Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density inside the target produced by the EMD device. One approach is to develop a computational model providing a quantitative and reliable analysis about the distribution of . In this paper, we set up a mathematical model of a typical EMD shock, bearing in mind that we are aiming to compute the current density distribution inside the human body with a pair of inserted darts. The safety issue of TASER is directly related to the magnitude of at the region of the darts where the current density is highly concentrated. Hence, fine computation of near the dart is essential. For such numerical simulations, serious computational difficulties are encountered in dealing with the darts having two different very sharp corners, tip of needle and tip of barb. The boundary of a small fishhook-shaped dart inside a large computational domain and the presence of corner singularities require a very fine mesh leading to a formidable amount of numerical computations. To circumvent these difficulties, we developed a multiple point source method of computing . It has a potential to provide effective analysis and more accurate estimate of near fishhook-shaped darts. Numerical experiments show that the MPSM is just fit for the study of EMD shocks.
Mots-clés : electro-muscular disruption (EMD) device, electrical current density, Maxwell equations, non-smooth boundary, elliptic partial differential equations, corner singularity
@article{M2AN_2007__41_3_447_0,
author = {Lee, Jeehyun and Seo, Jin Keun and Woo, Eung Je},
title = {Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {447--459},
publisher = {EDP-Sciences},
volume = {41},
number = {3},
year = {2007},
doi = {10.1051/m2an:2007030},
mrnumber = {2355707},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007030/}
}
TY - JOUR AU - Lee, Jeehyun AU - Seo, Jin Keun AU - Woo, Eung Je TI - Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 447 EP - 459 VL - 41 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007030/ DO - 10.1051/m2an:2007030 LA - en ID - M2AN_2007__41_3_447_0 ER -
%0 Journal Article %A Lee, Jeehyun %A Seo, Jin Keun %A Woo, Eung Je %T Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 447-459 %V 41 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007030/ %R 10.1051/m2an:2007030 %G en %F M2AN_2007__41_3_447_0
Lee, Jeehyun; Seo, Jin Keun; Woo, Eung Je. Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 3, pp. 447-459. doi : 10.1051/m2an:2007030. http://www.numdam.org/articles/10.1051/m2an:2007030/
[1] and, The index of isolated critical points and solutions of elliptic equations in the plane. Ann. Scoula. Norm. Sup. Pisa Cl. Sci. 19 (1992) 567-589. | Numdam | Zbl
[2] , and, Optimal size estimates for the inverse conductivity poblem with one measurement. Proc. Amer. Math. Soc. 128 (2000) 53-64. | Zbl
[3] Amnesty International, Internet site address: http://web.amnesty.org/library/index/engamr510302006
[4] , and, Electrical impedance tomography. SIAM Rev. 41 (1999) 85-101. | Zbl
[5] , On uniqueness of recovery of a discontinuous conductivity coefficient. Comm. Pure Appl. Math. 41 (1988) 856-877. | Zbl
[6] and, Ventricular Fibrillation after Stun-Gun Discharge. N. Engl. J. Med. 353 (2005) 958-959.
[7] ,, and, On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography. SIAM J. Math. Anal. 34 (2002) 511-526. | Zbl
[8] ,, and, Uniqueness and convergence of conductivity image reconstruction in magnetic resonance electrical impedance tomography. Inverse Probl. 19 (2003) 1213-1225. | Zbl
[9] and, Determining conductivity by boundary measurements. Comm. Pure Appl. Math. 37 (1984) 113-123. | Zbl
[10] ,, and, Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm. IEEE Trans. Biomed. Eng. 49 (2002) 160-167.
[11] , Excited delirium and its correlation to sudden and unexpected death proximal to restraint (Canada: Victoria Police Department) http://www.taser.com/facts/medical_info.htm (2004).
[12] ,,,,,, and, Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT). Physiol. Meas. 24 (2003) 579-589.
[13] and, Efficacy and Safety of Electrical Stun Devices, A Potomac Institute for Policy Studies Report: No. 05 . 04, http://www.potomacinstitute.com/research/Stun%20Devices%20Report_FINAL.pdf (2005).
[14] ,, and, Cardiac Safety of Neuromuscular Incapacitating Defensive Devices. PACE Supplement 1 (2005) 284-287.
[15] ,, and, Three Dimensional Electrical Impedance Tomography. Nature 380 (1996) 509-512.
[16] , Reconstructions from boundary measurements. Ann. Math. 128 (1988) 531-577. | Zbl
[17] ,,,,, and, Conductivity and current density image reconstruction using harmonic algorithm in magnetic resonance electrical impedance tomography. Phys. Med. Biol. 48 (2003) 3101-3016.
[18] ,,,,, and, Magnetic resonance electrical impedance tomography: phantom experiments using a 3.0 Tesla MRI system. Magn. Reson. Med. 51 (2004) 1292-1296.
[19] ,, and, Electrical conductivity imaging using gradient decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT). IEEE Trans. Med. Imag. 23 (2004) 388-394.
[20] ,,,, and, Visible Korean Human: Improved Serially Sectioned Images of the Entire Body. IEEE Trans. Med. Imag. 24 (2005) 352-360.
[21] and, A backprojection algorithm for electrical impedance imaging. SIAM J. Appl. Math. 50 (1990) 216-243. | Zbl
[22] ,, and, Measurement of nonuniform current density by magnetic resonance. IEEE Trans. Med. Imag. 10 (1991) 362-374.
[23] , A uniqueness results on inverse conductivity problem with two measurements. J. Fourier Anal. App. 2 (1996) 515-524.
[24] ,, and, Reconstruction of conductivity and current density images using only one component of magnetic field measurements. IEEE Trans. Biomed. Eng. 50 (2003) 1121-1124.
[25] ,, and, Reconstruction of current density distributions in axially symmetric cylindrical sections using one component of magnetic flux density: computer simulation study. Physiol. Meas. 24 (2003) 565-577.
[26] and, A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125 (1987) 153-169. | Zbl
[27] Taser M26 and X26 manuals, http://www.taser.com/index.htm
[28] , Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains. J. Func. Anal. 59 (1984) 572-611. | Zbl
[29] , Electromuscular Incapacitating Devices. Proc. IFMBE 2005 9 (2005) 150-151.
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