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Mathematical framework for current density imaging due todischarge of electro-muscular disruption devices

Published online by Cambridge University Press:  02 August 2007

Jeehyun Lee ,
Jin Keun Seo  and
Eung Je Woo
Jeehyun Lee
Affiliation:
Department of Mathematics, Yonsei University, Korea. [email protected]
Jin Keun Seo
Affiliation:
Department of Mathematics, Yonsei University and National Institute for Mathematical Science, Korea. [email protected]
Eung Je Woo
Affiliation:
College of Electronics and Information, Kyung Hee University, Korea. [email protected]
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Abstract

Electro-muscular disruption (EMD) devices such as TASER M26 andX26 have been used as a less-than-lethal weapon. Such EMD devicesshoot a pair of darts toward an intended target to generate anincapacitating electrical shock. In the use of the EMD device,there have been controversial questions about its safety andeffectiveness. To address these questions, we need to investigatethe distribution of the current density J inside the targetproduced by the EMD device. One approach is to develop acomputational model providing a quantitative and reliable analysisabout the distribution of J. In this paper, we set up amathematical model of a typical EMD shock, bearing in mind that weare aiming to compute the current density distribution inside thehuman body with a pair of inserted darts. The safety issue ofTASER is directly related to the magnitude of |J| at the regionof the darts where the current density J is highlyconcentrated. Hence, fine computation of J near the dart isessential. For such numerical simulations, serious computationaldifficulties are encountered in dealing with the darts having twodifferent very sharp corners, tip of needle and tip of barb. Theboundary of a small fishhook-shaped dart inside a largecomputational domain and the presence of corner singularitiesrequire a very fine mesh leading to a formidable amount ofnumerical computations. To circumvent these difficulties, wedeveloped a multiple point source method of computing J. It hasa potential to provide effective analysis and more accurateestimate of J near fishhook-shaped darts. Numerical experimentsshow that the MPSM is just fit for the study of EMD shocks.

Keywords

Electro-muscular disruption (EMD) deviceelectrical current densityMaxwell equationsnon-smoothboundaryelliptic partial differential equationscornersingularity.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 3 , May 2007 , pp. 447 - 459
Copyright
© EDP Sciences, SMAI, 2007

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References

Alessandrini, G. and Magnanini, R., 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.
Alessandrini, G., Rosset, E. and Seo, J.K., Optimal size estimates for the inverse conductivity poblem with one measurement. Proc. Amer. Math. Soc. 128 (2000) 53–64. CrossRef
Amnesty International, Internet site address: http://web.amnesty.org/library/index/engamr510302006
Cheney, M., Isaacson, D. and Newell, J.C., Electrical impedance tomography. SIAM Rev. 41 (1999) 85–101. CrossRef
Isakov, V., On uniqueness of recovery of a discontinuous conductivity coefficient. Comm. Pure Appl. Math. 41 (1988) 856–877. CrossRef
Kim, P.J. and Franklin, W.H., Ventricular Fibrillation after Stun-Gun Discharge. N. Engl. J. Med. 353 (2005) 958–959. CrossRef
Kim, S.W., Kwon, O., Seo, J.K. and Yoon, J.R., On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography. SIAM J. Math. Anal. 34 (2002) 511–526. CrossRef
Kim, Y.J., Kwon, O., Seo, J.K. and Woo, E.J., Uniqueness and convergence of conductivity image reconstruction in magnetic resonance electrical impedance tomography. Inverse Probl. 19 (2003) 1213–1225. CrossRef
Kohn, R. and Vogelius, M., Determining conductivity by boundary measurements. Comm. Pure Appl. Math. 37 (1984) 113–123. CrossRef
Kwon, O., Woo, E., Yoon, J.R. and Seo, J.K., Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm. IEEE Trans. Biomed. Eng. 49 (2002) 160–167. CrossRef
D. Laur, 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).
Lee, B.I., Oh, S.H., Woo, E.J., Lee, S.Y., Cho, M.H., Kwon, O., Seo, J.K. and Baek, W.S., Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT). Physiol. Meas. 24 (2003) 579–589. CrossRef
D.K. Mcbride and N.B. Tedder, 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).
Mcdaniel, W.C., Stratbucker, R.A., Nerheim, M. and Brewer, J.E., Cardiac Safety of Neuromuscular Incapacitating Defensive Devices. PACE Supplement 1 (2005) 284–287. CrossRef
Metherall, P., Barber, D.C., Smallwood, R.H. and Brown, B.H., Three Dimensional Electrical Impedance Tomography. Nature 380 (1996) 509–512. CrossRef
Nachman, A., Reconstructions from boundary measurements. Ann. Math. 128 (1988) 531–577. CrossRef
Oh, S.H., Lee, B.I., Woo, E.J., Lee, S.Y., Cho, M.H., Kwon, O. and Seo, J.K., Conductivity and current density image reconstruction using harmonic B z algorithm in magnetic resonance electrical impedance tomography. Phys. Med. Biol. 48 (2003) 3101–3016. CrossRef
Oh, S.H., Lee, B.I., Lee, S.Y., Woo, E.J., Cho, M.H., Kwon, O. and Seo, J.K., Magnetic resonance electrical impedance tomography: phantom experiments using a 3.0 Tesla MRI system. Magn. Reson. Med. 51 (2004) 1292–1296. CrossRef
Park, C., Kwon, O., Woo, E.J. and Seo, J.K., Electrical conductivity imaging using gradient B z decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT). IEEE Trans. Med. Imag. 23 (2004) 388–394. CrossRef
Park, J.S., Chung, M.S., Hwang, S.B., Lee, Y.S., Har, D.H. and Park, H.S., Visible Korean Human: Improved Serially Sectioned Images of the Entire Body. IEEE Trans. Med. Imag. 24 (2005) 352–360. CrossRef
Santosa, F. and Vogelius, M., A backprojection algorithm for electrical impedance imaging. SIAM J. Appl. Math. 50 (1990) 216–243. CrossRef
Scott, G.C., Joy, M.L.G., Armstrong, R.L. and Henkelman, R.M., Measurement of nonuniform current density by magnetic resonance. IEEE Trans. Med. Imag. 10 (1991) 362–374. CrossRef
Seo, J.K., A uniqueness results on inverse conductivity problem with two measurements. J. Fourier Anal. App. 2 (1996) 515–524.
Seo, J.K., Yoon, J.R., Woo, E.J. and Kwon, O., Reconstruction of conductivity and current density images using only one component of magnetic field measurements. IEEE Trans. Biomed. Eng. 50 (2003) 1121–1124.
Seo, J.K., Kwon, O., Lee, B.I. and Woo, E.J., 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. CrossRef
Sylvester, J. and Uhlmann, G., A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125 (1987) 153–169. CrossRef
Taser M26 and X26 manuals, http://www.taser.com/index.htm
Verchota, G., Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains. J. Func. Anal. 59 (1984) 572–611. CrossRef
Webster, J.G., Electromuscular Incapacitating Devices. Proc. IFMBE 2005 9 (2005) 150–151.