Journal of Medical Engineering & Technology, 2010; Early Online, 1–14

Innovation
Estimating the probability that the Taser1 directly causes human
ventricular fibrillation

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H. SUN{, D. HAEMMERICH{, P. S. RAHKOx and J. G. WEBSTER*{
{Department of Electrical and Computer Engineering, 1415 Engineering Drive, University of Wisconsin,
Madison, WI 53706, USA
{Division of Pediatric Cardiology, Medical University of South Carolina, 135 Rutledge Avenue, Charleston,
SC 29425 USA
xDepartment of Medicine, University of Wisconsin, 600 Highland Ave Madison, WI 53792, USA
{Department of Biomedical Engineering, University of Wisconsin, 1550 Engineering Drive, Madison,
WI 53706 USA
(Received 20 March 2009; accepted 23 November 2009)

This paper describes the first methodology and results for estimating the order of
probability for Tasers1 directly causing human ventricular fibrillation (VF). The
probability of an X26 Taser1 causing human VF was estimated using: (1) current density
near the human heart estimated by using 3D finite-element (FE) models; (2) prior data of
the maximum dart-to-heart distances that caused VF in pigs; (3) minimum skin-to-heart
distances measured in erect humans by echocardiography; and (4) dart landing
distribution estimated from police reports. The estimated mean probability of human
VF was 0.001 for data from a pig having a chest wall resected to the ribs and 0.000006 for
data from a pig with no resection when inserting a blunt probe. The VF probability for a
given dart location decreased with the dart-to-heart horizontal distance (radius) on the
skin surface.
Keywords: Finite-element method; Cardiac stimulation; Electromuscular incapacitating
device; Electrical safety; Taser1; Simulation

1. Introduction
The Taser1 was designed to electrically stimulate skeletal
muscles in order to incapacitate offenders so they can be
apprehended [1] and is currently in use by law enforcement.
During training, police officers are Tasered in the back,
which does not cause ventricular fibrillation (VF). In
contrast, offenders may be Tasered over the heart, which
may cause VF. However many deaths following Taser1 use
may be caused by drug overdose, positional asphyxia, or
other causes. This study focuses on determining whether
VF can be directly caused by Taser1 use. The Taser1
impulses occur about 20 times per second for 5 s. The

vulnerable period during the T wave will be hit for every
heart beat.
It is difficult to achieve sustained VF in small hearts.
Geddes [2] found the minimum cardiac critical mass for
sustained VF was 18 g. Malkin et al. [3] found 7 g guinea
pig hearts could consistently sustain tachyarrhythmias only
when preceded by a rapid pacing protocol. Malkin and de
Jongh Curry [4] found 7 g guinea pig hearts and 1 ms
rectangular pulses from 10 to 160 Hz induced VF sustained
for at least 10 s. Holden et al. [5] applied simulated M26
and X26 Taser1 waveforms to the ventricular epicardial
surface of guinea pig isolated spontaneously beating 3 g
hearts using a 6 6 3 mm electrode, and were unable to

*Corresponding author. Email: webster@engr.wisc.edu
Journal of Medical Engineering & Technology
ISSN 0309-1902 print/ISSN 1464-522X online ª 2010 Informa UK Ltd.
http://www.informaworld.com/journals
DOI: 10.3109/03091900903509149

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2

H. Sun et al.

induce VF. They increased the X26 Taser1 waveform more
than 240-fold higher than current densities predicted from
their modelling and were unable to induce VF. They
concluded ‘a lack of arrhythmogenic action of the M26 and
X26 Taser device’. Thus Tasers1 have never caused VF in
small hearts. However Tasers1 have caused VF in the
much larger live pig hearts [6–8]. The similarities between
this study and that of Holden et al. [5] are that we both used
electromagnetic modelling of the human. However, our
study used actual X26 waveforms to actual 9 mm electrodes in intact live pigs with 400 g hearts, which correspond
most closely with live humans, and achieved sustained VF,
whereas Holden et al. [5] were unable to achieve VF with
simulated X26 waveforms.
This study was designed to determine the mean of
probability of Tasers1 (model X26) causing VF in humans
through electrical stimulation, using (1) computer models,
(2) data on dart-to-heart distances that caused VF from
two pig studies, (3) human skin-to-heart minimum distances measured using echocardiography, and (4) data on
Taser1 dart landing statistics from police reports [1].
2. Methods and examples
This study examined the Taser1 model X26, so in the
following sections we will refer to this model as ‘Taser’. By
‘VF distance’ we mean the maximum distance between
Taser dart tip and heart at which VF can be induced. VF
distance is the same as ‘dart-to-heart VF distance’. ‘VF
skin-to-heart distance’ indicates the VF distance plus the
dart length inside the skin.
Two sets of sedated pig study results were used. In one
study, the pig chest wall was resected and a sharp dart
approached the heart [9]. In a second study, a blunt dart
was inserted from the pig’s skin [10]. The dart was blunt to
ensure it does not puncture the heart.
Cell stimulation strength–duration curves derived from
the resistor–capacitor (R–C) cell-membrane models show
that the cell stimulation caused by short duration electric
pulses is governed by the charge. At the surface of the
heart, for the short duration pulses of Tasers, charge
density or the electric field/duration time threshold causes
excitation [11]. Our key strategy to solve the problem was
to estimate the area of the chest skin surface where, if a
Taser lands, VF will likely ensue. This area was determined
by whether the charge density induced on any point of the
heart exceeds the VF threshold charge density. The area is a
function of the minimum skin-to-heart distance (given by
human echocardiography experiments), the shape of the
human torso and heart geometry (using a typical geometry)
[12,13], the length of the dart (measured fixed length), the
charge from the dart (constant for Tasers of the same type),
the assumption about how close the dart tip has to be in
order to cause VF (measured by pig experiments) and the
VF threshold of human heart stimulation. Once known,

