# Concept proposal and evaluation: Patient and resource virtualization in emergency departments

Michael Schlecht, Vincent Cheutet, Jessica Florencia, Thierry Moyaux, Lorraine Trilling, Guillaume Bouleux, Sarah Devidal, Aymeric Cantais

## ► To cite this version:

Michael Schlecht, Vincent Cheutet, Jessica Florencia, Thierry Moyaux, Lorraine Trilling, et al. Concept proposal and evaluation: Patient and resource virtualization in emergency departments. 14th International Workshop on Service-Oriented, Holonic and Multi-Agent Manufacturing Systems for Industry of the Future (SOHOMA 2024), Sep 2024, Augsburg, Germany. hal-04755092

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<figure><img src="image_1.png" /></figure>
# Concept proposal and evaluation: Patient and resource virtualization through emergency department simulation

Michael Schlecht<sup>1, 2</sup>, Vincent Cheutet<sup>1</sup>, Jessica Florencia<sup>1</sup>, Thierry Moyaux<sup>1</sup>, Lor-raine Trilling<sup>1</sup> and Guillaume Bouleux<sup>1</sup>

<sup>1</sup> INSA Lyon, Université Lumière Lyon 2, Université Claude Bernard Lyon 1, Université Jean Monnet Saint-Étienne, DISP UR4570, Villeurbanne, 69621, France,
[firstname.lastname]@insa-lyon.fr

<sup>2</sup> CHU de Saint-Étienne, Av. Albert Raimond, 42270 Saint-Priest-en-Jarez,
[firstname.lastname]@chu-st-etienne.fr

**Abstract.** Emergency departments provide immediate medical care to patient with acute conditions. Uncertainties in patient flows are a major challenge in emergency departments. Patients arrive unplanned and their needs are not clear upon their arrival. The prediction of the patient's length of stay and system load is barely possible. The concept of patient (product) and resource visualization in the digital shadow can reduce uncertainty by providing real-time prediction. However, in literature there are barely concept implementations available. This work contributes by proposing a concept for real-time prediction, that is based on process mining and data-driven simulation. The paper describes the imple-mentation of the concept and provides an illustrative case study. Patient and re-source virtualization enhance system control by providing predictive infor-mation, that were not available before. Further, this paper evaluates the feasibil-ity of transferring to an operating emergency department and the required per-formance.

**Keywords:** Digital Shadow, Data-driven Simulation, System Control.

## 1 Introduction

Emergency departments, commonly referred to as EDs, are strategic sectors within the hospital chain. These systems are specialized units and provide immediate medical care to patients with acute illnesses and injuries. Patients arrive at the ED either by walking in or by ambulance, undergo a sequence of tests and treatments (pathways), and eventually leave for home or to the actual hospital for further evaluation and long-term hospitalization. The emergency process is marked by a high degree of uncertainty [1]. The arrivals of patients are unplanned and highly volatile. Patients arrive with a wide range of injuries and diseases that are often unknown to the doctors at the moment of arrival and need to be discovered during the patients' pathway through the ED. Due to inherent uncertainties in patients' arrivals and pathways, controlling ED systems is a challenging task for decision-makers.
New concepts such as the digital shadow, as well as product and resource virtualization, can support system control by simulating physical products in the virtual space [2]. In these concepts, simulation reveals how physical products react to occurring circumstances. However, it is important to highlight that product virtualization in the context of EDs refers to patient virtualization [3]. Patient virtualization can show how existing patients are affected by changed conditions, such as the arrival of new patients. Further, simulation can forecast occurring waiting lines and waiting times. Decision-makers can use the received knowledge to act on the physical system and impact the patients’ journey. Therefore, decision-makers need the ability to predict at each moment the existing patients’ future pathways and occurring situations, while considering the uncertainty given by the arrival patterns and pathways of new patients. This work proposes and evaluates a concept for patient and resource virtualization in EDs, and discusses strategies and requirements for its implementation.

The paper is organized as follows: Section 2 reviews the literature, particularly regarding the extraction of simulation data and data-driven modeling; Section 3 describes the concepts for patient and resource virtualization; Section 4 illustrates the case study and provides the evaluation; and Section 5 gives conclusion and forecast.

