PIERS ONLINE, VOL. 3, NO. 2, 2007
178
Comparison of Maximum Induced Current and Electric Field
from Transcranial Direct Current and Magnetic Stimulations of a
Human Head Model
Mai Lu1 , T. Thorlin2 , Shoogo Ueno3 , and Mikael Persson4
1
4
Department of Signals and systems, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden
2
Department of Neurology, Institute for Clinical Neuroscience, Sahlgrens University Hospital
Bla Straket 7, SE 413 45 Gothenburg, Sweden
3
Department of Biomedical Engineering, Graduate School of Medicine
University of Tokyo, Tokyo 113-0033, Japan
Department of Signals and Systems, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden
Abstract— As important non-invasive techniques in brain stimulation, transcranial direct current stimulation (tDCS) and transcranial magnetic stimulation (TMS) have been studied and
compared in this paper by employing impedance method and a 3D human head model. The
quantitative analysis of distributions of current density and electric field by tDCS and TMS have
been presented. Results are compared and potential applications are discussed.
DOI: 10.2529/PIERS060906193504
1. INTRODUCTION
Transcranial magnetic stimulation (TMS) is a technique for stimulating the brain. Transcranial
magnetic stimulation uses powerful rapidly changing magnetic fields to induce electric fields in
the brain by electromagnetic induction without the need for surgery or external electrodes. As a
non-invasive method to stimulate brain, TMS has attracted considerable interest as an important
tool for studying the functional organization of the human brain as well as a therapeutic tool in
numerous clinical trials to improve a variety of psychiatric diseases [1, 2].
Recently another non-invasive method transcranial direct current stimulation has been developed. The tDCS method involves application of low intensity direct current stimulation of cortex
through large surface scalp electrodes. The principle of how tDCS works in the brain is roughly
the same as that of TMS. They both seek to make neurons in the prefrontal cortex more excitable.
tDCS has already been shown to improve implicit motor learning, and visuo-motor coordination.
Moreover, with regard to neurologic diseases e.g., epilepsy, depression, migraine, and Parkinson’s
disease, it offers new interesting therapeutic option [3, 4].
Although tDCS shows promise in fighting psychiatric disorders, we need to know a lot more
before it can be accepted as an effective treatment method. To date the spatial distribution of
the current density and electric field within the volume of the human brain for tDCS is largely
unknown. Also there has been no comparison between the tDSC and TMS methods. This is main
motivation of the present work. By employing the impedance method, and a 3D human head
model, this paper provides a quantitative analysis and a comparison of current density and electric
field distributions in the human head model by tDCS and TMS.
2. HUMAN HEAD MODEL
In this paper we use a 3D human head model obtained from Brooks Air Force Laboratory, USA.
The model which has 24 different tissues is based on anatomical slices from a male cadaver and it
is originally obtained from the Visible Human Project. The electrical properties are modeled using
the 4-Cole-Cole model [5]. Typical sliced layer in the head model and tissue colour palette for part
of the tissues are shown in Fig. 1. Conductivities of some important tissues used in the present
paper are given in Table 1.
3. 3-D IMPEDANCE METHOD
The human head model is described using a uniform 3D Cartesian grid and is composed of small
cubic voxels. Assuming that, in each cell, the electric conductivities are isotropic and constant in
PIERS ONLINE, VOL. 3, NO. 2, 2007
cut z=120 mm
250
250
200
200
150
150
y [mm]
z [mm]
cut y=110 mm
100
100
50
50
0
0
50
100
x [mm]
150
179
200
(a)
0
0
50
100
x [mm]
150
200
(b)
(c)
Figure 1: Typical sliced layers in human head model. (a) cross section at y = 110 mm, (b) cross section at
z = 120 mm, (c) Tissue color Palette.
Table 1: Tissue properties used in the calculations.
Tissue
BLOOD
BONE.MARROW
CEREB.SPIN.FL
FAT
LIGAMENTS
NERVE.(spine)
GRAY.MATTER
WHITE.MATTER
SKIN-DERMIS
Conductivity σ[S/m]
(TMS case)
7.00e-01
2.52e-3
2.00e+00
2.34e-02
3.85e-01
3.21e-02
1.07e-01
6.55e-02
2.01e-4
Conductivity σ[S/m]
(tDCS case)
7.00e-01
5.00e-04
2.0e+00
1.00e-02
2.5e-01
6.00e-03
2.00e-02
2.00e-02
2.00e-04
all direction, the model is represented as a 3D network of impedances. The impedances for various
directions can be written as
∆m
i, j, k
Zm
=
(1)
∆n∆p(σ + jω²)
where i, j, k indicate the cell index; ∆m, ∆n, and ∆p are the size of the voxels in m, n, p directions.