this area can be multiplied by the known likelihood of a
dart hitting that area (which is calculated from police data).
To estimate the surface area given one human geometry,
all the above conditions are known except the VF threshold
of human heart stimulation. The human VF threshold for
short-duration electrical stimulation is not available in the
literature. Our pig experiments measured VF distances but
the charge density VF thresholds could not be measured.
Therefore pig VF distances were used to derive internal VF
thresholds using our finite element (FE) computer models.
For the same current waveform with the same duration,
that is, same charge, current density per unit inserted
current can be used as the internal VF threshold. The
charge density is defined as charge per unit area and charge
density is the integration of the current density over time.
Since current density scales linearly with total injected
current and it is assumed charge density scales linearly with
the total charge in the same proportion, the charge density
is only related to the total charge and the current density
per unit inserted current. Since we care about charge
density only, and the total charge is the same for the same
Taser, the charge was not needed. Charge is only useful
when extending the X26 results to other types of EMDs.
Therefore the current density values for 1 A inserted
current were calculated in our FE models.
Current density can be directly calculated by our
electrostatic FE models since the problem could be
approximated as an electrostatic problem in the Taser’s
operating spectrum. The quasi-electrostatic hypothesis was
studied in chapter 2 of [14].
Thus, internal human VF current density thresholds were
first derived using the current density values per unit
inserted current at distances from the skin that equalled the
pig experiment VF distances caused by a Taser dart placed
at similar settings of pig experiments (between ribs) using
3D FE models. In these models we assume that dart-toheart VF distances are the same in pigs and humans.
Such internal VF thresholds calculated by FE models are
useful to derive the VF stimulation area on the skin surface.
All current density values are computed for a 1 A inserted
current and dart placement is moved on the skin surface
with respect to the heart.
Three factors on which VF depends are VF thresholds,
human anatomies and dart landing locations. Different pigs
have different VF thresholds. Different humans also have
different VF thresholds, as well as having different skin-toheart distances. To estimate the probability of VF, we need
to combine information from humans, pigs and dart
locations. However, an atlas of anatomy data for all sizes
of humans was not available.
We modelled the differences in humans by using data of
the minimum skin-to-heart distances measured by echocardiography. A fixed torso anatomy had a global coordinate system noted as x0 , y0 , z0 assuming one
typical human heart and ribs anatomy. A movable local

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Taser1 directly causes human ventricular fibrillation

coordinate system noted as x, y, z permitted the FE model
dart to move around relative to the heart of the fixed global
coordinate system (figure 1). A local system with limited
geometry size also allowed fine FE meshes. The current
density values at the heart for different dart locations and
heart depths were compared to the internal VF thresholds
to determine whether or not VF could occur.
Contours on planes parallel to the skin were deployed to
simplify the process so the problem can be solved by
checking a series of heart slice contours and current density
contours on these planes. A human heart geometrical
model [13] was sliced to show heart boundary contours on
planes parallel to the front skin. Ribs were projected to
determine which electric current density contours should be
used when moving the dart—the contours for a dart
between ribs or a dart on top of ribs or touching ribs.
Current density contours with the internal VF threshold
values were determined on the same planes, and were
generated for different dart locations relative to ribs
(between ribs, on top of ribs or sternum). We determined
the area where VF could be induced if the dart lands in this
location by moving a dart on the torso skin and comparing
the current density values inside the heart with internal VF
threshold values on all planes parallel to the skin. If the
electric current density contour on a plane caused by the
dart intersects the heart slice on the same plane, the dart
lands in an area where VF will be caused. Details will
follow in x2.2.1.
Finally, dart landing statistics were included to calculate
the mean and variance of the total probability of VF. From

Figure 1. The general model with two coordinate systems.
The x, y, z coordinate system is the local coordinate system
for each dart location with the centre of the dart-skin
interface as the origin. The x0 , y0 , z0 coordinate system is the
global coordinate system for the torso.

3

the equivalent dart area where VF will be caused, we
derived the mean and variance of the conditional probability of VF given a dart location on the skin and the dart
location radii where VF will be caused.
For the convenience of illustrating the process, a list of
variables shown in figure 2 follows. Variables starting with
y are distances along the y axis in the local coordinate
system, which is perpendicular to the skin. In the variable
subscript, ‘d’ indicates ‘dart’, ‘h’ indicates ‘heart’, ‘s’
indicates ‘skin’, ‘c’ indicates ‘contour’, ‘min’ indicates
‘minimum’, and ‘VF’ indicates ‘ventricular fibrillation’.
.

.

.

ydh_VF (mm): Dart-to-heart distance that caused VF in
pig experiments [9,10] where a dart was inserted
between ribs. We assume humans have the same VF
distance as pigs.
ysh_VF (mm): ydh_VF þ dart length. Skin-to-heart distance that caused VF in pig experiments, for a dart
inserted between ribs, which follows ysh_VF ¼ ydh_VF þ 9
(mm).
ysh_min (mm): Minimum human skin-to-heart distances
considered for a given VF skin-to-heart distance ysh_VF,
which follows the relation that 10 ysh_min ysh_VF
(mm).

Figure 2. Side view of skin, heart slices, and electric current
density contour planes. One plane is 12 mm away from the
skin. The deepest plane considered is 23 mm away from the
skin if the VF skin-to-heart distance is 23 mm. All distances
are in mm, using the local coordinate system.

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H. Sun et al.

. N_ysh_min: Number of humans with minimum skin-toheart distances in the 1 mm bin [ysh_min71, ysh_min]
(mm) from echocardiography data.
. P_ysh_min: Probability of humans in the bin (ysh_min – 1,
ysh_min), which is estimated as N_ysh_min divided by total
number of humans (150) in the echocardiography data.
. ysc (mm): Skin-to-contour locations of electric current
density contour planes considered (distances from the
skin) in the y-direction, which follow the constraint that
ysh_min ysc ysh_VF. Because only the electric current
density contour planes that could intersect a heart slice
and could have larger current density than the VF
threshold, that is, closer to the skin than the VF skinto-heart distance ysh_VF needed to be considered.
ysc ¼ ysh_min þ yh_depth.
. yh_depth (mm): Human heart slice depths (distance of a
heart slice to the front of the heart), which follow the
relation that yh_depth ¼ ysc7ysh_min (mm). So 0
yh_depth yh_depth_max ¼ (ysh_VF 7 ysh_min) (mm). For
example, the slice at the depth yh_depth ¼ 0 mm was
roughly just one point. Since 0 ysh_VF 33 mm,
10 mm ysh_min ysh_VF, 0 ysh_VF – ysh_min 23 mm,
the deepest heart slice yh_depth_max that needed to be
considered was 23 mm.
. A_ysh_min_ydh_VF (cm2): Area where the dart caused
current density at any point of heart 4 VF threshold)
for a given minimum skin-to-heart distance ysh_min
(mm) and a given VF dart-to-heart distance ydh_VF
(mm). This area was the union of the locations causing
VF for all heart slices under consideration.
. P_hitting1cm2_ysh_min: The probability of a hit in 1 cm2
in B3 and C3 grids [8] on the front chest for this group
of subjects with given minimum skin-to-heart distances
in the bin (ysh_min – 1, ysh_min).
. PVF_ysh_min: Probability of human VF for this group of
subjects with given minimum human skin-to-heart
distance in the bin (ysh_min – 1, ysh_min), which follows
the equation that PVF_ysh_min ¼ A_ysh_min_ydh_VF
(cm2) 6 P_hitting1cm2.
The following subsections give further details.
2.1. FE modelling
In order to compute the probability of the Taser electrically
inducing human VF, different human heart locations and
different dart locations would usually require different
geometrical models. If a single mesh representing one
person’s anatomy or dart location were created for each
combination, the calculation times would have been
prohibitively long. Instead a simplified general model was
designed to make the work solvable. That is, a fine mesh
FE model was created only around a dart including a small
and reasonable region where the dart could cause VF. By
‘general’, we mean we did not create multiple FE models

for all combinations of heart locations and dart locations.
A simplified general model was created for each dart/
human interaction scenario (arcing though the air to one
point on the skin, a dart inserted between ribs, on top of
ribs), by virtue of the following attributes and assumptions
of the problem:
(1)

