ELECTROMUSCULAR INCAPACITATING DEVICE SAFETY

Transcription

1 ELECTROMUSCULAR INCAPACITATING DEVICE SAFETY Hongyu Sun*, Jiun-Yan Wu*, Rami Aballah**, an John G. Webster*** *University of Wisconsin-Maison/Department of Electrical an Computer Engineering **American University of Beirut/Department of Electrical Engineering, Beirut, Lebanon ***University of Wisconsin-Maison/Department of Biomeical Engineering, 1550 Engineering Drive, Maison WI USA Abstract: Electromuscular incapacitating evices (EMD) are known as stun guns, or Tasers. This paper will present methos an preliminary results to etermine if Tasers can irectly electrocute the heart. Our goal is to evelop safety stanars that can be use in a bench test for EMDs without animal experiments. By combining our results from finite element moelling an existing stuies one at 60 Hz, we evelop methos of etermining the artto-heart istance causing ventricular fibrillation (VF) an a bench test stanar base on waveform charge ensity. Introuction Electromuscular incapacitating evices (EMDs), such as Tasers, provie less lethal options esigne to temporarily incapacitate, confuse, elay, or restrain an aversary in a variety of situations. EMDs generate short uration electrical pulses [1]. The effective charge elivere to the subject may excite the heart an cause VF. Amesty International states that 70 people have ie after being Tasere [2]. The implication is that Tasers are killing these people. Thus some jurisictions have banne Tasers an police then use bullets to incapacitate. There is also a recent case [3] of VF after a Taser ischarge. Alternative hypotheses for eath following EMD shock inclue positional asphyxia, skeletal muscle amage causing hyperkalemia an aciosis, heat an rugs [4]. Tests on swine show a cariac safety factor of 15 to 42 [5], an recent report finings also inicate that stun guns are relatively safe [6]. This paper proposes a FEM moel to estimate the minimum art-to-heart istance where EMD can not irectly cause VF. Methos Membrane Excitation Moel: A membrane uner subthreshol conitions can be escribe by a uniformly istribute leakage resistance an parallel capacitance [7]. When a stimulus current epolarizes the resting membrane beyon the threshol voltage, an action potential is generate an the cell is excite. The minimum require stimulus constant current I of uration can be expresse as, Vth I = R (1 m e b = ) 1 e (1) where V th is the threshol voltage (about 20 mv for excitation); is the stimulus uration; is the membrane time constant, which is equal to the lumpe membrane resistance R m times the lumpe membrane capacitance C m ; b, the rheobasic current, is the minimum stimulating current neee for long urations an is equal to V th b = (2) Rm is the membrane time constant, which is equal to the lumpe membrane resistance R m times the lumpe membrane capacitance C m. That is, = R C m m (3) Strength Duration Curve: The strength uration curve shown in Figure 1 was escribe by Gees an Baker [7] for the relation between the minimum require stimulus current to excite cells an the pulse uration. The analytical strength uration curve can be irectly erive from the membrane excitation moel in equation (1). It is easy to show charge Q = I remains approximately constant for short uration pulses. b Q = I = 1 e (4) For short uration pulses where / is small, the threshol charge Q is approximately constant since for small /, e 1 (5)