## 2 Literature review

Providing the ability to predict is particularly enabled by the emergence of new concepts and technologies such as the digital shadow, process mining and data-driven simulation. An example of using process mining and simulation modeling for the design of an ED is presented in [4]. In these works, the authors extract historical patient data, particularly the patients’ arrivals and pathways, and use these data for simulation modeling. A general methodology for data acquisition and analysis to support system evaluation and simulation is presented in [5], though the authors propose using this methodology for manufacturing systems. Adaptation for the context of emergency systems is presented in Fig. 1 and locates the linked technologies. Differences exist in the tracking of patients’ treatments (activities) in the ED, compared to the flow of physical workpieces on the shopfloor in manufacturing.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Methodology for data acquisition and simulation in ED, based on [5]</figcaption></figure>

When treating patients, doctors and nurses interact with the hospital's information system to retrieve and update patients' information. For each transaction, information ( timestamps ) is populated to a database by an automated data flow, corresponding to
the concept of the digital shadow [6]. The concept of the digital shadow is used to manage all information about the current state and history of the physical object (ED) in a virtual object (data storage). Based on this data storage, process mining enables discovering historical treatments, calculating new measures (KPI), and providing new insights about the ED-process [7]. Extracted knowledge enables ad-hoc evaluations and building of models, particularly when using data-driven simulation [8]. Simulation in dynamic models generates knowledge that is not explicit in the mined patient data. The digital shadow provides raw data, process mining enables the extraction of relevant simulation data, and data-driven simulation enables patient virtualization.

## 2.1 Data analytics

In the presented methodology, the data storage serves the purpose of managing event logs that describe historical events, particularly the beginning and end of treatments. In EDs, each event has a timestamp and information about the associated patients and executing resources [9]. The collected events are used in literature to extract the clinical pathways of treated patients. Augusto et al. in [10] present a method for pathway discovery. The authors use the extracted pathways to build an agent-based model. In a case study, they simulate the patient flows and evaluate consequences when changing the medical decision process. For the purpose of building simulation models from mined patient data, Mogollon et al. in [11] highlight the need to derive arrival patterns (hourly arrival rates), patient pathways (sequences of activities), and activity durations (statistical laws). For deriving these elements, the authors propose a tool to automate the data acquisition for model building of EDs [12]. The proposed methods correspond to those that are regularly used in literature to provide simulation data:

* **Arrival patterns** describe the patient arrivals at the ED. The literature often uses hourly arrival rates to model variations during the timespan of the day, such as in [13], [14], [15]. Alternatively, the inter-arrival-time (IAT) defines the time between arrival of two patients. To model variation in arrival rates and IAT, the literature regularly uses stochastic laws on the rates and IAT, as in [16].

* **Patient pathways** define for each patient the sequence of treatments. The literature regularly uses a Markov process for providing stochastic pathways [17], [18], [19]. When applying a Markov process, for each treatment in a patient's pathway, the succeeding activity is defined by the probabilities of a transition matrix.

* **Treatment durations** define the amount of time that is required to finish a treatment in a patient's pathway. Analysis of historical data shows that similar treatments can have different durations. Thus, durations are modeled by stochastic laws. The literature uses distribution fitting to identify these laws [13], [15], [20].

Using these methods, the authors extract new information and knowledge. New information can be used to evaluate the system performance directly via the calculation of KPIs, such as waiting times and length of stay. Beyond new knowledge, particularly the arrival patterns, patient pathways, and treatment durations serve as input for simulation and define the structure of the simulation model.
## 2.2 Simulation modeling

In Fig 1, simulation modeling corresponds to two activities: evaluation and simulation. When evaluating, the literature tries to exploit knowledge directly in order to better understand the system. An example is given in [21], where the authors use knowledge to directly analyze the patient pathways via extracted transition matrices and provide new metrics that were not available before. When using simulation, the literature uses the extracted knowledge to model the system and get a better understanding by executing simulation experiments [22]. Particularly in the context of manufacturing literature, many authors provide methods for simulation modeling from data [23], [24], [25]. When setting up simulation models from data, the literature uses predefined libraries with reusable classes of generic system behavior. Predefined classes provide the generic behavior of products (patient), resources (doctors, nurses) and processes (treatments). For setting up models, an algorithm instantiates objects from predefined classes, according to the simulation data. Implementing such an algorithm enables building models and running experiments on request and is an enabler for providing simulation as a service [26] for real-time simulation and prediction.