(2)
(3)
(4)

(5)

(6)

The 9-mm dart penetrates the skin by 9 mm if between
the ribs, or hits the ribs with a shorter penetration
depth of 5 mm, or the Taser electrically arcs through
the air to a single point on the skin.
The current density decreases dramatically with
distance away from the dart.
To determine VF only the current density at the heart
is of interest.
From VF distances in pig data [9,10], only thin
humans with a short dart-to-heart distance need to be
considered as we did not find VF induced above a
certain dart-to-heart distance.
Similarly, the short dart-to-heart distances required
for VF necessitate the dart being over the heart.
Tissues in this domain such as intercostal muscle,
heart and blood have roughly similar conductivities
except for the ribs and sternum.
Lungs were not included in the model between the
dart and heart due to modelling the worst-case
considerations: lungs are usually not on the shortest
path between the skin and the heart, as shown in [10].
Deflated lungs at the end of expiration have similar
conductivity as muscle and inflated lungs would cause
lower current density in the heart. If you are thin and
put your fingers between your ribs right over your
heart (at the point of maximum impulse) you can feel
your heart beating right on the other side of your ribs
during the portion of the breathing cycle when the
lungs are deflated. The 9-mm dart of a Taser can easily
penetrate the skin, 5 mm of fat into the intercostals
muscle and get within 2 mm of the heart. Hence we
assume lack of skin, fat and lung tissue.

The current density values for a 1 A inserted current at
the same dart-to-heart distance and for approximately the
same dart placement as in the pig experiments [9] (sharp
dart inserted between ribs) generated internal VF threshold
current density values. The FE modelling results showed
that the difference of the current density values at the heart
locations caused by blunt and sharp darts could be ignored.
Thus the internal VF threshold current densities for VF
distances for pig data using a blunt dart [14] used the sharp
dart in the FE modelling.
For other dart placements (on top of ribs or sternums),
the FE models were used to calculate the current density
while keeping the injected current constant. For a human
with different anatomy, characterized by the minimum
skin-to-heart distance, the current density values at

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different skin-to-heart distances could be derived from the
same model without creating new FE geometry for new
anatomy due to attributes (1)–(6) above.
2.1.1. Software and hardware. ABAQUS 6.5 (ABAQUS,
Providence, RI, USA) was used to solve the FE model for
current density. MSC PATRAN 2005 (MSC Software
Corporation, Santa Ana, CA, USA) was used to generate
the geometry and generated the mesh input file for
ABAQUS. MATLAB 7.4 was used to preprocess and
postprocess the input and output data for ABAQUS. Each
ABAQUS model was run on a computer with Linux
operating system. It required 3 GB of memory, at least 4.08
GB hard drive allocated for generated files, and took about
1.5 h with an additional 0.5 h for postprocessing using
MATLAB. Each PATRAN model was run on a Sun Blade
1000 computer with a UNIX operating system that had a
2.5 GB memory, and took about 3 h [14].
2.1.2. Geometry modelling. FE models with simplified
geometry were created using the PATRAN software. FE
models of a box size of 60 6 40 6 60 mm with one dart
inserted in the centre of the skin surface and other surfaces
grounded were designed to compute current densities
between the dart and human heart.
The VF dart-to-heart distances from pig experiments
ranged from 0 to 24 mm and had a 2 mm resolution. For
the 9-mm long dart, the human VF skin-to-heart distances
would range from 9 to 33 mm. Thus only heart slices
located less than 33 mm deep from the skin had to be
considered to match the pig experimental data. The current
density decreased dramatically away from the dart tip, so
placing the current sink depth at 40 mm was satisfactory
for a human torso thickness of about 180 mm.
Two dart types were modelled, both with a diameter of
0.8 mm and length of 9 mm. The sharp dart with omitted
barb was modelled as a cylinder of 6 mm abutted to a
cone of 3 mm for all results in this paper, unless
specifically labelled blunt. We assumed the barb does
not make a significant difference to current density at the
heart and it was omitted for simplicity. The tip-less blunt
dart was modelled as a 9-mm long cylinder. An electric
arc passing from the dart though clothing to the skin was
modelled with the current injected at a single point on
the skin.
A source voltage (þ5 V) was assigned to the dart surface,
or to one mesh node when an electric arc was simulated. A
sink voltage (–5 V) was assigned to the five surfaces other
than the skin. While Taser devices have two darts, we used
only a single dart in the models because in preliminary
models we found similar current density values around a
single dart model as in two-dart models due to the large
distance (416 cm) between the darts. The resulting current
densities in the model were scaled such that the total
inserted current was 1 A.

5

The size of two ribs was determined by measuring the rib
cross section in figure 4 of [15]. The ribs were modelled as
elliptical cylinders 5 mm below the skin with a width of
12 mm, a thickness of 5.12 mm, a length of 60 mm and a
separation of 18 mm. The rest of the box outside of the
elliptical cylinders was assumed to be muscle. The sternum
was modelled as an elliptical cylinder with a width of
30 mm [16], a thickness of 10 mm [17] with the same
conductivity as bone. All the elliptical cylinders in the
model had a length of 60 mm which was the same as the
box. The models for the situations when the dart was
inserted between ribs, touching one rib, on top of one rib
(the length of dart penetration was only 5 mm) and at a
single point on the skin were created in PATRAN.
2.1.3. Mesh generation and tissue properties. The dominant
tissues between skin and heart are muscle and cartilage. Far
away from the sternum the ribs are bone with low
conductivity. Near the sternum over the heart the ribs
consist of cartilage with medium conductivity for people
below 35 years of age, and of bone with low conductivity
for people older than 35 years. By setting the conductivity
of the two ribs the same as bone, a new model for ribs was
obtained, and another model without ribs or cartilage was
obtained by setting the conductivity of the two ribs the
same as muscle. Comparison of ribs, cartilage or muscle
was conducted for a dart inserted between ribs.
All tissues were treated as isotropic. We did not model
the anisotropic characteristics of the bidomain model
because of computer limitations. Ribs had conductivities
for bone or cartilage while all other tissues had conductivities of muscle. Table 1 provides the number of tetrahedral
elements and the conductivity of each tissue. The conductivity values were based on the frequency-dependent
tissue conductivity model developed by Gabriel et al. [18].
A frequency of 5 kHz was chosen since it is the first
dominant peak of the X26 power density spectrum [14]. A
tetrahedron element type was chosen since its shape was
suitable to generate a quality mesh for geometry with
curvatures such as darts and ribs in our application. We
used a global element edge length of 1 mm for non-rib
parts. The accuracy of FE models with tetrahedral elements
of a global edge length of 1 mm was validated by a
convergence test and by comparing results with those
obtained by other methods, such as analytical equations.
The element size was small enough so that the 2-mm
resolution pig experimental data could be used effectively,
but not so small that there were too many elements to
permit ABAQUS to solve the problem.
2.2. VF probability calculation
2.2.1. Determining dart locations where VF will be caused.
For a given person (the minimum skin-to-heart distance
ysh_min and VF threshold) and given dart location and given