2 Thus equation (4) reuces to Q = b (6) 60 Hz VF Threshols: VF threshols at 60 Hz are extensively stuie an stanars are wiely evelope. A review paper [10] of these stuies shows that espite the ifferent conitions uner which each experiment is performe, the fibrillating current ensity for 60 Hz ecreases with increase area an approaches a minimum RMS value of 5 µa/mm 2, i.e. a single peak value of 7.1 µa/mm 2, as shown in Figure 2. Figure 1: Normalize Current, Charge an Energy with Respect to Normalize Stimulus Duration c is the Chronaxie an is Equal to [7] Current Density: When we iscuss membrane excitation, it is more useful to use current ensity J rather than current I, because it constrains our iscussion to a constant number of cells within a unit area. The current ensity is efine as current per area (J = I/A). For long uration excitations ( 10 times longer than ), the require current ensity for excitation approaches a constant value. However, for short uration excitations ( 10 times shorter than ), the require current ensity increases exponentially, as shown in Figure 1.. Charge Density: Equation (6) shows that for a short uration excitation, the require charge for excitation approaches a constant value. To iscuss the amount of charge acting on a constant number of cells, we also use charge ensity D rather than charge for the following iscussion. The charge ensity is efine as charge per unit area (D = Q/A). It reaches a minimum value for short uration currents as shown in Figure 1. We efine the require charge ensity for short uration excitation to cause VF as D VF. Excitation an Ventricular Fibrillation: To generate an extrasystole a small number of cariac cells nee to be epolarize. However, to cause VF a critical mass of cariac cells nees to be excite uring the early phase of recovery where higher currents are require [8, page 189]. VF threshols similar to excitation threshols follow a strength uration curve but it is shifte up by a factor that varies epening on the type an position of the electroes use. For a bipolar electroe consisting of two wires wrappe aroun an insulating tube an suture to the myocarium of ogs, Jones an Gees [9] foun that excitation threshols have a strength uration curve with time constant equal to 0.25 ms whereas VF threshols curves have a time constant equal to 1.7 ms. Thus the ratio of VF to excitation threshol varies between 150 an 50 as the uration of the stimulus is increase from 1 ms to 10 ms. Figure 2: Fibrillating Current Density Decreases with Increase Electroe Area [10] This threshol is obtaine for uration of exposure to the 60 Hz stimulus exceeing 1 s. Reilly [8, page 212] shows that there is at least a 10 times increase in VF threshols for uration of exposure shorter than 20 ms where we can view the 60 Hz current as a single stimulus. At urations less than 1 cycle (16 ms), we can consier the 60 Hz current as a single stimulus of uration equal to half the perio (8 ms). Therefore, the single peak minimum fibrillating current ensity for an 8 ms single stimulus is at least 71 µa/mm 2. Incluing the factor of area in equation (1) with time constant for VF equal to 1.7 ms as mentione above, we can use the current ensity foun at 8 ms to approximate the rheobasic fibrillating single peak current ensity (enote as J b ) as b J b = (7) A In this stuy, J b = 70 µa/mm 2 is chosen. Figure 3 summarizes the previous iscussion: Point A represents the single peak fibrillating current ensity for 60 Hz with exposure time longer than 1 s [10]. Then, we can move to point B which shows the VF threshol for single stimulus of uration 8 ms [8, page 212]. For short uration pulses at C, such as Tasers, we can move along the upper strength uration curve whose time constant is 1.7 ms to preict the VF threshol. The lowest strength uration curve has a time constant of 0.25 ms an it shows that at 8 ms (point D) the excitation threshol is 60 times less than that at point B [9].

3 These observations can be further verifie by applying the Taser waveforms to a parallel RC moel. Assuming that 20 mv can excite the cell [7], we can use equation (2) with the previously foun rheobasic current ensity of 70 µa/mm 2 to yiel R = 286 Ω. Knowing that the time constant for fibrillation is 1.7 ms yiels C = 5.9 µf. Figure 5 shows that the maximum voltage is attaine at 7.5 µs for the M26 an at 127 µs for the X M26 X26 15 Voltage (mv) 10 5 Figure 3: Ventricular an Excitation Threshols for Different Stimulus Duration Taser waveforms: EMDs generate voltages of about 50 kv, currents of about 2 to 15 A, pulse urations of about 10 to 80 µs, repetition rates of about 20 pulses/s, for about 5 s [1]. Figure 4 shows measure waveforms for one pulse of the X26 an M26 Taser. At these short uration pulses, the maximum epolarization voltage epens only on the amount of charge elivere across the capacitor. As an example, for the M26, it is the charge elivere uring the first half perio (7.8 µs) that etermines the fibrillating threshol an for the X26 it is the charge elivere uring the first 164 µs. Figure 4 shows the M26 an the X26 waveforms for a typical loa of 300 Ω. By integrating the current waveforms, we can obtain the maximum charge elivere by the X26 which is 130 µc at 164 µs an by the M26 which is 103 µc at 7.8 µs. Current (A) M26 X Time (µs) Figure 4: Taser Waveforms Measure at a 300 Ω Loa Typical of the Boy Duration (µs) Figure 5: Simulate Membrane Depolarization Behavior for the X26 an M26 Tasers Preicting the VF Threshol for EMD: To fin the VF threshol for EMDs we nee to approximate the minimum fibrillating charge ensity enote as D VF, which approaches a constant value for typical EMD urations. Incluing the area factor, we can use equation (6) to relate the charge ensity to the rheobasic current ensity which we foun earlier to yiel D VF = J b (8) Although EMD stimuli are applie for 2 to 5 s, they cannot be consiere as repetitive stimuli since the current impulses are elivere at very low uty cycle (less than [11]) so that effect of each pulse is isolate from the others. Stuies have shown that for uty cycle less than 0.1, the effect of prolonge stimulation no longer ecreases VF threshol [12]. Therefore, for EMD threshols we can use the rheobasic current ensity foun above for a single stimulus which is 70 µa/mm 2. Substituting into equation (8) with equals 1.7 ms yiels a minimum fibrillating charge ensity for EMD of 119 nc/mm 2. Figure 6 shows the variation of charge an current ensity with respect to stimulus uration for VF threshols. It shows that charge ensity, unlike current

