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Prehosp Emerg Care. 2004 Jul-Sep;8(3):292-7.

Mathematical determination of external defibrillators needed at mass gatherings.

Author information

  • 1Department of Emergency Medicine, West Virginia University, Morgantown 26506-9149, USA. tcrocco@hsc.wvu.edu



To develop a mathematical formula that assists in determining the number of automated external defibrillators (AEDs) needed at sites of mass gatherings.


Twenty (10 male, 10 female) healthy volunteers (equally divided between age groups 21-30 and 31-40 years) responded to mock cardiac arrests in a sports stadium. Seven different first-responder scenarios were simulated (ascending and descending three separate stairway slopes (22 degrees, 39 degrees, and 69 degrees ), as well as a response across a horizontal (0 degrees ) surface. To assess the impact of spectator congestion, the same volunteers conducted each scenario in an empty and full stadium. The quantitative relationship between time and distance was then plotted for each situation. Using the quantitative relationship, the area a first responder can cover in a specified time was calculated.


The formula for the total number of AEDs needed in a stadium (or other mass gathering site) can be expressed as follows: Total AEDs=[A(1)/(Ds(1)xDh(1))]+[A(2)/(Ds(2)xDh(2))]+[A(3)/(Ds(3)xDh(3))] where A(1), A(2), and A(3) represent the total areas of a stadium with a slight, moderate, or steep stairway slope, respectively; Ds(1), Ds(2), and Ds(3) represent the stairway distance a first responder must ascend or descend for each slope; and Dh(1), Dh(2), and Dh(3) are the horizontal distances a responder can run in the time remaining.


Given a medical director's targeted response times and goals, the optimal number of AEDs required at a mass gathering can be calculated using time versus distance relationships. Future studies should evaluate the impact of the mathematically derived optimal number of AEDs at mass gatherings.

[PubMed - indexed for MEDLINE]
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