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H. Sun et al.

Taser, the VF probability was either 1 or 0. Heart and ribs
anatomy and current density contours around a dart with
the values of the internal VF thresholds were considered
together to determine the dart locations where VF will be
caused.
The minimum skin-to-heart distances ysh_min for standing humans measured from echocardiography in the Adult
Echocardiography Laboratory at the University of Wisconsin Hospital and Clinics were used to characterize
variations of human anatomy [14,19]. The studies were
performed on standard ultrasound equipment manufactured by Philips Medical Systems (Andover, MA, USA),
Siemens Acuson (Malvern, PA, USA), or General Electric
(Waukesha, WI, USA). Standard adult transducers were
used. Transducers were evaluated to check for accuracy of
the measurement capability of the systems using standard
phantoms. 2D echocardiograms were performed in 150
consecutive adults. Three views were obtained, the first
being the best possible parasternal (sternal border) long
axis (vertical) view of the heart, the second being the best
apical (tip) four-chamber view of the heart and the third
being the best subcostal (under ribs) four-chamber view.
For each imaging location an average of 10 beats were
obtained during quiet respiration. After the recordings of
the images in the subjects were made, the information was
downloaded into a Camtronics Workstation. Images were
analysed to determine the shortest linear distance from
sector origin (skin surface) to epicardial surface. Using the
analysis package on the workstation, the workstation was
calibrated, and the calibration marks on the ultrasound
loop for each measurement were made. Data were
mean + standard deviation (SD), analysed by ANOVA.
The other parts of human anatomy used a typical
anatomy of the heart and ribs. To create a typical anatomy,
the Utah ribs [12] and Texas heart [13] (figures 3–6) were
combined by rescaling and translating the Texas heart
mesh. The relative location of the heart to ribs in x0 and z0
directions was verified by checking with anatomy experts
and references [20]. The relative distance of the heart from
the front of skin in the y0 direction was not considered,
since later the heart was placed at different y distances
according to the echocardiography data, and current
density in the heart for that heart location was determined.
Since the x0 –z0 plane (chest frontal plane) differs from the
x–z plane where the dart was inserted in the FE model, the
anatomy geometry was rotated to align the chest frontal
surface x0 –z0 plane with the FE model x–z plane.
The current density values at the locations corresponding
to the VF distances away from the skin on the axis
perpendicular to the skin caused by a sharp dart inserted
between two ribs made of cartilage were used as the internal
current density VF thresholds for all VF distances
measured from the pig experiments. The contours of
electric current density caused by a dart on planes parallel
to the skin and contours of heart slices parallel to the skin

were generated. The electric current density contours for
the dart between the ribs and hitting the ribs were used to
calculate the probability of VF. The dart touching the rib
was similar to between the ribs as shown in [14], so these
were combined. Thus the current density contour for a dart
between the ribs was used for the dart touching the ribs.
For a specific dart location, when any heart boundary
contour at any depth yh_depth intersected with the current
density contour with the value of the internal VF threshold
on that plane ysc (¼ ysh_min þ yh_depth), it was assumed that
VF occurs, given that VF threshold. This contour
examination was performed for planes at distances
ysc ¼ yh_depth þ ysh_min from the skin. The dart was moved
around on the skin surface to derive the area where VF will
be caused for the given heart location. Convolving the
current density contour with the internal VF threshold
value corresponding to a given VF distance and the heart
slice area on the same plane, parallel to the skin, results in
the dart area where VF will be caused for that plane, given
the VF distance. Both heart boundary contours and current
density contours were approximated as circles. Then, the
dart area where VF will be caused considering a certain
plane parallel to the skin was estimated as a circle with a
radius of the sum of the radii of the heart slice and
the electric current density contour, with the value of the
internal VF threshold on the same heart slice caused by the
dart placed on the skin (figure 3).
For the locations where ribs were above the heart, the
current density contours for a dart hitting ribs were used.

Figure 3. Dart location area (at the skin) most likely to
cause VF for a heart slice (at a given depth below the
horizontal striped circle) is estimated as a horizontal striped
circle with a radius of the sum of (1) the heart slice radius
(vertical striped circle) and (2) the electric current density
contour (dashed line circumference) on the heart slice
caused by the dart placed on the skin. For the heart
locations (less than 33 mm from the skin), heart slices
closer to skin have a smaller radius but have a larger
current density contour. So all heart slices for one given
heart location must be checked to determine a maximum of
the sum of the heart slice radius and the electric current
density contour on the heart slice caused by the dart placed
on the skin.

Taser1 directly causes human ventricular fibrillation

7

Table 1. Description of the models.
Tissue
Two elliptical ribs

Other parts in the box

Number of tetrahedrons

Global edge length (GEL)

Minimum edge length

56 842{
58 083{
59 119x
1 177 199{
1 168 989{
1 128 226x

4.7 mm
4.7 mm
4.7 mm
1 mm
1 mm
1 mm

GEL 6 0.1
GEL 6 0.1
GEL 6 0.1
GEL 6 0.2
GEL 6 0.2
GEL 6 0.2

Conductivity (S m71) at 5 kHz
0.17552
0.020346
0.33653
0.33653
0.33653
0.33653

(cartilage)
(rib)
(muscle)
(muscle)
(muscle)
(muscle)

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{The model has a sharp dart with 0.8 mm diameter.
{The model has a blunt dart with 0.8 mm diameter.
xThe model has one node electric source as arc of dart.

