## 2 Materials and Methods
### Data Collection in the Case Study  
We collected data and information in a single pilot case study of the specific operating conditions of an ES that was allocated in a hospital in order to verify the analysis. The location of the case study was the adult emergency department (AED) of a university hospital, which was built from 1969 to 1978 and inaugurated in 1981. The hospital has six floors and a gross built area of 36,000.00 m\({}^{2}\), 874.88 m\({}^{2}\) of which are AED-occupied. Access to documents, interviews, and technical visits was possible due to the academic cooperation agreement. This allowed the systematization and analysis of unpublished information about the building and its activities and functions. In the data collection process, we considered ESs and support activities for emergency services. In this way, the scope of the survey covered the activities that were conducted on three floors of the hospital.  
\begin{table}
\begin{tabular}{c c} \hline
**No** & **Processes/Activities** \\ \hline
1 & when an actor circulates in the environment \(j\) to perform the activity \(i\) \\ \hline
2 & when an intermediary activity \(i\) occurs in the environment \(j\) \\ \hline
3 & when the end activity \(i\) occurs in the environment \(j\) \\ \hline \end{tabular}
\end{table}
Table 1: Types of relationships for an activity carried out in an environment.  
\begin{table}
\begin{tabular}{c c} \hline
**N\({}^{\mathbf{o}}\)** & **Comparative Relationship** \\ \hline
1 & \(i\) and \(j\) relationship not predicted or detected \\ \hline
2 & \(i\) and \(j\) relationship predicted and unconfirmed \\ \hline
3 & \(i\) and \(j\) relationship predicted and confirmed \\ \hline \end{tabular}
\end{table}
Table 2: The analyzed congruence conditions.  
Activity Flow and Allocation Mapping  
The environment-functional analysis was carried out by studying the flow of activity and its relationship with the built floors to determine the physical footprint of the departments linked to the ESs [1; 20]. The information about the activities was obtained through semi-structured interviews, which were conducted between October 2021 and June 2022, with 13 key healthcare professionals who were highly engaged in healthcare processes (Table 3). The respondents were selected because they occupied management and operational roles. Thus, it was possible to obtain a strategic and practical understanding of the services provided and the relationships between activities. The identification of interviewees was achieved by consulting the board and examining information such as professional training, time in the office, and employee recognition.  
In the semi-structured interviews, the interviewers used a script to address the interviewees. The interviewers could elaborate on the questions based on this script as they obtained responses [58]. The interview dynamic consisted of asking the interviewed healthcare workers to describe the following three aspects of the work for which they were responsible: (a) the routine sequence of activities, (b) the occurrences of interactions with other workers' roles and activities, and (c) the allocation of activities in the floor space, differentiating between whether each activity was a middle or an end activity. The support material consisted of an interview script (S1), a spreadsheet to write down the activities, and floorplans to locate the activities and trace routes (Figure 1). Audio of the face-to-face interviews and the videos of the remote interviews were recorded with the prior authorization of the individual participants.  
Additional information was included subsequently, through observation of the interview records. For example, the relationships between each activity and the people/departmental functions involved were detailed.