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TBME-00604-2005.R3
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Finite Difference Modeling of the Anisotropic
Electric Fields generated by Stimulating Needles
used for Catheter Placement
James Ch. Davis, Norman E. Anderson, Jason G. Ramirez, F. Kayser Enneking, and Mark W. Meisel
Abstract— The use of peripheral nerve blocks to control pain
is an increasing practice. Many techniques include the use of
stimulating needles to locate the nerve of interest. Though success
rates are generally high, difficulties still exist. In certain deeper
nerve blocks, two needles of different geometries are used in the
procedure. A smaller needle first locates a nerve bundle, and then
is withdrawn in favor of a second, larger needle used for injection.
The distinct geometries of these needles are shown to generate
different electric field distributions, and these differences may
be responsible for failures of the second needle to elicit nerve
stimulation when placed in the same location as the first. A 3D finite difference method has been employed to numerically
calculate the electric field distributions for a commercial set of
stimulating needles.
Index Terms— Anesthesiology, Electric fields, Finite difference
methods.
I. I NTRODUCTION
R
EGIONAL anesthetic techniques involve the use of local
anesthetics to block neural impulse transmission from
the peripheral nerves to the central nervous system. The
application of local anesthetic can be done as a single bolus
injection producing several hours of pain control. This type of
regional anesthesia is termed peripheral nerve blockade (PNB).
Local anesthetic medication can also be delivered over time
through a catheter placed adjacent to nerves involved in pain
transmission. This type of regional anesthesia is known as
continuous peripheral nerve blockade (CPNB) and may result
in pain control lasting several days. Both PNB and CPNB can
provide excellent surgical anesthesia and postoperative analgesia for a variety of surgical procedures. Additionally, they
Manuscript received November 18, 2005. This work was supported, in part,
by the NSF through DMR-0305371 and by the University of Florida through
the University Scholars and the Alumni Fellows Programs.
J. Ch. Davis, formally with the Department of Physics, University of
Florida, Gainesville, FL 32611-8440 USA, is now with the Department of
Physics, Ohio State University, Columbus, OH 43210-1117 USA, (email:
lorentztrans@yahoo.com).
N. E. Anderson, formally with the Department of Physics, University of
Florida, Gainesville, FL 32611-8440 USA, is now working at CH2M Hill,
Gainesville, FL 32614-7009, USA.
J. G. Ramirez, formerly with the Department of Anesthesiology, University of Florida, Gainesville, FL 32611-8440, is now at the University
of Colorado Health Sciences Center, Denver, CO 80262, USA, (email:
jramirez@sdapc.com).
F. K. Enneking is with the Department of Anesthesiology, University of
Florida, Gainesville, FL 32611-8440 USA, (email: kenneking@anest.ufl.edu).
M. W. Meisel is with the Department of Physics, University of Florida,
Gainesville, FL 32611- 8440 USA, (email: meisel@phys.ufl.edu).
Copyright (c) 2006 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending an email to pubs-permissions@ieee.org.
have been shown to decrease the incidence of postoperative
nausea and vomiting, reduce oral narcotic side effects, and
improve sleep quality [1-3].
Placement of a PNB is typically done with a special needle,
capable of transmitting an electric current from a power
source to the neural structure. A neural target is located
by applying a voltage to the needle, thereby generating a
field of current splaying from the needle tip. When the field
approaches, the nerve of interest is stimulated, as evidenced
by a motor response (muscle contraction). Local anesthetic
is then deposited through the needle in close proximity to
the nerve. The needle is then removed, and over the course
of several minutes, the local anesthetic acts to block nerve
transmission. A similar procedure is followed for CPNB, in
which a catheter is threaded through the needle system and
left near the target nerve. Medication can be infused directly
to the nerve of interest for a prolonged period of time through
the catheter.
