Optimal deployment of automated external defibrillators in a long and narrow environment

PLOS ONE RESEARCH ARTICLE Optimal deployment of automated external defibrillators in a long and narrow environment Chih-Hao Lin1, Kuan-Chao Chu2, Jung-Ting Lee ID3*, Chung-Yao Kao4 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 1 Department of Emergency Medicine, College of Medicine, National Cheng Kung University Hospital, National Cheng Kung University, Tainan, Taiwan, 2 Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan, 3 School of Medicine, College of Medicine, National Sun Yat-Sen University, Kaohsiung, Taiwan, 4 Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan * Abstract OPEN ACCESS Citation: Lin C-H, Chu K-C, Lee J-T, Kao C-Y (2023) Optimal deployment of automated external defibrillators in a long and narrow environment. PLoS ONE 18(2): e0264098. https://doi.org/ 10.1371/journal.pone.0264098 Editor: Billy Morara Tsima, University of Botswana School of Medicine, BOTSWANA Received: January 29, 2022 Accepted: January 4, 2023 Published: February 14, 2023 Copyright: © 2023 Lin et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: The results described in this paper were obtained by mathematical analysis on a proposed model and verified by numerical computations using the C++ programming. The compilable source codes of the C++ program are uploaded as supporting information. All other relevant information is within the manuscript. Funding: This study was funded by the Taiwan Ministry of Science and Technology (Grant numbers: C.-H. Lin: MOST 105-2314-B-006-069, C.-H. Lin: MOST 106-2314-B-006-003, C.-H. Lin: Aim of the study Public access to automated external defibrillators (AEDs) plays a key role in increasing survival outcomes for patients with out-of-hospital cardiac arrest. Based on the concept of maximizing “rescue benefit” of AEDs, we aimed to propose a systematic methodology for optimizing the deployment of AEDs, and develop such strategies for long and narrow spaces. Methods We classified the effective coverage of an AED in hot, warm, and cold zones. The AEDs were categorized, according to their accessibility, as fixed, summonable, or patrolling types. The overall rescue benefit of the AEDs were evaluated by the weighted size of their collective hot zones. The optimal strategies for the deployment of AEDs were derived mathematically and numerically verified by computer programs. Results To maximize the overall rescue benefit of the AEDs, the AEDs should avoid overlapping with each other’s coverage as much as possible. Specific rules for optimally deploying one, two, or multiple AEDs, and various types of AEDs are summarized and presented. Conclusion A methodology for assessing the rescue benefit of deployed AEDs was proposed, and deployment strategies for maximizing the rescue benefit of AEDs along a long, narrow, corridor-like, finite space were derived. The strategies are simple and readily implementable. Our methodology can be easily generalized to search for optimal deployment of AEDs in planar areas or three-dimensional spaces. PLOS ONE | https://doi.org/10.1371/journal.pone.0264098 February 14, 2023 1 / 12 PLOS ONE MOST 107-2314-B-006-003, and C.-Y. Kao: MOST 109-2221-E-110-031) and National Cheng Kung University Hospital of Taiwan (Grant numbers: C.H. Lin: NCKUH-11203003). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Optimal deployment of automated external defibrillators in a long and narrow environment Introduction Sudden cardiac arrest is a major public health issue worldwide [1,2] and accounts for up to 20% of deaths in Western societies [3,4]. Out-of-hospital cardiac arrest (OHCA) describes an event of cardiac arrest before the patient is transferred to a hospital; that is, the cardiac arrest could occur in the field, in the community, at the patient’s home or workplace [5,6]. The first and second most common locations for an OHCA were at a residence and in public, respectively [7]. OHCAs are witnessed by a layperson in 37% of cases and by an emergency medical services (EMS) provider in only 12% of cases [7]. The survival rate after an OHCA is very low; at least 90% to 95% of these individuals do not survive despite resuscitation attempts [8]. Evidence indicates that when the OHCA is caused by ventricular tachycardia or fibrillation, defibrillation is an effective treatment [9]; however, its effectiveness diminishes with each passing minute [5,10]. Public access to automated external defibrillators (AEDs) plays a key role in increasing the survival of patients with OHCA who have a shockable cardiac rhythm [11–13]. Although AEDs are widespread, OHCAs defibrillated by bystanders before EMS arrival remains low, only approximately 2–4% [14]. Therefore, to achieve the maximum benefit of public AEDs, careful evaluation of AED locations is required. While mathematical optimization has been used for assessing optimal locations for the AED deployment [15–19], most of these studies focus on numerical analysis/simulation of retrospective data. To our knowledge, few studies, if any, had taken an analytical approach to derive generalizable rules or strategies for the optimal AED deployment. In this study, we aimed to explore such strategies for a finite one-dimensional space, which is a suitable model for long corridor-like areas, such as trains, platforms in a train station, long tunnels, etc. By simplified yet reasonable assumptions, we derived simple rules for the optimal AED deployment that would maximize AED accessibility within a specified time frame. Methods A location where an AED is placed is deemed "optimal" if the AED can be accessed within a specific time when OHCA occurs. Two essential factors need to be considered for assessing optimal AED deployment: time to acquire the AED and the probability of occurrence of OHCAs. The first factor leads to the notion of effective AED coverage. Effective coverage of an AED The sooner an AED is applied, the higher the survival chance of the OHCA [5,10]. According to timeliness of AED availability, the areas surrounding the AED are differentiated into three zones: hot, cold, and warm. • Hot Zone: This is a region where an AED can be acquired to provide the best survival chance. According to the American Heart Association’s suggestion, the AED needs to be applied to patients with OHCA within one minute [7]. An OHCA event is said to be within the effective coverage of an AED if it occurs within the hot zone of the AED. • Cold Zone: This is a region where it takes longer time to obtain an AED than waiting for the EMS to arrive. An (...truncated)