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

Jeehyun Lee; Jin Keun Seo; Eung Je Woo

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 3, page 447-459
  • ISSN: 0764-583X

Abstract

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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 J 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 J. 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 |J| at the region of the darts where the current density J is highly concentrated. Hence, fine computation of J 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 J. It has a potential to provide effective analysis and more accurate estimate of J near fishhook-shaped darts. Numerical experiments show that the MPSM is just fit for the study of EMD shocks.

How to cite

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Lee, Jeehyun, Seo, Jin Keun, and Woo, Eung Je. "Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices." ESAIM: Mathematical Modelling and Numerical Analysis 41.3 (2007): 447-459. <http://eudml.org/doc/250066>.

@article{Lee2007,
abstract = { 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 J 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 J. 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 |J| at the region of the darts where the current density J is highly concentrated. Hence, fine computation of J 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 J. It has a potential to provide effective analysis and more accurate estimate of J near fishhook-shaped darts. Numerical experiments show that the MPSM is just fit for the study of EMD shocks. },
author = {Lee, Jeehyun, Seo, Jin Keun, Woo, Eung Je},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Electro-muscular disruption (EMD) device; electrical current density; Maxwell equations; non-smooth boundary; elliptic partial differential equations; corner singularity.},
language = {eng},
month = {8},
number = {3},
pages = {447-459},
publisher = {EDP Sciences},
title = {Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices},
url = {http://eudml.org/doc/250066},
volume = {41},
year = {2007},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2007/8//
PB - EDP Sciences
VL - 41
IS - 3
SP - 447
EP - 459
AB - 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 J 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 J. 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 |J| at the region of the darts where the current density J is highly concentrated. Hence, fine computation of J 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 J. It has a potential to provide effective analysis and more accurate estimate of J near fishhook-shaped darts. Numerical experiments show that the MPSM is just fit for the study of EMD shocks.
LA - eng
KW - Electro-muscular disruption (EMD) device; electrical current density; Maxwell equations; non-smooth boundary; elliptic partial differential equations; corner singularity.
UR - http://eudml.org/doc/250066
ER -

References

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  1. G. Alessandrini and R. Magnanini, 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.  Zbl0793.35021
  2. G. Alessandrini, E. Rosset and J.K. Seo, Optimal size estimates for the inverse conductivity poblem with one measurement. Proc. Amer. Math. Soc.128 (2000) 53–64.  Zbl0944.35108
  3. Amnesty International, Internet site address: URIhttp://web.amnesty.org/library/index/engamr510302006
  4. M. Cheney, D. Isaacson and J.C. Newell, Electrical impedance tomography. SIAM Rev.41 (1999) 85–101.  Zbl0927.35130
  5. V. Isakov, On uniqueness of recovery of a discontinuous conductivity coefficient. Comm. Pure Appl. Math.41 (1988) 856–877.  Zbl0676.35082
  6. P.J. Kim and W.H. Franklin, Ventricular Fibrillation after Stun-Gun Discharge. N. Engl. J. Med.353 (2005) 958–959.  
  7. S.W. Kim, O. Kwon, J.K. Seo and J.R. Yoon, On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography. SIAM J. Math. Anal.34 (2002) 511–526.  Zbl1055.35142
  8. Y.J. Kim, O. Kwon, J.K. Seo and E.J. Woo, Uniqueness and convergence of conductivity image reconstruction in magnetic resonance electrical impedance tomography. Inverse Probl.19 (2003) 1213–1225.  Zbl1054.35134
  9. R. Kohn and M. Vogelius, Determining conductivity by boundary measurements. Comm. Pure Appl. Math.37 (1984) 113–123.  Zbl0586.35089
  10. O. Kwon, E. Woo, J.R. Yoon and J.K. Seo, Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm. IEEE Trans. Biomed. Eng.49 (2002) 160–167.  
  11. 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).  
  12. B.I. Lee, S.H. Oh, E.J. Woo, S.Y. Lee, M.H. Cho, O. Kwon, J.K. Seo and W.S. Baek, Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT). Physiol. Meas.24 (2003) 579–589.  
  13. D.K. Mcbride and N.B. Tedder, Efficacy and Safety of Electrical Stun Devices, A Potomac Institute for Policy Studies Report: No. 05 . 04, (2005).  URIhttp://www.potomacinstitute.com/research/Stun%20Devices%20Report_FINAL.pdf
  14. W.C. Mcdaniel, R.A. Stratbucker, M. Nerheim and J.E. Brewer, Cardiac Safety of Neuromuscular Incapacitating Defensive Devices. PACE Supplement1 (2005) 284–287.  
  15. P. Metherall, D.C. Barber, R.H. Smallwood and B.H. Brown, Three Dimensional Electrical Impedance Tomography. Nature380 (1996) 509–512.  
  16. A. Nachman, Reconstructions from boundary measurements. Ann. Math.128 (1988) 531–577.  Zbl0675.35084
  17. S.H. Oh, B.I. Lee, E.J. Woo, S.Y. Lee, M.H. Cho, O. Kwon and J.K. Seo, Conductivity and current density image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography. Phys. Med. Biol.48 (2003) 3101–3016.  
  18. S.H. Oh, B.I. Lee, S.Y. Lee, E.J. Woo, M.H. Cho, O. Kwon and J.K. Seo, Magnetic resonance electrical impedance tomography: phantom experiments using a 3.0 Tesla MRI system. Magn. Reson. Med.51 (2004) 1292–1296.  
  19. C. Park, O. Kwon, E.J. Woo and J.K. Seo, Electrical conductivity imaging using gradient Bz decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT). IEEE Trans. Med. Imag.23 (2004) 388–394.  
  20. J.S. Park, M.S. Chung, S.B. Hwang, Y.S. Lee, D.H. Har and H.S. Park, Visible Korean Human: Improved Serially Sectioned Images of the Entire Body. IEEE Trans. Med. Imag.24 (2005) 352–360.  
  21. F. Santosa and M. Vogelius, A backprojection algorithm for electrical impedance imaging. SIAM J. Appl. Math.50 (1990) 216–243.  Zbl0691.65087
  22. G.C. Scott, M.L.G. Joy, R.L. Armstrong and R.M. Henkelman, Measurement of nonuniform current density by magnetic resonance. IEEE Trans. Med. Imag.10 (1991) 362–374.  
  23. J.K. Seo, A uniqueness results on inverse conductivity problem with two measurements. J. Fourier Anal. App.2 (1996) 515–524.  
  24. J.K. Seo, J.R. Yoon, E.J. Woo and O. Kwon, Reconstruction of conductivity and current density images using only one component of magnetic field measurements. IEEE Trans. Biomed. Eng.50 (2003) 1121–1124.  
  25. J.K. Seo, O. Kwon, B.I. Lee and E.J. Woo, 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. J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. Math.125 (1987) 153–169.  Zbl0625.35078
  27. Taser M26 and X26 manuals, http://www.taser.com/index.htm  
  28. G. Verchota, Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains. J. Func. Anal.59 (1984) 572–611.  Zbl0589.31005
  29. J.G. Webster, Electromuscular Incapacitating Devices. Proc. IFMBE 20059 (2005) 150–151.  

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