3 .

 3 Figure 3. a) STM image (25x25 nm 2 , Vs = -1.3 V, It = 7 pA, T = 110 K) representing an nano-pore inside the supramolecular network. b) The same nano-pore fully filled with rod-like structure released by STM tip during scanning. c) Three STM images (10x20 nm 2 , Vs = -1.3 V, It = 7 pA, T = 110 K) showing the growth of rod-like structure in a nanopore.

Figure 4 .

 4 Figure 4. (a) top view, (b) side view and(c) zoom view of the optimized supercell used to determine the electronic structure of PDB-OC10 adsorbed on Si(111))√3x√3R30°-B surface by DFT. Clearly in (a), the C10 chains of PDB-OC10 (92 atoms) are well-aligned along Si-adatom rows that we have identified within the substrate (582 atoms) through brighter color for clarity. The density of states (DOS) and the projection (PDOS) profiles of the system are reported in(d) where the PDOS of aromatic (CC) and aliphatic carbon atom (CH) are the summed contribution of each species around O moieties, all projections are multiplied by 40.

Figure 5 .

 5 Figure 5. C-O bond activation and cleavage followed by oligomerisation of the ensuing alkyl radicals on a Si(111)√3x√3R30°-B surface. 1) DEA process by electron attachment leading to the formation of a radical-anion at Vs < -4.5 V. C-O bond cleavage leading to the formation of a phenoxide anion and an alkyl radical. The combination of these two steps is the initiation step of the radical oligomerisation of alkyl chains. 2) Propagation of the radical oligomerisation. A chain-transfer reaction of radical leads to the growth of the length of produced alkanes. 3) Termination of the radical oligomerisation by two main mechanisms: combination between two radicals or disproportionation.

Acknowledgements

We thank Dr B. Grandidier (IEMN, Lille, France) and Dr M.-L. Bocquet (ENS, Paris, France) for fruitful discussions. The authors acknowledge the financial support from the French National Research Agency through contract OVATION (ANR-19-CE09-0020) and from the Pays de Montbéliard Agglomération. C.M.T. is grateful to the Institut Universitaire de France (IUF). A.R. acknowledges the support from the Natural Sciences and Engineering Research Council of Canada (NSERC), and he is grateful to Calcul Québec and Compute Canada for providing computational resources.

Conflicts of interest

There are no conflicts to declare.