## 2.3 Discussion

This analyzed literature tackles the challenges in product and resource virtualization through the concepts of the digital shadow (data acquisition), process mining (data analytics) and data-driven simulation (simulation modeling). Data acquisition and data analytics provide relevant simulation data and data-driven simulation generates valid simulation models. Simulation enables decision-makers to predict the future of the virtualized patients and resources. However, in this process, a gap spans across data analytics and simulation modeling, in line with [27], [28]:

* **Simulation Modeling:** The presented methods enable modelers to build a general model of the system and its behavior. However, generated models are in an initial state where the ED is empty, beds are not occupied, and doctors and nurses are idle. For patient and resource virtualization, the initial state of the digital model should correspond to the physical system; therefore, model initialization is needed.

* **Data Analytics:** Regarding the problem of initialization, the bottleneck does not only exist in providing an initialized model. Before modeling, it is necessary to extract relevant simulation data that describes the initial state. In the literature there is neither a definition of the required data nor the required methods available.

This paper addresses two challenges. The first challenge is to **provide a concept for patient and resource virtualization**, enabling the prediction of patient journeys and resources waiting lines in real-time. This concept requires receiving data from the hospital's information system through the digital shadow, extracting relevant simulation data, building simulation models, and running experiments in real-time. These activities require time and performance for execution. Furthermore, the problem gets exacerbated when multiple simulation experiments are required to provide robust predictions. The requirements regarding the dimensions of time and performance are
not yet clear and need to be explored. Therefore, the second challenge is to evaluate
**the required time and performance for real-time prediction**, based on patient and
resource virtualization. For concept and performance evaluation, this paper aims to
provide the implementation and validation of the concept in an illustrative case study.

3 Concept proposal

For providing real-time prediction, we propose a procedure that sets up models and
runs simulation experiments upon reception of updates from the physical system. The
digital shadow instantly mirrors events in the physical system to the virtual system via
an automated data-flow. Changes in the patients' conditions, such as the degradation
of their health, are implicit in these data. Process mining and data-driven simulation
transfer this information in the simulation model. Since changes in the patients' con-
ditions are implicitly modeled. Simulation predicts the patients' journeys, based on
the most recent situation of the ED. The procedure is illustrated in **Fig. 2**.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Procedure for providing prediction on system change</figcaption></figure>

The procedure is regularly triggered by events in the physical system, such as the
arrival/departure of patients and the beginning/end of treatments. The procedure starts
with extending the database by the new event. An algorithm extracts the stochastic
patient model (hourly arrival rates, patient pathways, treatment durations) and the
initial situation (current patients) from the database. In a loop, the algorithm runs
stochastic simulation experiments to predict future scenarios. Therefore, the algorithm
first generates simulation data from the initial situation and the patient model, and
then builds and executes a simulation model based on the simulation data. An algo-
rithm uses the simulation results of the stochastic scenarios and calculates an average
prediction. The prediction describes the most likely future scenario for the moment
when the event that initially triggered this procedure arrived in the database.

The following subsections detail the steps and implementation of the procedure:
Section 3.1 explains the extraction of the patient model from the event log; Section
3.2 covers the extraction of the moment-specific initial situation and experiment-
specific simulation data; and Section 3.3 describes the generation of the model and
simulation of experiments from the simulation data. Additionally, the concept of the
model is presented in detail [29] and was implemented using the simulator AnyLogic.

**3.1 Extract patient arrivals and pathways**

We assume all data about the beginning and end of treatments are available in an
event log within the hospital's information system. **Fig. 3** provides on the left an ex-
emplary historical schedule of a set of virtual patients. Multiple activities enable ex-
tracting simulation data: Calculation of the IAT provides the arrival pattern (historical
arrivals); mapping of events provides the corresponding treatments and their dura-
tions; removal of the waiting times provides the sequence of treatments each patient
underwent (historical pathways and durations); extraction of Emergency Severity
Index (ESI) provides the patients' severity index. **Fig. 3** shows the output on the right.