For the locations where the heart was exposed without ribs,
the current density contours for a dart inserted between the
ribs were used.
The overall dart area where VF will be caused for a
person with a heart at a given minimum skin-to-heart
distance ysh_min (i.e. measured at the location where the
heart is closest to the skin) using a certain VF distance
ydh_VF from pig data was estimated by the union of the dart
areas where VF will be caused if a dart hits within that area,
considering all planes of the heart parallel to the skin
deducting the sternum area, where a dart will not penetrate
near the heart. Assuming the circles on different planes are
concentric, the largest radius where VF will be caused over
all planes corresponded to the union of all heart slices for
each heart location. For the heart locations we were
interested in (less than 33 mm from the skin), when the
heart slice radius increases, the electric current density
contour on the heart slice decreases. So the sum of the two
does not have a monotonic trend. Therefore we examined
all the heart planes/slices to determine a maximum size of
the radius where VF will be caused. Such procedures were
then repeated for each VF distance from the pig datasets.
To illustrate how to determine dart locations where VF
will be caused for a given VF distance threshold and human
heart location, we give an example using some figures that
would normally appear in the results section. The following
example is for a dart-to-heart VF distance ydh_VF of 14 mm
and a person with minimum skin-to-heart distance ysh_min
of 11 mm.
First using the FE model shown in figure 4, the current
density values at these locations corresponding to VF
distances on the y-axis (dart direction) for the dart inserted
between the ribs were found using interpolated current
density values on the y axis for the dart-to-heart distances
ydh_VF of 0, 2, 4, 6, . . ., 24 mm, or ysh_VF ¼ 9, 11, 13, 15, . . .,
33 mm. These yielded the internal VF threshold current
density values (figure 5). For a given dart-to-heart VF
distance of ydh_VF ¼ 14 mm, the VF skin-to-heart distance
would be ysh_VF ¼ ydh_VF þ 9 ¼ 14 þ 9 ¼ 23 mm. The current density along the y-axis at y ¼ 23 mm was 358 A m72,
according to figure 5. Therefore, 358 A m72 was used as the
internal VF threshold current density for the pig data that
caused VF on the heart 14 mm from the dart tip.

Figure 4. The cut view of the mesh from the
60 6 40 6 60 mm FE model for the sharp dart of 0.8 mm
diameter on the plane of x ¼ 0 shows a 9 mm dart between
two 5 6 12 mm elliptical ribs spaced 18 mm apart and
5 mm away from skin.
For each pig VF skin-to-heart distance of ysh_VF (mm),
the humans with their hearts located at various minimum
human skin-to-heart distances ysh_min based on echocardiography data were studied. The considered ysh_min for a
given ysh_VF follows 10 mm ysh_min ysh_VF, where
10 mm is the shortest distance from echocardiography.
For each person with the heart front located at ysh_min, only
heart slices at depths less than or equal to the VF skin-toheart distance ysh_VF needed to be considered, since from
the pig data no VF occurs at larger depths. This example
used the pig VF skin-to-heart distance of ysh_VF ¼ 23 mm,
so the minimum human skin-to-heart distances considered
were larger than 10 mm and smaller than the VF skin-toheart distance ysh_VF of 23 mm. Also a minimum human
skin-to-heart distance of 11 mm lies in the range of [10 mm,
23 mm]. For this distance of 11 mm along the y-axis from

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8

H. Sun et al.

Figure 5. For a 1-A inserted current, the contour lines of
current density (A m72) on the plane of x ¼ 0 for a sharp
0.8 mm dart. The current density values along the dart
direction (y) pointed toward the heart will be used as the
internal VF threshold current density values for the
corresponding VF distances. Current density numbers have
three significant digits. All distances are in mm, using the
local coordinate system.
the skin to the front of the heart, we needed to decide how
many heart slices needed to be considered. The deepest
considered heart slice in this example was located at the VF
skin-to-heart distance ysh_VF from the pig data used, that is,
23 mm. The depth relative to the front of the heart for the
heart slice was labelled on the heart contour map (figure 7).
The depth of the heart slice was simply the distance of the
heart slice to the front of the heart. The depth of the
deepest considered heart slice was the y-axis location of
the deepest heart slice minus the y-axis location of the front
of the heart: yh_depth_max ¼ ysh_VF – ysh_min ¼ 23 – 11 ¼
12 mm (figures 2, 7). Therefore the relevant heart slices
considered were at depths of 0 yh_depth yh_depth_max ¼
12 mm. The equivalent radii of the heart boundary contours were estimated by the distances between the contours
and the origin on the diagonal lines of the contour squares.
We needed to consider current density contours and
heart slices on a series of planes located at y-axis
coordinates ysc, where ysh_min ysc ysh_VF. In this example, 11 mm ysc 23 mm.
First we looked at a specific plane ysc ¼ 23 mm. The
current density contours on the y ¼ 23 mm plane for a dart
inserted between the ribs is shown in figure 6. In figure 6, we
looked for the current density contour with the value of the
internal VF threshold 358 A m72 determined from figure 5.
It had a radius of about 18 mm. Since the front of the heart
was at y ¼ 11 mm, the heart slice depth on this plane for
this person was 23 mm – 11 mm ¼ 12 mm. From the
overlaid graph of ribs and heart slices (figure 7), the heart
slice at that slice depth 12 mm had a radius of about 33 mm

Figure 6. For a 1-A inserted current, the contour lines of
current density (A m72) on the plane of y ¼ 11 mm for a
sharp dart inserted between two cartilage ribs (two pairs of
dotted lines). VF y ¼ ? (where ? is the number shown) by
each contour line labels the VF distance plus dart length
(9 mm) predetermined from figure 5 for the internal VF
threshold with the current density value of that contour line
in figure 6. So each contour line in figure 6 encircles an area
subject to VF when a dart lands at the origin (x ¼ 0, z ¼ 0)
and between ribs, for the labelled VF y ¼ ?. Current density
numbers have three significant digits.
in chapter 4, table 1 of [14]. The dart area where VF will be
caused on the skin surface for this heart slice in this
example was estimated to have a radius of 33 mm þ
18 mm ¼ 51 mm, if using the contour for a dart between
ribs.
Then we examined all planes considered. In this example,
minimum skin-to-heart distance ysh_min was 11 mm; these
planes were at distances [11 mm, . . ., 23 mm] from the skin
as shown in table 2.
2.2.2. Mean estimation of VF probability. After determining
dart locations where VF will be caused for all relevant
human minimum skin-to-heart distances and pig VF
distances, the total probability of Tasers directly causing
VF in humans was estimated by combining these data with
the dart landing probability distribution in table B-1 of [1].
The probability of a hit in 1 cm2 in the frontal chest
area for each group of human minimum skin-to-heart
distances (P_hitting1cm2_ysh_min) was calculated [9,10]
using dart landing data and human height of the group.
Multiplying this probability by the dart location area
(in cm2) where VF will be caused for the same group

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(A_ysh_min_ ydh_VF) yielded the human VF probability for
this group PVF_ysh_min. The mean of the total VF
probability was obtained by aggregating PVF_ysh_min over
all groups of human minimum skin-to-heart distances and
pig data, assuming the dart landing locations, the pigs in
the pig experiments and the humans in the echocardiography experiments were all independent with equal
probability of occurrence, and assuming the human VF

Figure 7. Contours of the rotated ventricle slices at depths 0
to 24 mm under rotated ribs. Values on the contours show
the depths (distance to the plane closest to the rotated skin
with the same rotated angle). The heart slice at depth i mm
was labelled with i. Depth i corresponds to yh_depth (column
4 in tables 2 and 3). The front view of the 0 mm depth heart
slice closest to the skin shows that the closest place was on
the right ventricle. Gray colour indicates the projected
sternum and ribs. Axes use the global coordinate system,
while heart depths are relative to the front of heart.