A typical procedure for placement of a CPNB system
involves the use of two stimulating needles, a small one (Braun
Stimuplex 21G) and a larger one (Braun Contiplex 18G),
Figs. 1-2. The Stimuplex is first inserted near the neural target,
and through visible muscle responses, the correct location
and depth of neural tissue can be ascertained. The Stimuplex is preferable for initial location since the smaller gauge
minimizes any potential tissue or vascular injury. Once the
desired location is identified, the Stimuplex is withdrawn, and
the Contiplex needle is introduced at the location and depth
where optimal nerve stimulation occurred. After the Contiplex
needle placement is adjusted to optimize stimulation, the local
anesthetic is injected, and a nonstimulating catheter can be
inserted through the Contiplex system.
This dual system is employed for deep perineural catheter
placement locations such as the lumbar plexus and works well
in a majority of catheter placements. Occasionally, a neural
structure is easily identified with the Stimuplex needle, but lost
upon placement of the Contiplex needle, despite meticulous
technique. Previous studies have investigated the effects of
shaft insulation and injectates on electric field distribution [4,
5], but not geometric variations between needles. Obvious
design features, including diameter and area of insulating
coverage, differ between the Stimuplex and Contiplex needles.
It is reasonable to assume that differences are present in the
stimulating field surrounding each needle tip. In an effort to
better understand the process of CPNB, we present numerically calculated stimulating fields present at the tip of the
TBME-00604-2005.R3
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Stimuplex and Contiplex needle systems.
II. M ODEL
The stimulating needles used in CPNB procedures locate
the nerve of interest by causing an electric depolarization of
the nerve, through an induced stimulus current, which elicits a
~ induced by the needle
motor response. The current density, J,
~ by Ohm’s law,
is related to the electric field E
~ .
¯E
J~ = σ̄
(1)
¯ is the conductivity tensor associated with the medium.
Here, σ̄
The uninsulated areas of the stimulating needles can be considered equipotential surfaces of potential V , and the electric
field is then calculated from the electric potential using
~ = −∇V
~
E
.
(2)
The previous equations imply that the current density, and
therefore the condition for nerve stimulation, can be determined from the electric potential. The problem then becomes
a matter of solving Poisson’s equation having a source region
g(x, y, z),
∇2 V = g(x, y, z) ,
(3)
with appropriate boundary conditions. These boundaries simply reflect the size and shape of the stimulating needle’s
conductive and resistive surfaces.
Previous efforts showed that the grounded tissue/air boundary had no effect on the field distribution surrounding the needle tip, so the outer boundary condition is assumed continuous
to simplify the problem [4]. The outer shaft of the needles
will not substantially affect the electric potential due to the
Teflon insulation. In the Contiplex needle, the inner surface
is insulated with Teflon (see Fig. 2), so this surface does not
contribute to the electric field profiles. Although the inside of
the Stimuplex needle is bare, the inner metal surface is not in
immediate contact with, i.e. it is sufficiently spatially remote
from, the tissue being probed, so it is not considered in our
analysis. Hence, the region at the tips of the needles, where
the insulation is not present, is taken as the only source of
electric field for the model calculations.
III. M ETHODS
Though exact solutions for very simple needle geometries
have been found [6], Poisson’s equation is not easily solved
by analytical techniques for the complex geometries of the
needles investigated. However, finite difference and finite element methods can be employed to numerically solve Poisson’s
equation [7]. The finite difference method was employed
because it is easily adapted to 3-dimensions (3-D).
In order to probe the effect of needle geometry on nerve
stimulation, a model consisting of a voltage source region
g(x, y, z), at the terminal end of the needle and a region of
finite and constant conductivity surrounding the tip was used.
Any differences seen in field profiles under these conditions
will also be seen in a variable conductivity region such as
the body [8]. In order to accurately model the needles, the
uninsulated regions at the tips of the needles were measured
under a microscope with the aid of an objective micrometer.
Two of these magnified images are shown in Figs. 1 and 2.
