# Spatiotemporal Optimization for the Placement of Automated External Defibrillators Using Mobile Phone Data

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## Abstract

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## 1. Introduction

## 2. Overlayed Spatio-Temporal Optimization Method

#### 2.1. Optimizing AED Placement by Hour

- h = denotes each hour;
- H = denotes the set of 24 h 1, …, h…, 24;
- i = denotes each POI site;
- ${I}_{h}$ = denotes the set of POI sites for each hour;
- j = denotes each AED candidate site;
- J = denotes the set of AED candidate sites;
- ${a}_{i}$ = the number of visitors to be served at POI site i;
- k = the number of AEDs to be located;
- ${d}_{ij}$ = the shortest distance from site i to site j;
- S = the distance beyond which a POI site is considered uncovered;
- $N}_{i}=\{j\in J|{d}_{ij}\u2a7dS\$, denotes the set of AED candidate sites that can cover visitors in the POI site I;
- ${Z}_{h}$ = denotes the number of covered POI visitors;
- $\begin{array}{cc}{x}_{j}=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{an}AED\mathrm{is}\mathrm{allocated}\mathrm{to}\mathrm{site}j\hfill \\ 0\hfill & \mathrm{else}\hfill \end{array}\right.\hfill & \\ {y}_{i}=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{one}\mathrm{or}\mathrm{more}\mathrm{AED}\mathrm{candidate}\mathrm{sites}\mathrm{are}\mathrm{established}\mathrm{at}\mathrm{sites}\mathrm{in}\mathrm{the}\mathrm{set}{N}_{i}\hfill \\ 0\hfill & \mathrm{else}\hfill \end{array}\right..\hfill & \\ & & \end{array}$

#### 2.2. Identifying the Final Solution of Optimized AEDs

- ${h}^{\prime}$ = also denotes each hour, used for distinguishing itself from h;
- H = denotes the set of 24 h 1, …, h…, 24;
- i = denotes each POI site;
- ${I}_{h}$ = denotes the set of POI sites for each hour;
- ${j}^{\prime}$ = denotes each optimized AED;
- ${J}_{{h}^{\prime}}^{\prime}$ = denotes the set of optimized AEDs for each hour;
- $Min({d}_{{J}_{{h}^{\prime}}^{\prime}i})$ = denotes the minimum distance between each site in the set of optimized AEDs and a POI site;
- S = the distance beyond which a POI site is considered uncovered;
- ${O}_{i}$ = denotes whether a POI site i is covered by a set of optimized AEDs;
- ${a}_{i}$ = the number of visitors to be served at POI site i;
- ${R}_{{J}_{{h}^{\prime}}^{\prime}{I}_{h}}$ = denotes the optimized AED coverage rate for each hour ${h}^{\prime}$;
- ${N}_{{J}_{{h}^{\prime}}^{\prime}}$ = denotes the average performance of each hour’ s set of optimized AEDs.

#### 2.3. Cost-Coverage Increment Analysis

## 3. Application in Washington DC

#### 3.1. Data Source and Preprocessing

#### 3.1.1. POI Visit Data

#### 3.1.2. Existing AEDs and AED Candidate Sites

#### 3.1.3. Hospital and Residential Data

#### 3.2. Analysis

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^{®}CPU E5-1650 6 cores 3.78-GHz processor and 128 GB of RAM.