4 ensity, ecreases for a short uration stimulus an reaches a minimum for urations shorter than 200 µs. where Q x is the charge of the given current waveform; D VF is charge ensity VF threshol; J b is the rheobasic current ensity VF threshol an b is the VF time constant. Hence, for a location insie the tissue (such as the heart location nearest the art), if equation (10) is satisfie, that location is safe from VF. The minimum art-to-heart istance at which the given EMD can not irectly cause VF is estimate by the minimum art-toheart istance at which the current ensity satisfies equation (10). Results Figure 6: The Variation of Charge an Current Density with Respect to Stimulus Duration for VF Threshols Finite Element Moelling of Current Density Insie Heart: The effect of the electroe geometry an tissue properties on the current ensity can be etermine by finite element metho (FEM) moelling. A simple axisymmetric FEM [13] moel can calculate an estimate current ensity aroun the Taser art. Bench Test Stanar for EMD: The iea of the bench test stanar without experiments on live animals follows: We have the rheobasic current ensity J b causing VF (70 µa/mm 2 is chosen in this stuy) an the time constant (1.7 ms) that causes VF, we can obtain the charge ensity D VF for the Taser causing VF accoring to equation (8) as state above. Thus for any EMD, we can measure its current waveform at a typical loa (300 Ω in this stuy), we can compute the maximum charge Q x elivere by integration. Then base on the FEM moelling results, we can obtain the current ensity J at any location of the boy for any current value I inserte into the art (here 1 A is chosen for convenience). For the measure current the charge ensity D x is We create our inital computer moel of Taser current ensity using MSC Patran 2001 r2a an Abaqus on a Sun Blae 1000 workstation with 2.5 GB memory, an Matlab on Winows XP 5.1 with 1 GB memory. The moel is a 2-D axisymmetric moel with cross section of size 150 mm 250 mm an uniform conuctivities. The Taser art has a length of 9 mm an iameter of 1 mm. 1 A current is applie to the art at the center of the top surface an flows to the groun on both sies an the bottom surface. The mesh size aroun the art (the 40 mm 20 mm area) is 0.5 mm. The outsie mesh size is 2 mm. Figure 7 shows a zoom-in view (20 mm 20 mm) of the current ensity contour aroun the art for 1 A inserte current. The art geometry is marke using otte lines. Note that the maximum current ensity is at the tip of the art an the current ensity ecreases rapily away from the art tip. Linear interpolation an average current ensity for each element are use in Figure 7. J D x = Q x (9) I where J is the current ensity etermine by the FEM moel for inserte current I. Then if the resulting charge ensity D x at a istance from the heart is less than the fibrillating charge ensity D VF (D VF = 119 nc/mm 2 ) then the EMD is safe at the given istance from the heart. In sum, this criteria is J D Jb VF < I = I (10) Qx Qx Figure 7: Zoom-in View of Current Density J(µA/mm 2 ) Coutour Aroun the Taser Dart Electroe for 1 A Inserte Current Figure 8 shows the log scale current ensity J (µa/mm 2 ) for 1 A inserte current on the y-axis (actually rawn using ata in the range of x < 0.5 mm)