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Exemplary patient journeys and extraction of historic simulation data</figcaption></figure>

In the illustrative case, the diagram ends 860 minutes after observation start (red line) and reveals the current situation in the physical system. Due to the end of the records, no information is available about future patient arrivals, treatments, and their durations for patients who are already in the ED, as well as the required time to finish treatments that have already started. The table illustrates the extracted patient arrivals, pathways and treatment durations, a grey background identifies available knowledge about ED history. The red lines in the diagram and table illustrate the limits of the available information. In the example, we consider all patients up to patient 82 (P82) as finished (left the ED) and remaining patients as unfinished (are in the ED). The structure of the table and data up to P82 can serve as input for data-driven modeling.

**3.2 Extracting initial state data and predicting future scenarios**

Additional activities are needed to get initial state and future situation. A general,
stochastic patient model is required and defined by the patient arrivals, their pathways
and corresponding treatment durations. The model is to be derived from the finished
patients. For defining the patient arrivals, for each severity level the hourly arrival
rates are extracted. The arrival rates describe the arrival patterns for clusters of pa-
tients (1-5), based on their severity index and the time of their arrival, using a stochas-
tic law. For defining the patient pathways, transition matrices (from-to matrix) are
derived from the patients' sequences of treatment, describing the probabilities of tran-
sitioning from one treatment to another, for each severity level in the patient popula-
tion. For defining the treatment durations, for each type of treatment such as registra-
tion or seeing a doctor, the durations are analyzed. Distribution fitting provides a den-
sity function giving the likelihood of a particular duration for a treatment to occur.

The patient arrival, patient pathways and treatment durations define a general, sto-
chastic model of the patient population. However, they do not provide information
about the initial state of the system. The initial state describes the initial situation in the physical system for each simulation experiment to be executed. Each situation is defined by the number and type (ESI) of patients that are already in the system as well as their location (bed) and the progress of their journey. Consequently, this information, through the assignment to resources, also defines the initial state of the doctors and nurses involved in the treatments. The initial state is given by the unfinished patients (IAT and ESI) as well as the finished and unfinished activities of their pathways. The data correspond to the data illustrated in **Fig. 3** above the red line.

Data-driven simulation requires datasets that describe the particular simulation experiments for each situation in the physical system. The initial state describes patients that are already in the system and patient model describes the general behavior of future patients. New datasets (right) describing particular situations are generated from initial state (left), as illustrated in **Fig. 4**. The initial state is derived from historic data by removing patients that are already finished and left the ED in the moment of simulation. The future situation is derived from the stochastic patient model for a predefined duration, such as one hour. For the predefined duration, new patient arrivals are scheduled by applying the hourly arrival rates. Each arriving patient begins with the registration activity. For each patient, starting from the last available activity, the transition matrix is applied to predict the future treatments. For treatments that were not finished within the historical data, the fitted distributions are used to derive the remaining treatment durations. This procedure creates a dataset with new arrivals and pathways of future patients in virtual scenarios (right). For ensuring stochastic correctness of the predictions, the process is repeated to generate multiple scenarios.

<table><thead><tr><th>ID</th><th>IAT</th><th>ESI</th><th>Step 1</th><th>Step 2</th><th>Step 3</th><th>Step 4</th><th>Step</th></tr></thead><tbody><tr><td>83</td><td>20</td><td>4</td><td>reg(8)</td><td></td><td></td><td></td><td></td></tr><tr><td>84</td><td>7</td><td>5</td><td>reg(8)</td><td></td><td></td><td></td><td></td></tr><tr><td>85</td><td>16</td><td>4</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>86</td><td>10</td><td>5</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>87</td><td>10</td><td>4</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>...</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Generate Variant