#### 3.3. Results

#### 3.3.1. Applying the OSTO in Washington DC

#### 3.3.2. Relocating Existing AEDs in Washington DC

#### 3.3.3. Cost–Coverage Increment Curve

## 4. Discussion

#### 4.1. Comparison of Current Planning and Optimized Planning of AEDs

#### 4.2. Designing an Inclusive Strategy Considering Potential OHCA Distributions across All Space–Time Ranges

#### 4.3. Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Myat, A.; Song, K.J.; Rea, T. Out-of-hospital cardiac arrest: Current concepts. Lancet
**2018**, 391, 970–979. [Google Scholar] [CrossRef] [PubMed] - American Heart Association. Highlights of the 2020 American Heart Association’s Guidelines for CPR and ECC. Available online: https://cpr.heart.org/-/media/cpr-files/cpr-guidelines-files/highlights/hghlghts_2020_ecc_guidelines_english.pdf (accessed on 10 October 2022).
- Berger, S. Survival from out-of-hospital cardiac arrest: Are we beginning to see progress? J. Am. Heart Assoc.
**2017**, 6, e007469. [Google Scholar] [CrossRef] - Valenzuela, T.D.; Roe, D.J.; Cretin, S.; Spaite, D.W.; Larsen, M.P. Estimating effectiveness of cardiac arrest interventions: A logistic regression survival model. Circulation
**1997**, 96, 3308–3313. [Google Scholar] [CrossRef] [PubMed][Green Version] - Aufderheide, T.; Hazinski, M.F.; Nichol, G.; Steffens, S.S.; Buroker, A.; McCune, R.; Stapleton, E.; Nadkarni, V.; Potts, J.; Ramirez, R.R.; et al. Community lay rescuer automated external defibrillation programs: Key state legislative components and implementation strategies: A summary of a decade of experience for healthcare providers, policymakers, legislators, employers, and community leaders from the American Heart Association Emergency Cardiovascular Care Committee, Council on Clinical Cardiology, and Office of State Advocacy. Circulation
**2006**, 113, 1260–1270. [Google Scholar] [PubMed][Green Version] - Hazinski, M.F.; Idris, A.H.; Kerber, R.E.; Epstein, A.; Atkins, D.; Tang, W.; Lurie, K. Lay rescuer automated external defibrillator (“public access defibrillation”) programs: Lessons learned from an international multicenter trial: Advisory statement from the American Heart Association Emergency Cardiovascular Committee; the Council on Cardiopulmonary, Perioperative, and Critical Care; and the Council on Clinical Cardiology. Circulation
**2005**, 111, 3336–3340. [Google Scholar] - Public Access Defibrillation Trial Investigators. Public-access defibrillation and survival after out-of-hospital cardiac arrest. N. Engl. J. Med.
**2004**, 351, 637–646. [Google Scholar] [CrossRef][Green Version] - Gundry, J.W.; Comess, K.A.; DeRook, F.A.; Jorgenson, D.; Bardy, G.H. Comparison of naive sixth-grade children with trained professionals in the use of an automated external defibrillator. Circulation
**1999**, 100, 1703–1707. [Google Scholar] [CrossRef][Green Version] - Lee, J.H.; Lee, D.E.; Ryoo, H.W.; Moon, S.; Cho, J.W.; Kim, Y.J.; Kim, J.K.; Kim, J.H.; Lee, K.W.; Jin, S.c.; et al. Public awareness and willingness to use automated external defibrillators in a metropolitan city. Clin. Exp. Emerg. Med.
**2021**, 8, 1. [Google Scholar] [CrossRef] - Merchant, R.M.; Asch, D.A. Can you find an automated external defibrillator if a life depends on it? Circ. Cardiovasc. Qual. Outcomes
**2012**, 5, 241–243. [Google Scholar] [CrossRef][Green Version] - Ho, C.; Lui, C.; Tsui, K.; Kam, C. Investigation of availability and accessibility of community automated external defibrillators in a territory in Hong Kong. Hong Kong Med. J.
**2014**, 20, 371–378. [Google Scholar] [CrossRef] - Karlsson, L.; Hansen, C.M.; Wissenberg, M.; Hansen, S.M.; Lippert, F.K.; Rajan, S.; Kragholm, K.; Møller, S.G.; Søndergaard, K.B.; Gislason, G.H.; et al. Automated external defibrillator accessibility is crucial for bystander defibrillation and survival: A registry-based study. Resuscitation
**2019**, 136, 30–37. [Google Scholar] [CrossRef][Green Version] - Kwon, P.; Lee, Y.; Yu, K.; Lee, W.H. A Study of optimal location and allocation to improve accessibility of automated external defibrillator. J. Korean Soc. Surv. Geod. Photogramm. Cartogr.
**2016**, 34, 263–271. [Google Scholar] [CrossRef][Green Version] - American Heart Association. Part 7: Systems of Care. Available online: https://cpr.heart.org/en/resuscitation-science/cpr-and-ecc-guidelines/systems-of-care (accessed on 10 October 2022).
- Chan, T.C.; Li, H.; Lebovic, G.; Tang, S.K.; Chan, J.Y.; Cheng, H.C.; Morrison, L.J.; Brooks, S.C. Identifying locations for public access defibrillators using mathematical optimization. Circulation
**2013**, 127, 1801–1809. [Google Scholar] [CrossRef][Green Version] - Claesson, A.; Bäckman, A.; Ringh, M.; Svensson, L.; Nordberg, P.; Djärv, T.; Hollenberg, J. Time to delivery of an automated external defibrillator using a drone for simulated out-of-hospital cardiac arrests vs. emergency medical services. JAMA
**2017**, 317, 2332–2334. [Google Scholar] [CrossRef] - Leung, K.B.; Brooks, S.C.; Clegg, G.R.; Chan, T.C. Socioeconomically equitable public defibrillator placement using mathematical optimization. Resuscitation
**2021**, 166, 14–20. [Google Scholar] [CrossRef] [PubMed] - Cardiac Arrest Registry to Enhance Survival. Measuring Outcomes. Improving Care. Saving Lives. Cardiac Arrest Registry to Enhance Survival. Available online: https://mycares.net/ (accessed on 10 October 2022).
- Washington DC Fire and EMS Department. Utstein Survival Report. FY 2019 FEMS Utstein Report. Available online: https://fems.dc.gov/ (accessed on 10 October 2022).