9

probability had same equal mean and variance as in data
from each pig.
Conditional VF probability was estimated for each
dart-to-heart radius (horizontal distance) on the frontal
chest plane (i.e. a plane perpendicular to the dart
insertion direction). The estimated conditional VF probability for a certain dart-to-heart radius is where the
proportion of samples with a dart area radius is equal to
or larger than that dart-to-heart radius. More details are
given in x2.2.5.
2.2.3. Estimating the variance of the VF probability. There
were three sources of variance for the VF probability:
humans (echocardiography data for skin-to-heart distances), pigs (VF distance data) and dart hitting data.
Briefly, pigs were assumed independent and each pig (not
the VF threshold values provided by pigs) had equal
probability. Humans were assumed independent and each
human had equal probability. For given pig data, VF
probability values for humans were assumed independent
and had a same mean and variance. But human VF
probability values for one pig datum may have different
mean and variance from human VF probability values for
another pig datum. The human VF probability values
follow a mixture of the conditional distributions given each
pig. Dart hittings provided a multiplier (proportion of
hittings falling in B3 and C3 grids) when calculating
probability values. The hitting proportion was assumed
independent with pigs and humans. So the expectation of
the product was the product of the expectations and the
variance was also derived.
First the sample mean and sample variance of human VF
probability, given each pig datum, were calculated. Then
the sample means based on each pig datum were averaged
to get the sample mean aggregated over all pigs and
humans. The sample variances based on each pig datum

Table 2. Probability results based on pig data using blunt probe [19] of VF skin-to-heart distance ysh_VF ¼ 8 þ 9 ¼ 17 mm), internal
VF threshold current density ¼ 773 A m72 for 1 A inserted current.
ysh_min (Min. skin
to heart distances
for the given VF
dart-to-heart
distance)
17
16
15
14
13
12
11
10

P_ysh_min ¼ N_ysh_min /150
(Fraction of
population with
min skin to heart
distance ysh_min)
0.0133
0.00667
0
0
0.02
0.00667
0.00667
0

ysc ¼ [ysh_min,
ysh_min þ
1, . . ., ysh_VF]
(Electric current
density contour
plane locations)

yh_depth ¼ ysc – ysh_min ¼
[0, 1, . . ., ysh_VF – ysh_min]
(Heart slice depths)

A_ysh_min_ydh_VF (cm2)
(Area where the dart
was most likely
to cause VF)

[17]
[16, 17]

[ 0]
[ 0, 1]

0
0.00716

[13, . . ., 17]
[12, . . ., 17]
[11, . . ., 17]

[0, . . ., 4]
[0, . . ., 5]
[0, . . ., 6]

0.532
1.61
3.33

PVF_ysh_min ¼
A_ysh_min_ydh_VF 6
P_hitting1cm2_ysh_min
(VF Probability for
people with ysh_min)
0
0.00000267
0
0
0.000204
0.000583
0.0012
0

The population VF probability estimated (by summing the products of columns 2 and 6) for pig data using a blunt probe VF dart-to-heart distance,
ydh_VF, of 8 mm is 0.0000161.

10

H. Sun et al.

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were averaged to get the sample variance aggregated over
all pigs and humans.
The count of hits falling in B3 and C3 grids was assumed
a binomial distribution. The mean of the proportion was
estimated as the count of hits in B3 or C3 divided by the
total count of hits. Then based on independence between
hitting and humans or pigs, the variance of the product was
derived.
2.2.5. Conditional VF probability as a function of dart-toheart horizontal distance (radius). Intuitively, the closer the
dart to the heart, the more likely VF would be caused.
Although a dart on a circle with a certain radius from the
heart could not cause VF if the dart were located on top of
the sternum, in this process, the estimation of dart area
radius most likely to cause VF was based on a situation
where the dart does not land on the sternum. This will
overestimate the conditional VF probability. But the goal
of the paper is to study the total VF probability, not the
conditional VF probability. It is more of interest to verify
the relation between the conditional VF probability and the
dart-to-heart radius.
The equivalent dart location radii (before considering the
sternum) where VF would be caused were already
calculated for each human and pig datum when calculating
the total VF probability. Assuming the VF probabilities for
each human datum and pig datum were independent with
equal probability, for a certain dart-to-heart horizontal
distance, the proportion of samples with a radius where VF
would be caused equal or larger than that distance was the
estimated VF probability for that distance. The distance
most likely to cause VF would be the locations appearing
most frequently.
Given a dart on a circle of a given radius r, reusing the
symbols used in derivation for the dart hitting count in
Appendix 2.2 in [14], assume a randomly-drawn sample of l
samples were independent and have the same probability W
of VF, then the count of VF in l trials, denoted by O, has a
binomial distribution with parameters W and l.
EðOÞ ¼ l W; VarðOÞ ¼ l Wð1ÀWÞ;

ð1Þ

where O is the number of samples with radius where VF
would be caused equal to or larger than r and l ¼ mn.
^ ¼O
W
l
^
^
^ WÞ
^ ¼ Wð1 À WÞ :
Varð
l