<table><caption>**Fig. 4.** Generation of datasets for predictive scenarios</caption><thead><tr><th>ID</th><th>IAT</th><th>ESI</th><th>Step 1</th><th>Step 2</th><th>Step 3</th><th>Step 4</th><th>Step</th></tr></thead><tbody><tr><td>83</td><td>20</td><td>4</td><td>reg(8)</td><td>doc(13)</td><td></td><td></td><td></td></tr><tr><td>84</td><td>7</td><td>5</td><td>reg(8)</td><td>test(10)</td><td>doc(6)</td><td></td><td></td></tr><tr><td>85</td><td>16</td><td>4</td><td>reg(6)</td><td>doc(12)</td><td></td><td></td><td></td></tr><tr><td>86</td><td>10</td><td>5</td><td>reg(8)</td><td>test(13)</td><td>doc(7)</td><td>test(10)</td><td>doc(22)</td></tr><tr><td>87</td><td>10</td><td>4</td><td>reg(13)</td><td>test(15)</td><td>doc(9)</td><td></td><td></td></tr><tr><td>...</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

## 3.3 Data-driven modeling and simulation

Data-driven modeling builds a model from provided datasets and runs simulation experiments. The general process, models, and algorithms for data-driven modeling in discrete-event simulation (DES) is provided in [29] since a further elaboration is not provided in this paper. Data-driven modeling provides an initialized model of the ED, and simulation provides the waiting lines and patients' lengths of stay for the stochastic scenarios in a dynamic environment. **Fig. 5** provides an exemplary illustration of simulated waiting times and patients' lengths of stays of one future scenario. However, these outputs provide just one possible future scenario for a single initial situation in the ED's lifecycle; they are not sufficient for evaluation. Hence, model building and simulation is repeated by the algorithm to simulate each stochastic scenario. For each moment of the prediction time, an algorithm calculates the average length of waiting lines within the set of stochastic scenarios from the simulation data.
<figure><img src="image_5.png" /><figcaption>Fig. 5. Illustrative prediction of waiting times in predictive scenarios</figcaption></figure>

# 4 Concept evaluation

The concept was implemented in a virtual environment, based on the patient data of the Saint-Étienne University Hospital. The pediatric department provided a dataset with information about 1161 patients that were treated in the ED between 01.01.2024 and 15.01.2024. For the case study, a timeframe of one hour from 08.01.2024 at 15:00 was chosen. This hour represents a typical peak system load scenario. During this time, 20 simulation experiments were generated following each occurring event to predict the next hour. To derive the stochastic patient model, data from the previous 7 days was used to effectively represent the current patient population. Based on the case study, the feasibility and added value for system control was evaluated.

## 4.1 Evaluation of feasibility and value in control

The implementation provides predictions for each situation occurring in the ED, defined by a certain initial state, for the next hour. These predictions enable the recognition of upcoming bottlenecks and allow for system adjustments. For illustration, **Fig. 6** shows the length of the waiting lines over a two-hour span, starting from 15:00 on 08.01.2024. Specifically, the illustration displays the actual waiting lines (black), the predicted waiting lines from 15:41 to 16:00 (blue) and the standard deviation. The prediction indicates a peak at 15:50, followed by a reduction in queue lengths. This prediction was then compared with the actual evolution of the waiting lines in the physical system. The deviation increases with increasing forecast time.

<figure><img src="image_6.png" /><figcaption>Fig. 6. Prediction for one hour at 08.01.2024 at 15:41</figcaption></figure>
For the chosen time of the case study, a linear trend was calculated for the 68 situations (initial states) that occurred. The predicted trend (positive/negative) was correct for 62 situations, which provides a positive ratio of about 91% for this hour. However, there are limitations to be discussed: The linear trend is an imprecise measure to predict and evaluate the variety of future scenarios. It is still unclear how to evaluate the variety of experiments (1360 experiments) that occurred in 68 situations, with 20 stochastic variants per situation, using condensed measures. While the global trend generally provided a good prediction of the increase and decrease of waiting lines, the evaluation of the slope and position of individual trends at each moment was often imprecise. More work is needed to improve the quality of prediction.

The stochastic nature of the prediction brings additional discussion points. The prediction represents an average future scenario, based on the patient model of the previous seven days, but the actual system behavior may not align with the average day, rendering the prediction inaccurate. Furthermore, hourly arrival rates were not able to predict the intra-hourly patient arrivals that were unequally distributed. In the case, low arrival rates were observed from minutes 0 to 30 and 90 to 120, with high rates occurring from 30 to 90. However, these rates did not align with hourly patterns from 0 to 60 and 61 to 120, resulting in inaccuracies when comparing waiting lines.