- SafeGraph. Places Data Curated for Accurate Geospatial Analytics. Available online: https://www.safegraph.com/ (accessed on 10 October 2022).
- North American Industry Classification System. Introduction to NAICS. Available online: https://www.census.gov/naics/ (accessed on 10 October 2022).
- Becker, L.; Eisenberg, M.; Fahrenbruch, C.; Cobb, L. Public locations of cardiac arrest: Implications for public access defibrillation. Circulation
**1998**, 97, 2106–2109. [Google Scholar] [CrossRef][Green Version] - Fedoruk, J.; Currie, W.L.; Gobet, M. Locations of cardiac arrest: Affirmation for community Public Access Defibrillation (PAD) Program. Prehospital Disaster Med.
**2002**, 17, 202–205. [Google Scholar] [CrossRef] - Fredman, D.; Haas, J.; Ban, Y.; Jonsson, M.; Svensson, L.; Djarv, T.; Hollenberg, J.; Nordberg, P.; Ringh, M.; Claesson, A. Use of a geographic information system to identify differences in automated external defibrillator installation in urban areas with similar incidence of public out-of-hospital cardiac arrest: A retrospective registry-based study. BMJ Open
**2017**, 7, e014801. [Google Scholar] [CrossRef][Green Version] - Chan, T.C.; Demirtas, D.; Kwon, R.H. Optimizing the deployment of public access defibrillators. Manag. Sci.
**2016**, 62, 3617–3635. [Google Scholar] [CrossRef][Green Version] - Sun, C.L.; Karlsson, L.; Morrison, L.J.; Brooks, S.C.; Folke, F.; Chan, T.C. Effect of Optimized Versus Guidelines-Based Automated External Defibrillator Placement on Out-of-Hospital Cardiac Arrest Coverage: An In Silico Trial. J. Am. Heart Assoc.
**2020**, 9, e016701. [Google Scholar] [CrossRef] - Boutilier, J.J.; Brooks, S.C.; Janmohamed, A.; Byers, A.; Buick, J.E.; Zhan, C.; Schoellig, A.P.; Cheskes, S.; Morrison, L.J.; Chan, T.C. Optimizing a drone network to deliver automated external defibrillators. Circulation
**2017**, 135, 2454–2465. [Google Scholar] [CrossRef] - Bagai, A.; McNally, B.F.; Al-Khatib, S.M.; Myers, J.B.; Kim, S.; Karlsson, L.; Torp-Pedersen, C.; Wissenberg, M.; van Diepen, S.; Fosbol, E.L.; et al. Temporal differences in out-of-hospital cardiac arrest incidence and survival. Circulation
**2013**, 128, 2595–2602. [Google Scholar] [CrossRef] [PubMed][Green Version] - Brooks, S.C.; Schmicker, R.H.; Rea, T.D.; Aufderheide, T.P.; Davis, D.P.; Morrison, L.J.; Sahni, R.; Sears, G.K.; Griffiths, D.E.; Sopko, G.; et al. Out-of-hospital cardiac arrest frequency and survival: Evidence for temporal variability. Resuscitation
**2010**, 81, 175–181. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gurobi Optimization. Introducing Gurobi 10.0. Available online: https://www.gurobi.com/ (accessed on 10 October 2022).
- Church, R.; ReVelle, C. The maximal covering location problem. Pap. Reg. Sci. Assoc.
**1974**, 32.1, 101–118. [Google Scholar] [CrossRef] - Open Data DC. Engage with the District through Government Open Data. Available online: https://opendata.dc.gov/ (accessed on 10 October 2022).
- Geofabrik Download Server. Download Openstreetmap Data for This Region: United States of America. Available online: http://download.geofabrik.de/north-america/us.html (accessed on 10 October 2022).
- United States Geological Survey. Available online: https://www.usgs.gov/u.s.-board-on-geographic-names/download-gnis-data (accessed on 10 October 2022).
- Bohannon, R.W. Comfortable and maximum walking speed of adults aged 20–79 years: Reference values and determinants. Age Ageing
**1997**, 26, 15–19. [Google Scholar] [CrossRef][Green Version] - Rawls, J. A Theory of Justice; Routledge: New York, NY, USA, 2004; pp. 229–234. [Google Scholar]
- Van Wee, B.; Geurs, K. Discussing equity and social exclusion in accessibility evaluations. Eur. J. Transp. Infrastruct. Res.
**2011**, 11, 4. [Google Scholar] - Adabag, A.S.; Luepker, R.V.; Roger, V.L.; Gersh, B.J. Sudden cardiac death: Epidemiology and risk factors. Nat. Rev. Cardiol.
**2010**, 7, 216–225. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**A Matrix Describing the Process of the Overlayed Spatio-Temporal Optimization. Both ${h}_{1},{h}_{2},{h}_{3},\cdots ,{h}_{24}$ and ${h}_{1}^{\prime},{h}_{2}^{\prime},{h}_{3}^{\prime},\cdots ,{h}_{24}^{\prime}$ refer to 24 h a day. ${I}_{1},{I}_{2},{I}_{3},\cdots ,{I}_{24}$ indicate 24 hourly sets of POI visitor distribution. ${J}_{1}^{\prime},{J}_{2}^{\prime},{J}_{3}^{\prime},\cdots ,{J}_{24}^{\prime}$ represents 24 hourly AED solutions computed based on the visitor distribution of the hour itself. ${R}_{h{h}^{\prime}}(h,{h}^{\prime}\in 1,2,3,\cdots ,24)$ means the optimized AED coverage rate applying the ${h}^{\prime}$th solution on hth set of POI visitor distribution. ${N}_{1},{N}_{2},{N}_{3},\dots ,{N}_{24}$ means the 24 average performances for each solution. For instance, ${N}_{1}$ is averaged over ${R}_{11},{R}_{12},{R}_{13},\dots {R}_{124}$, and ${N}_{2},{N}_{3},\dots ,{N}_{24}$ is calculated similarly.