A cubic mesh of size (201)3 was generated, using MATLAB, with a mesh size of 0.03 mm. As stated earlier, this
problem reduces to solving Poisson’s equation, which can be
written in 3-D finite difference form as
1
[V (i − 1, j, k) + V (i + 1, j, k)
V (i, j, k) =
6
+ V (i, j − 1, k) + V (i, j + 1, k)
+ V (i, j, k − 1) + V (i, j, k + 1)
− h3 g(i, j, k) .
(4)
Here h is the mesh size and is used to represent the size
of the source element for calculation. The source points are
initialized to 0.5 V to provide the conditions of an average
minimum current, 0.5 mA, needed for stimulation, assuming a
load resistance of 1 kΩ [9]. Although the maximum magnitude
of applied voltage is, in clinical practice, user controlled, it is
not tuned continuously while inserting the needles. Therefore,
our results, obtained under constant voltage conditions, will
scale linearly with respect to the field strength that is applied.
The successive-over-relaxation method was used to iteratively
solve for the potential throughout the mesh. In order to use
this method, we define the following residual
R(i, j, k) = V (i − 1, j, k) + V (i + 1, j, k)
+ V (i, j − 1, k) + V (i, j + 1, k)
+ V (i, j, k − 1) + V (i, j, k + 1)
− 6V (i, j, k) − h3 g(i, j, k) .
(5)
The electric potential can then be calculated at each mesh
point using R(i, j, k) for the nth iteration multiplied by a
convergence factor ω to increase the convergence rate, i.e.
ω
(6)
V n+1 (i, j, k) = V n (i, j, k) + Rn (i, j, k) .
4
Generally convergence factors between 1 and 2 are used; in
this case a value of 1.2 produced an acceptable convergence
rate for the simulation. As convergence is reached, R(i, j, k)
tends to zero, so the iterative process was stopped when the
average value of R(i, j, k) was less than 1.0 × 10−5 . This
convergence limit leads to an average error in V of less than
1%. Using this convergence factor and limit, the simulations
generally converged after 600 iterations.
Once V was calculated, MATLAB’s gradient calculation
tool was utilized to determine the magnitude of the electric
field distribution. Contour maps were generated for several
planes around the needle tips and these maps were then used
to depict the field profiles at a variety of positions and angles
for the two needles.
IV. R ESULTS
Figures 3-6 summarize the results of the simulations for
the Stimuplex and Contiplex needles. The points taken as
equipotential areas (uninsulated conducting surfaces of the
needles), are depicted by black points in each image. Each
graph is a two-dimensional (2-D) slice of the computed 3D field, and the insets display the orientation of this plane.
TBME-00604-2005.R3
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Figures 3 and 4 show slices perpendicular to the shaft (z) axis
for each needle, while Figs. 5 and 6 provide a different view.
It should be noted for all graphs that the intensity of fields
will scale linearly with source point voltage, and therefore the
graphs will retain their shape under any physically meaningful
change in applied tip voltage.
Figures 3 and 4 are a set of planes taken perpendicular to
both needle’s shafts at 0.3 mm above the needle point (a),
exactly touching the point (b), and 0.3 mm below the point
(c). In Fig. 3, the strongest field produced by the Stimuplex
is found at the needle pinnacle, and along the 30◦ uninsulated
tip face. The Contiplex graphs (Fig. 4) have fewer points of
constant voltage in this model, as a result of less uninsulated
area on the needle. As illustrated in Fig. 4, the Contiplex also
produces a strong field at the pinnacle, but, partially due to a
shallower bevel angle, exhibits a less circularly homogeneous
field compared to the Stimuplex.
Figure 5A shows the electric fields on a plane across the face
of the Stimuplex needle. Conversely, Fig. 5B represents the
field that would result across the same plane if the Stimuplex
were replaced by the Contiplex at the same insertion angle and
tip location. This scenario mimics the ideal clinical case where
the Stimuplex is inserted at a 30◦ angle to the target nerve for
initial location, and then replaced by the Contiplex at the same
insertion angle and tip location. Even with this assumption
of perfect clinical technique, the electric field is decreased
considerably, and the areas of maximum field strength are
limited to the upper region of the graph. These results directly
mimic the case where nerve stimulation occurs readily with the
Stimuplex needle, but is lost upon switching to the Contiplex.