To improve predictions, two strategies were identified: increasing the precision of patient models and developing them in real-time. For increasing the precision of the stochastic patient model, hourly arrival rates could be replaced by intra-hourly arrival rates (e.g., quarter-hourly) and transition matrices could be provided for more granular patient clusters (e.g., ESI and IAT). However, increasing precision of stochastic models increases the size of the required data. When increasing the granularity without increasing the amount of data, the sampled patient models will approach reality until they finally reproduce the actual population without uncertainty. For developing a stochastic patient model in real-time, the patient model could be extracted from the previous hour instead of the previous seven days. However, this reduces the amount of data and may hinder the creation of stochastically relevant patient models. Depending on historical events, both strategies can be problematic. For example, during a terrorist attack, using data from the previous seven days does not predict the increased system load due to the attack, and after the attack, using data from the previous hour does not predict the decrease in system load as the system relaxes. The crucial challenge is to identify these dependencies in the patient model in real-time.

## 4.2 Evaluation of performance

During simulation, the time for experimentation was measured to evaluate the performance and discuss requirements for implementation. During the observation phase, 68 different situations occurred, with uneven distribution. Intervals between situations and new simulation experiments ranged from a minimum of 14 seconds to a maximum of 247 seconds, with the risk of extreme values. The time for simulation of 20 experiments was measured individually for providing simulation data and data-driven simulation. Generating simulation data for one situation (20 experiments) takes about 4 seconds (0.20 seconds per experiment), and data-driven simulation takes around 5
seconds (0.25 seconds per experiment). This leads to a delay of approximately 9 seconds for providing predictions after a new situation occurs in the physical system. The time to extract the stochastic patient model strongly depends on the size of the historical data, as we propose to derive it only at given intervals, such as hourly or daily, to reduce delay. We conclude that real-time prediction based on this concept is not possible. Assuming 20 experiments are executed, there is a delay of 9 seconds.

In this concept, data analysis was done in a Python environment, simulation was performed in DES software, and Excel files were used as an interface. Employing alternative interfaces, such as CSV files, establishing direct communication between data science and simulation, or integrating both into a unified environment, might reduce the delay. Further, simulation experiments were executed sequentially; distributed simulation might help to reduce the delay as well. As a result, a real-time prediction in terms of 'instantly' was not achieved. However, the concept allows predictions with a short delay after a change in the physical system. In the authors' opinion, additional predictions between occurring states in the physical system bring no added value, since the initial situation and patient model remain unchanged.

# 5 Conclusion and future works

This paper provided a concept for the implementation of a digital shadow for prediction in system control. The purpose of this paper was to evaluate the feasibility and added value in system control, as well as the requirements for system performance. Experimentation provided acceptable results in the context of performance. Therefore, the next objectives are the implementation in a physical system that can provide larger datasets and enable the monitoring of actual operations over an extended period. For implementation, it is recommended to separate the extraction of stochastic models, which could be done on a daily basis, from the generation of simulation data and data-driven simulation, which should be done for each situation. This strategy, along with direct interfaces and distributed simulation, can provide predictions that are close to real-time. However, to provide reliable predictions, there is a need to test alternative methods for creating simulation data.

In the case study, patient and resource virtualization were used to predict the current patients' lengths of stay and the evolution of resources' waiting lines. When implemented, both concepts enable decision-makers to control the ED by recognizing critical situations before they actually occur. However, due to uncertainties, the virtualization of individual patients was experienced as imprecise, while the virtualization of waiting lines (a set of patients) provided an average and seemed to be more trustworthy. Additionally, the large number of experiments, which includes both stochastic variants and numerous initial situations, generates substantial amounts of data. More research is needed to identify the appropriate measures that will help decision-makers draw accurate conclusions. The quality of the predictions and the added value of new measures are to be evaluated in large-scale case studies.

**Acknowledgments:** This work is part of the JUNEAU project, funded by ANR (Agence Nationale de la Recherche – France) under grant ANR-22-CE46-0010-01.
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