**Figure 3.**A Matrix Showing the Whole Process of the OSTO on the Case in Washington DC (k = 100). All numbers in Figure 3 are percentages. Numbers in black show the AED coverage rate when applying the solution in a specific hour (e.g., ${J}_{1}^{\prime}$) to cover a visitor distribution at all hours (e.g., ${h}_{1}$, ${h}_{2}$, $\dots $, ${h}_{24}$). Numbers in red show 24 of the average performances $\left({N}_{{J}_{{h}^{\prime}}^{\prime}}\right)$ of each solution. The number marked in red bold is the highest average performance 17.25% (when ${J}_{19}^{\prime}$ is applied to all hours).

**Figure 4.**Optimized AED coverage rate. The optimized AED coverage rate (${R}_{{J}_{h}^{\prime}{I}_{h}}$) refers to the coverage rate using the set of optimized AEDs in a specific hour to cover the visitor distribution of the hour itself. For each hour, the error bar is generated from resampling 61,575 visitors from the total number of visitors 100 times.

**Figure 5.**Kernel Density Maps of Visitors and Corresponding Optimized AED Locations at Three Particular Hours (k = 100).

**Figure 6.**Comparison between the Average Performance of Optimized AEDs and the Optimized AED Coverage Rate across 24 h (k = 100). The average performance of each set of optimized AEDs (${N}_{{J}_{{h}^{\prime}}^{\prime}}$) refers to the average performance applying each set of optimized AEDs to 24 sets of visitor distributions. The smoothed line is calculated based on a cubic spline with a lambda of 0.05.

**Figure 7.**Comparison of the Distributions between Existing AEDs and Relocated AEDs in Washington DC. (

**b**,

**d**) shows the detailed locations of existing and relocated AEDs in a zoomed area. The kernel density maps (

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**c**) are computed based on the locations of existing and relocated AEDs.

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Mu, L.; Zhang, D.; Rajbhandari-Thapa, J.; Chen, Z.; Pagán, J.A.; Li, Y.; Son, H.; Liu, J. Spatiotemporal Optimization for the Placement of Automated External Defibrillators Using Mobile Phone Data. *ISPRS Int. J. Geo-Inf.* **2023**, *12*, 91.
https://doi.org/10.3390/ijgi12030091

**AMA Style**

Zhang J, Mu L, Zhang D, Rajbhandari-Thapa J, Chen Z, Pagán JA, Li Y, Son H, Liu J. Spatiotemporal Optimization for the Placement of Automated External Defibrillators Using Mobile Phone Data. *ISPRS International Journal of Geo-Information*. 2023; 12(3):91.
https://doi.org/10.3390/ijgi12030091

**Chicago/Turabian Style**

Zhang, Jielu, Lan Mu, Donglan Zhang, Janani Rajbhandari-Thapa, Zhuo Chen, José A. Pagán, Yan Li, Heejung Son, and Junxiu Liu. 2023. "Spatiotemporal Optimization for the Placement of Automated External Defibrillators Using Mobile Phone Data" *ISPRS International Journal of Geo-Information* 12, no. 3: 91.
https://doi.org/10.3390/ijgi12030091