ð2Þ

ð3Þ

3. Results
3.1. FE model results
We created FE models using the geometry similar to figure
4 with (1) the dart inserted between the ribs; (2) the dart

inserted touching the edge of one rib; (3) the dart inserted
on the centre top of one rib; (4) the dart away from the skin
with an electrical arc to skin, as a node on the skin between
two ribs; (5) a node on the skin in front of one rib edge; and
(6) a node on the skin in front of the centre of one rib. Here,
we reduced these to three example categories and only
present these: dart inserted 9 mm, dart inserted 5 mm, dart
as a node. For a dart hitting the ribs, its maximum current
density on the same heart slice was always smaller than that
for a dart between the ribs.
Results of current density on the y axis of the x ¼ 0
plane, for the two 0.8 mm diameter dart shapes (sharp
and blunt) show that (1) the current density for the blunt
dart was higher than the sharp dart, except at the end of
the dart; and (2) the difference at the dart tip was about
45%, and when close to the dart it was as large as 26%
although it was less than 10% after y ! 17 mm. Thus the
sharp dart model was always used. If the heart was
17 mm away from the skin, an approximate shape of the
dart (blunt) yielded the correct answer at the heart with
less than 9% error.
Figure 5 shows current density contours in the y–z plane
at x ¼ 0 for a sharp dart as used for the model of a dart
inserted between two ribs, for a 1 A inserted current. The
internal VF threshold current density values were determined using figure 5 corresponding to the pig VF distances.
For a given VF distance (for example VF skin-to-heart
distance y ¼ 23 mm) and the corresponding internal current
density VF threshold (358 A m72), the y ¼ 11 mm plane
had a larger VF threshold current density contour (about
18 mm radius) than the y ¼ 23 mm plane (about 1 mm
radius).
Figure 6 shows a sample current density contour on the
plane of y ¼ 23 mm, for 1 A inserted current. If an internal
VF threshold current density determined by figure 5 was
358 A m72, the current density values inside the contour
line in figure 6 with that value were greater than 358 A
m72. Therefore the area encircled by that contour line is
subject to VF for a dart inserted at the origin (x ¼ 0, z ¼ 0)
of figure 6, for the given VF y ¼ 23 mm.
In terms of current density caused at the heart, the dart
inserted between the ribs was the most likely to cause VF,
followed next by the dart touching ribs, followed then by
the Taser electric arc on one node between ribs and the dart
on the ribs. The results for the Taser electric arc on one
node and the dart on the cartilages were similar. Current
density distribution for the dart touching ribs was less than
10% different from current density for the dart between
ribs. That was because the dart depth for both cases was the
same (9 mm). The bones provided better shields for the
current than the cartilages.
The heart ventricles were sliced into surfaces parallel to
the skin, with a slice of depth 0 being the slice closest to the
skin (figure 7). Since the dart locations most likely to cause
VF were aligned with or larger than the heart contours, the

Taser1 directly causes human ventricular fibrillation

locations closer to the heart were more likely to cause VF
except above the sternum (where the dart does not
penetrate near the heart). The locations away from ribs
were more likely to cause VF than close to ribs. According
to our sternum modelling results, darts hitting sternum
locations did not cause VF. So the sternum area was
subtracted from the dart area most likely to cause VF based
on contour results for cartilage ribs to yield the final
estimated A_ysh_min_ydh_VF.

11

person with that skin-to-heart distance is vulnerable to a Taser
is listed in column 6. The sum of the products of column 6 with
the fraction of such minimum skin-to-heart distances
P_ysh_min (column 2) was the estimated probability of
0.0000161 for that VF distance data ysh_VF ¼ 8 mm.
Because the minimum human skin-to-heart distance
ysh_min from echocardiography data was larger than
9 mm, data for VF distances smaller than 9 mm did not
need to be considered.

Mean VF probability for data from a pig when using a blunt probe ½10Š
¼ VF probability for VF distance ydh VF of 2 mm  fraction of pig VF data at 2 mm

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þ VF probability for VF distance ydh
þ VF probability for VF distance ydh
þ VF probability for VF distance ydh
þ VF probability for VF distance ydh
þ VF probability for VF distance ydh

VF
VF
VF
VF
VF

of 4 mm  fraction of pig VF data at 4 mm
of 5 mm  fraction of pig VF data at 5 mm
of 6 mm  fraction of pig VF data at 6 mm
of 7 mm  fraction of pig VF data at 7 mm
of 8 mm  fraction of pig VF data at 8 mm

¼ 0 Â 1=10 þ 0:000000235 Â 2=10 þ 0:000000817 Â 1=10 þ 0:00000264 Â 2=10 þ 0:00000688 Â 1=10
þ 0:0000161 ðsee table 2Þ Â 3=10 ¼ 0:000006:

3.2. Calculating probabilities of VF
In [14] we used table B-5 of [1] to calculate dart hit areas.
Later we discovered errors in table B-5 (centre of grid box
F ¼ 0.06 from which height F ¼ 0.12, which does not match
figure B-1 of [1]). To improve accuracy of this paper we
measured distances on figure B-1 of [1]. The probability of a
hit in 1 cm2 frontal chest area by a dart (P_hitting
1cm2_ysh_min, a multiplier in column 6 in tables 2 and 3)
varies with the height of the subject with an estimated
mean ¼ (probability of hit in frontal chest area)/(area of
frontal chest area in cm2) ¼ [(number of hits in frontal chest
area)/(total number of hits)]/(area of frontal chest area in
cm2) ¼ [(373 þ 463)/3039]/786.7 ¼ 0.00035. Here 373 and 463
were hit counts from police reports provided in Table B-1 of
[1] for grids B3 and C3 on figure B-1. The total number of hits
was 3039. The frontal chest area was calculated from the area
of grids B3 and C3 on the frontal chest. We used the heights
for 150 people in the echocardiography data to scale figure B1 of [1] and derived the grids area estimated as about
786.7 cm2. This frontal chest area is smaller than that in [14],
which used Table B-5 of [1].
Table 2 shows an example for blunt probe pig data with VF
dart-to-heart distance ydh_VF of 8 mm. Several minimum skinto-heart distances need to be considered. For each minimum
skin-to-heart distance ysh_min (column 1), a range of heart
slices and electric current density contours for the same heart
slice located at skin-to-contour distances ysc (column 3) were
considered. The area of the heart slice at depth yh_depth
(column 4) can be found from figure 7. The probability that a

Estimated population variance and standard deviation of
the VF probability for data from a pig when using a blunt
probe were about 0.000000004 and 0.00006.
Similar calculations for resected chest wall pig data
yielded mean VF probability of 0.001. Estimated population variance and standard deviation of the VF probability
using resected chest wall pig data was about 0.000011 and
0.0034. Details for all dart-to-heart distances are in [14].
In both studies, bootstrap methods yielded approximately the same results of mean and variance. There was
very strong evidence against the hypothesis that the VF
probability was zero.
The estimated conditional VF probability as a function
of dart-to-heart radius (horizontal distance measured
parallel to skin surface) both for data from a pig having
a resected chest wall and for data from a pig when using a
blunt probe are in [14], chapter 4, figures 9–10. It is shown
that the VF probability decreases with the dart-to-heart
horizontal distance. The dart-to-heart radius most likely to
cause VF (the circle within which a dart could cause VF)
had a maximum of 53.2 and mean of 7.9 mm for data from
a pig having a resected chest wall, and a maximum of 17.3
and mean of 0.18 mm for data from a pig when using a
blunt probe. The dart-to-heart radius most likely to cause
VF describes a situation where the dart does not land on
the sternum.
4. Discussion and conclusions
Recently there has been considerable discussion on the
safety of Taser devices [1]. Since Tasers stimulate nerve and