5 versus the istance to the art tip. Nearest neighbor interpolation an current ensity at noes are use in Figure 8. meshe an conuctivities are assigne for each mesh. However, we nee finer mesh size aroun the art electroe, while the Utah torso mesh size may not be small enough. Finally, we may start from the Visible Human raw ata [16], o segmentation an assign the conuctivities. No moel shoul be use without verification. No institutional review boar woul permit tests to measure VF on humans. Therefore we will etermine the VF current ensity an art-to-heart istance uring tests on anesthetize swine, which will feel no pain. Results of these tests will likely change our initial estimates above. To compare with the results on swine, we plan to buil a FEM moel for swine. Acknowlegements Figure 8: Current Density J (µa/mm 2 ) Along the Axis (x < 0.5 mm) for 1 A Inserte Current in the Axisymmetric Moel Versus the Distance to Dart Tip (= 9 y) As an example we use the X26 an M26 waveforms shown in Figure 4 to fin the art-to-heart istance at which no VF occurs. In our FEM moel, we use 1 A current (I = 1 A) through the art for convenience. We use the 119 nc/mm 2 charge ensity fibrillating threshol (D VF = 119 nc/mm 2 ) preicte above. For the X26, Q x = 130 µc. Substituting into equation (10), the fibrillating current ensity is 915 µα/mm 2. Using Figure 8, the minimum art-to-heart istance where VF oes not occur for the X26 woul be about 7 mm. Similarly for the M26, Q x = 103 µc; the fibrillating current ensity is 1155 µα/mm 2 an the minimum art-to-heart istance is about 6 mm. Discussion The assumptions we mae for the FEM moel inclue: the tissue has uniform conuctivity an is axisymmetric; the contour map interpolation oes not change the values to the extent sensitive to our conclusion; an the 150 mm 250 mm moel results are similar to those that woul be obtaine from a full torso moel. One current limitation of the FEM moel is a lack of ata on tissue properties. Electrical tissue properties vary with locations in the boy. The Taser waveforms coul vary with ifferent Tasers, an ifferent iniviual Taser impulses. We just use one waveform as an example. These limitations may lea to misleaing moel results, which have to be consiere if moels are to be use to preict the safe art-to-heart istance. We attempte to use the human anatomy ata from Yale [14] which are alreay segmente, however, we foun skin tissues insie the boy. Currently we are attempting to use the Utah torso ata [15], which are This project was supporte by Grant No IJ-CX- K036 aware by the National Institute of Justice, Office of Justice Programs, US Department of Justice. Points of view in this ocument are those of the author an o not necessarily represent the official position or policies of the US Department of Justice. References [1] WEBSTER, J. G. (2005): Electromuscular Incapacitating Devices, Proc. IFMBE 2005, 9, p [2] Amnesty International, Internet site aress: [3] KIM, P. J., FRANKLIN, W. H. (2005): Ventricular Fibrillation after Stun-Gun Discharge, N. Engl. J. Me., 353, p [4] LAUR, D. (2004): 'Excite elirium an its correlation to suen an unexpecte eath proximal to restraint', (Canaa: Victoria Police Department) [5] MCDANIEL, W. C., STRATBUCKER, R. A., NERHEIM, M., an BREWER, J. E. (2005): 'Cariac Safety of Neuromuscular Incapacitating Defensive Devices', PACE Supplement 1, 28, pp. S [6] MCBRIDE, D. K., TEDDER, N. B. (2005): Efficacy an Safety of Electrical Stun Devices, A Potomac Institute for Policy Stuies Report: No , 20Devices%20Report_FINAL.pf [7] GEDDES, L. A., an BAKER, L. E. (1989): 'Principles of Applie Biomeical Instrumentation', 3r e., (John Wiley & Sons, New York), pp. 460 [8] REILLY, J. P. (1998): 'Applie Bioelectricity', (Springer-Verlag, New York). [9] JONES, M., AND GEDDES, L. A. (1977): 'Strength uration curves for cariac pacemaking an

6 ventricular fibrillation', Cariovascular Research Center Bulletin, 15, pp [10] ROY, O. Z. (1980): Summary of cariac fibrillation threshols for 60 Hz currents an voltages applie irectly to the heart, Me. & Biol. Eng. & Comput., 18, pp [11] Taser M26 an X26 manuals. [12] IEC (1987): 'Effects of current passing through the human boy IEC 479-2, 2n e.', (International Electrotechnical Commission, Geneva) [13] HAEMMERICH, D., CHACHATI, L., WRIGHT, A. S., MAHVI, D. M., LEE, F. T. an WEBSTER, J. G. (2003): Hepatic Raiofrequency Ablation With Internally Coole Probes: Effect of Coolant Temperature on Lesion Size, IEEE Trans. Biome. Eng., 50, pp [14] The Zubal Phantom, [15] NIH/NCRR Dataset Archive, ets.html [16] The National Library of Meicine's Visible Human Project, human.html