The effects of rotations about the shaft (z) axis are shown
in Fig. 6. Other than a 180◦ needle rotation, Figs. 5 and 6
represent the same field area. Comparing the two graphs, however, reveals major shifts in the Stimuplex field distribution,
and a less dramatic change in the Contiplex field. Additionally,
along this plane a similar field is produced by each needle. For
both needles, the field strength is decreased due to the z-axis
rotation, even while maintaining the same tip location. Nerve
stimulation in clinical practice could therefore be enhanced or
lost entirely because of this type of rotation.
V. D ISCUSSION
The results of our simulations demonstrate the inherent
inhomogeneity of electric field profiles formed by the two needles investigated. Although the model is artificial in assuming
a homogeneous conductive region within the body, incorporating a variable conductivity to reflect actual tissue variations
should maintain or magnify the deviations in current density
profiles [8]. The pinnacles of the needle tips both produce
high fields in their immediate vicinity, but the distributions
are otherwise dissimilar.
Since high field areas are seen around the entire tip face in
both needles, total current induced through a nerve bundle will
be highest when this face is parallel to the target nerve. For
the Stimuplex, a 30◦ beveled tip implies that this maximum
stimulation occurs with the shaft inserted at this angle to
the target. However, the Contiplex tip face makes a sharper
angle with the shaft (taken as 15◦ ), and thus maximum current
through a target is achieved when the needle is inserted nearly
parallel to the nerve. Since an insertion at such a sharp angle
to the target nerve is unlikely, this difference in tip angle could
explain a loss of stimulation upon needle replacement, even
when the Contiplex tip is inserted exactly where stimulation
previously occurred with the Stimuplex.
Similarly, the results show that a rotation about the shaft
(z) axis could have a large effect on current through a
nerve bundle. These rotations are difficult to eliminate entirely
during insertion, so the technique of actively rotating needles
in an exploratory fashion may be advisable to ascertain the
optimal orientation. Alternatively, using a flat tip needle for
initial nerve location could easily eliminate this dependence
on rotation.
A two needle system in CPNB placement is designed to
be less damaging by using a smaller needle for initial nerve
location, and a larger one for injection and catheter placement.
Inability to locate a target nerve by electric stimulation after
switching needles can be attributed to the different current
profiles generated by each needle. This loss of stimulation
presently occurs in a small, but significant percentage of these
procedures. Differences in the electric field profiles arising
from the two needles could be reduced in several ways. For
example, choosing needles with tip geometries that match
one another would reduce occurrences of stimulation loss,
thereby lessening the potential for tissue and nerve damage. In
particular, needles with identical bevel angles would produce
more similar fields. An overall increase in bevel angle will
reduce field variation due to rotations, though an increased
angle would not be practical with large gauge needles. On the
other hand, simply insulating a larger portion of the tip face
could have the same effect.
In new stimulating needle designs, the assumption that all
insulated needles produce identical fields should not be taken.
Even in procedures using a single needle to locate a nerve and
inject anesthetic, the field profile is vital to ensuring proper
placement. Successful anesthesia depends on the diffusion
characteristic of an anesthetic once injected, not whether nerve
stimulation has occurred. A needle design maximizing this
correspondence between injectate spread and electric field
distribution is ideal for any procedure. To this end, study of
injectate dispersion in conjunction with electric characteristics
would benefit future peripheral nerve blockading techniques.
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in the ambulatory setting–is it really worth it?,” Best Pract. Res. Clin.
Anaesthesiol., vol. 16, pp. 145-157, 2002.
[2] B. M. Ilfeld, D. E. Esener, T. E. Morey, and F. K. Enneking, “Ambulatory
perineural infusion: the patients’ perspective,” Reg. Anesth. Pain Med.,
vol. 28, pp. 418-423, 2003.
[3] F. K. Enneking and B. M. Ilfeld, “Major surgery in the ambulatory
environment: continuous catheters and home infusions,” Best Pract. Res.