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12

H. Sun et al.

skeletal muscle, they may also stimulate the heart (cardiac
muscle) and therefore one possible risk of Taser weapons is
that of inducing VF in humans. VF is fatal if not corrected
within minutes. Note that the VF mechanism is not
completely understood. Only VF caused by electrical
stimulation was studied in this paper. This paper only
considers one mechanism for induction of VF whereas in
fact other mechanisms might be more likely to result in VF
in some subjects, e.g. mechanical impact, stress, drug
overdose, or spontaneous VF due to heart dysfunction such
as coronary artery disease.
The goal of the current study was to estimate the risk
of inducing VF in humans by electrical stimulation by
Tasers, using computer models in combination with other
available data. Our computer modelling results show that
current density is very high near the Taser dart, and
rapidly decreases with increasing distance from the dart
(figure 5). Using previous data on distances between
Taser dart and heart at which VF could be induced in
pigs, we estimated internal current density VF thresholds
for different skin-to-heart distances (figure 5). Depending
on how deep the heart is located in a specific person, we
estimated the probability of inducing VF after Taser use
(see table 2). Combined with data on variability in heart
location among humans, we estimated the mean and
variance of the total probability of human VF after
Taser use, VF probabilities conditioned on dart-to-heart
horizontal distance and dart location radii most likely to
cause VF for two different pig studies.
The outer skin, fat and muscle layers in the pig study
using a blunt dart were not resected. Thus a portion of
the current inserted through the 9 mm dart could flow to
the outer layers (in the FE model it could not). At a VF
distance, the actual VF current density at the heart could
be lower than that estimated from the FE model. This
could explain the smaller dart-to-heart VF distance and
VF probability for data from a pig when using a blunt
probe than for data from a pig having a resected chest
wall. Nanthakumar et al. [7] placed subcutaneous darts
parallel to the skin of pigs and administered epinephrine
as a continuous intravenous infusion at a dose of 0.1 g
kg71 min71 to 0.7 g kg71 min71 titrated to increase the
animal’s heart rate to a 50% increase from the baseline
before discharges. They obtained VF for 1 X26 discharge
in 16 for a dart-to-heart distance of about 45 mm.
Dennis et al. [6] exposed pigs to two prolonged 40-s X26
discharges. They obtained VF for two out of six
experimental pigs for a dart-to-heart distance of about
45 mm. Walter et al. [8] exposed pigs to two 40-s X26
discharges. They obtained myocardial capture and postdischarge ventricular tachycardia for 1–17 s for all discharges, and VF for one out of eight pigs for a dart-toheart distance of about 45 mm. For data from a pig
having a resected chest wall [9] the average dart-to-heart
distance that caused VF was 17 mm. For data from a pig

when using a blunt probe [10] the average dart-to heart
distance that caused VF was 6.2 mm. While the five
studies used different testing techniques, all showed that
the probability of VF for some human locations is not
zero. The procedures used in the blunt probe study were
least disturbing to the pig and hopefully most accurate.
In addition to VF probability, we also calculated the
radius of the location area where the dart is most likely
to cause VF.
The estimated VF probability is contingent on a number
of assumptions and limitations from all steps of the whole
project: pig experiments, human data measurements, circuit
measurements and FE modelling. Each known or unknown
factor could contribute to the deviation of the estimation
away from the true value. For example:
(1) It was assumed that all darts were perpendicular to
the skin. Those darts with nonperpendicular angles
had a penetration depth of less than 9 mm.
(2) Our FE model used one centred dart surrounded by
grounding. The results may be slightly different using
two darts on a full torso model.
(3) The internal VF thresholds used FE models with a
sharp dart only.
(4) It was assumed that all darts were on bare skin. If
clothing were present, the arc may jump to the skin
but the penetration depth would be less than 9 mm.
(5) Our FE model used isotropic electric conductivities.
At Taser frequencies, intercostal skeletal muscles
have a small anisotropy.
(6) Isoflurane anaesthesia used during the pig studies
alters the VF induction in the pig, and increases the
VF threshold [21].
(7) VF induction in the human may differ from that in the
pig.
(8) Lungs were not considered.
(9) The human subjects in the echocardiography data
may not resemble the usual Taser subjects.
(10) The model simplification process tended to consider the worst case and tended to estimate a
probability higher than without the simplification.
But the estimated mean VF probability could not
be claimed as an upper bound for the true
probabilty because there are unclear effects of
many other factors besides FE modelling, known
or unknown.
Most of the assumptions would cause only a small change
in the result.
Predicting the likelihood of rare events is highly uncertain
in general. The Taser causing direct VF is a rare event, and
thus is difficult to estimate. There are many uncertainties in
the animal tests and the computer modelling. Thus these
results are a best estimate that provides an order of
magnitude of the probability of this rare event.

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Taser1 directly causes human ventricular fibrillation

The presented results may help to determine appropriateness of use for Tasers when apprehending offenders.
The dart-to-heart distances most likely to cause VF on
the skin plane (radius) were small (up to about 53 mm
for resected chest wall data). VF need not be fatal. It can
be reversed if a defibrillator is used within minutes.
Myerburg et al. [22] suggested that a defibrillator is
carried in police cars.
Necessary, but not sufficient, conditions for direct
electrocution of the heart by the Taser are (1) dart landing
in a frontal region near the heart suggested by our results
and results of others, and (2) cardiac arrest of the subject
shortly after Taser firing suggested by the literature.
Coroners should seek to confirm these conditions before
ascribing Tasers as a contributing cause of death. These
results suggest that during police training Taser darts
landing on the back of the torso are less likely to cause VF
than darts landing on the front because the back is farther
from the heart. For any electromuscular incapacitating
device that has (1) a pulse duration much shorter than the
time constant for cardiac excitation of about 2 ms, (2) low
duty cycles, and (3) a dart 9 mm long and 0.8 mm in
diameter, these results would be transferable by using the
strength–duration curve [11]. A standard for Tasers has
been proposed [23].
This is the first study that provides a positive numerical
estimate of the probability that Tasers can cause VF in
humans.
Acknowledgments
This project was supported by Grant No. 2004-IJ-CXK036 awarded by the National Institute of Justice, Office of
Justice Programs, US Department of Justice. Points of view
in this document are those of the authors and do not
necessarily represent the official position or policies of the
US Department of Justice.

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