CSIS Discussion Paper No.77 AED Optimal allocation of AED s by maximization of supply effect on demand density Yusuke KATAOKA, Yasushi ASAMI, Yasushi

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1 CSIS Discussion Paper No.77 AED Optimal allocation of AED s by maximization of supply effect on demand density Yusuke KATAOKA, Yasushi ASAMI, Yasushi ASARI and Kazuaki KOHRIYAMA Course of Socio-Cultural and Socio-Physical Environmental Studies, Graduate School of Frontier Sciences, University of Tokyo 5--5, Kashiwanoha, Kashiwa-shi, Chiba , Japan ukataoka@csis.u-tokyo.ac.jp

2 AED Optimal allocation of AED s by maximization of supply effect on demand density Yusuke KATAOKA, Yasushi ASAMI, Yasushi ASARI and Kazuaki KOHRIYAMA Abstract: A probability density function of demand for automated external defibrillators (AED's), which is based on the distribution of demand points by kernel density estimation method, is estimated from the data on occurrences of cardiopulmonary arrests. The probability that someone can be saved by AED's is formulated using probability of survival to hospital discharge. Supply effect is expressed as demand density multiplied by this probability of saving, and the locations of AED's are optimized by maximizing supply effect in the entire region. The results show that optimal locations tend to cover the center of the city and that the supply effect is approximately proportional to the number of AED's. Keywords:AEDautomated external defibrillator density distribution maximal covering spatial pattern probability of survival to hospital discharge AED Malcom AED et al.004 AED Crocco et al.004 AED AED AED GIS Graduate School of Frontier Sciences, University of Tokyo ukataoka@csis.u-tokyo.ac.jp AED

3 AED Sheather and Jones99 ).. (x,y) AED f ( xy, ) i (x i,y i ) Bowman and Azzelini, 997 x x i y y i f ( x, y) = K i K n h () x h y K ( ) n h x, h y () (x,i,y,i ) () n ( x x, i) ( y y ), i f ( x, y) = exp π hhn () x y i= hx hy Silverman, 986 n ()

4 .. 4) Maximal Covering Location Problem Church and ReVelle974 AED Brotcorne et al., 003 (3) (x,y) (x,j,y,j ) AED n ( ) ( (( ) ( ) )) g x, y = exp a x x, j + y y, j (4) j= American Heart Association, 000 n Alsalloum et al. 006 AED d 3) ( ) = exp( ad ) g d (3) a

5 (5) AED L ( ) x, y = f ( x, y) g( x, y) dxdy n ( x x, i) ( y y, ) i = exp π hhn x y i= hx hy n 5) ( (( ) ( ) )) exp a x x, j + y y, j dxdy j= d min d min = 4n + ahx + ahy n n a x x a y y exp + ah + ah x x, i + ahx ( x x, ) j erf hx 4ah + x y y, i + ahy ( x y, j) erf hy 4ah + y (, i, j) (, i, j) (5) (5) Maximize L x,, x,,, x, n, y,, y,,, y, n (8) erf( ) subject to d (9) z st, = ( x, s x, t) + ( y, s y, t) dmin s, t t erf ( z) = e dt 0 π (6) AED AED AED 4.. (5) (7) i= j= x y d s,t (9) (7) ( ) 3 4 L ( x,, x,,, x, n, y ),, y,,, y, n = n + ahx + ahy n ( ) ( ) 6) n a x, i x, j a y, i y, j exp i= j= + ahx + ah y (7) () (7).. Sheather and Jones99 3

6 a= m 5 400m ) (m) 4.3. AED (8) AED 30 (9) d min =400m (8) 9) (km) (3) 6 0% 7)AED 0 0 (3)

7 0 点配置図5 0 点配置図6 30 点配置 AED の最適配置地点と供給効果の密度分布 30 点配置 AED の最適配置地点と救命確率の密度分布 0 (km) 図 5,6 中の表記については以下の通り AED の最適配置地点および各々の密度濃線需要量密度淡線を示す等値線背景地図として河川鉄道弘前城を表記

8 5 6 AED (8) 0.0 % AED 0.08 AED AED AED AED AED AED 0.07

9 AED ) Sheather and Jones () f 0) Simonoff996 3) AED AED 4) AED 5) 6) 7) American Heart Association (000) 7%~0% ) AED ZmapTownII 9) MATLAB Optimization ) Toolbox 0) AED AED 3 AED 4

10 American Heart Association (000) Guidelines 000 for cardiopulmonary resuscitation and emergency cardiovascular care: International consensus on science, Circulation. Alsalloum, O.I. and Rand, G.K. (006) Extensions to emergency vehicle location models. Computers & Operations Research, 33, Bowman, A. and Azzelini, A. (997) Applied Smoothing Techniques for Data Analysis. Oxford: Oxford University Press. Brotcorne, L., Gilbert Laporte, G. and Semet, F. (003) Ambulance location and relocation models. European Journal of Operational Research, 47, Church R.L. and ReVelle C.S. (974) The maximal covering location problem. Papers of the Regional Science Association, 3, 0-8. Crocco, T.J., Sayre, M.R., Liu, T., Davis, S.M., Cannon, C. and Potluri, J. (004) Mathematical determination of external defibrillators needed at mass gatherings. Prehospital Emergency Care, 8, Malcom, G.E., Thompson, T.M. and Coule, P.L. (004) The location and incidence of out-of hospital cardiac Arrest in Georgia. Prehospital Emergency Care, 8, 0-4. Sheather, S.J. and Jones, M.C. (99) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, Silverman, B.W. (986) Density Estimation for Statistics and Data Analysis. London: Chapman and Hall. Simonoff, J.S. (996) Smoothing Methods in Statistics. New York: Springer-Verlag.

Kobe University Repository : Kernel タイトル Title 著者 Author(s) 掲載誌巻号ページ Citation 刊行日 Issue date 資源タイプ Resource Type 版区分 Resource Version 権利 Rights DOI

Kobe University Repository : Kernel タイトル Title 著者 Author(s) 掲載誌巻号ページ Citation 刊行日 Issue date 資源タイプ Resource Type 版区分 Resource Version 権利 Rights DOI 平均に対する平滑化ブートストラップ法におけるバンド幅の選択に関する一考察 (A Study about