Clin. Anaesthesiol., vol. 16, pp. 285-294, 2002.
[4] G. Bashein, R. H. Haschke, and L. B. Ready, “Electrical nerve location:
numerical and electrophoretic comparison of insulated vs uninsulated
needles,” Anesth. Analg., vol. 63, pp. 919-924, 1984.
[5] B. C. Tsui, A. Wagner, and B. Finucane, “Electrophysiologic effect of
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[6] M. M. Stecker, “Nerve stimulation with an electrode of finite size:
differences between constant current and constant voltage stimulation,”
Computers in Bio. and Med., vol. 34, pp. 51-94, 2004.
[7] M. N. O. Sadiku, Numerical Techniques in Electromagnetics. Boca Raton,
FL: CRC Press, 2000, ch. 3.
[8] V. T. Z. Krasteva, S. P. Papazov, and I. K. Daskalov, “Peripheral nerve
magnetic stimulation: influence of tissue non-homogeneity,” BioMed. Eng.
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[9] D. J. Ford, C. Pither, P. P. Raj, “Comparison of insulated and uninsulated
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Fig. 1. Side photographs of the Stimuplex (left) and Contiplex (right) needles
under a microscope. The Simuplex bevel angle was taken as 30 ◦ , while the
Contiplex bevel is approximately 15◦ . The light areas are covered with Teflon
insulation, while the darker region near the Stimuplex needle tip is bare metal.
The Contiplex has an exposed conducting surface completely perpendicular
to the microscope stage in this image, and therefore it is not visible in this
image.
Fig. 3. 2-D planar slices of the 3-D electric field around the Stimuplex
needle, taken perpendicular the shaft axis (z), with black dots representing an
overhead view of all voltage source points modeled. The needle tip is taken
as z = 0. Inset graphics include a line representing the approximate z-value
of the corresponding planar slice. The middle image (b) most closely mimics
the field present on the surface of a flat nerve bundle perpendicular to and
nearly touching the incoming needle tip.
Fig. 2. Frontal photographs of the Stimuplex (left) and Contiplex (right)
needles under a microscope. Bare metal surfaces of the Stimuplex needle are
the dark areas, while the thin uninsulated areas of the Contiplex needle are
indicated by black curves. Inner diameter of the Stimuplex shaft is 0.4 mm,
and the Contiplex inner shaft diameter is 1 mm.
James Ch. Davis started out as a child in the great
state of Ohio and moved to Florida when he was
young. After high school, he entered the Honors Program at the University of Florida, where he worked
in the experimental condensed matter physics group
of Mark W. Meisel. After four years of juggling
projects, including this one, James graduated with
a B.S. degree in Physics and, in Fall 2006, entered
the graduate program in physics at The Ohio State
University. An avid hiker of remote national trails,
James enjoys life and works at not being confused
with James C. Davis, a Professor of Physics at Cornell University.
TBME-00604-2005.R3
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Fig. 5. 2-D planar slices of the 3-D electric field around the Stimuplex (a)
and Contiplex (b) needles taken at a 30◦ angle to the shaft axis (z), with black
dots representing voltage source points as projected onto this plane. The inset
graphics illustrate the orientation of each plane. The shifts in field strength
and distribution between (a) and (b) are largely reflections of the different
bevel angles of each tip.
Fig. 4. 2-D planar slices of the 3-D electric field around the Contiplex
needle, taken perpendicular to the shaft axis (z), with black dots representing
an overhead view of all voltage source points modeled. The Contiplex profile
is seen to be significantly elongated, compared to the more symmetric field
of the Stimuplex. This difference is attributable, in part, to variation in the tip
angles with respect to the shaft.
Fig. 6. View of the electric field distribution for Stimuplex (a) at −30◦ and
Contiplex (b) at −30◦ with respect to the shaft. The inset graphics show the
orientation of each plane. Comparing Figs. 5 and 6 illustrates the effects of
a 180◦ rotation about the needle shaft (z) axis.
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