σ and ² are the conductivity and the electrical permittivity for the voxel(i, j, k). Kirchoff voltage
law around each loop in this network generates a system of equations for the loop currents. In
the case of TMS, these loop currents are driven by Faraday induction from the magnetic field of
the applicator. In the tDCS case, the currents are injected at the electrodes and then distributed
according to the Kirchoff laws. This system of equations is solved numerically using a standard
iterative method. The net induced currents within the head are then calculated from these known
loop currents. The induced electric field is in turn calculated from the net induced currents using
the Ohm’s law. Details implementation of the impedance method can be found in[6–8].
4. RESULTS AND DISCUSSIONS
For the tDCS calculation, we use a pair of large surface scalp electrodes with an area of 35cm2 that
are placed on the 3D head model in the bilateral position, as shown in Fig. 2(a). A direct current
of 1 mA is injected from right electrode and extracted the same current on the left side. For the
TMS calculation, we design a TMS coil with figure of eight shaped and place it near the left side
of head model (Fig. 2(b)). It consists of two circular coils with inner radius of 10 mm, and outer
radii 50 mm, and the number of wire turns in each wing is nr = 10. A typical clinic application
current (sine wave with current amplitude I = 7.66 kA, and working frequency f = 3.6 kHz with
repetition of 20 Hz) was implemented in the calculations.
By employing the impedance method as described in Section 3, the current density J and electric
PIERS ONLINE, VOL. 3, NO. 2, 2007
(a)
180
(b)
Figure 2: tDCS patch and TMS coil placed on the human head model. (a) tDCS, (b) TMS.
field E are calculated, and the results for tDCS and TMS cases are shown in Table 2 and Table 3,
respectively.
Table 2: Maximum values of current density J, electric field E and their 95%-CI in different tissues for tDCS
case.
Tissue Name
BLOOD..........
BODY.FLUID.....
BONE.MARROW....
CARTILAGE......
CEREB.SPIN.FL..
EYE.(lens).....
FAT............
GLANDS.........
LIGAMENTS......
MUSCOUS.MEMB...
MUSCLE.........
NERVE.(spine)..
GRAY.MATTER....
WHITE.MATTER...
CEREBELLUM.....
SKIN-DERMIS....
|J|
[mA/m2 ]
5.6e+02
2.4e+01
1.1e+03
1.1e+02
2.5e+03
1.1e+02
1.2e+04
3.4e+02
8.6e+03
6.2e+02
7.8e+03
3.7e+02
9.9e+02
3.5e+02
2.2e+02
1.0e+04
95%-CI
[mA/m2 ]
4.0e+01
2.7e+00
1.3e+02
6.3e+00
1.6e+02
1.2e+01
7.6e+02
6.6e+00
1.1e+03
9.0e+01
1.5e+03
4.4e+01
8.9e+01
4.0e+01
2.0e+01
5.8e+02
|E|
[mv/m]
8.0e+02
1.6e+01
2.1e+06
7.2e+02
1.2e+03
3.8e+02
1.2e+06
6.9e+02
3.4e+04
1.6e+06
3.9e+04
6.2e+04
5.0e+04
1.7e+04
5.4e+03
5.2e+07
95%-CI
[mv/m]
5.7e+01
1.8e+00
2.7e+05
4.2e+01
8.0e+01
4.1e+01
7.6e+04
1.3e+01
4.3e+03
2.2e+05
7.6e+03
7.4e+03
4.4e+03
2.0e+03
4.9e+02
2.9e+06
(x, y, z)
(unit: mm)
(104, 73,174)
(126, 74, 13)
( 72,126,197)
(103, 20, 85)
(144,132,163)
(128, 48,110)
( 69,114,202)
( 90,109,100)
( 71,114,200)
( 98, 69,113)
( 71,125,202)
( 89,106,106)
(133,137,163)
( 88,133,139)
( 64,147, 91)
(112,137,208)
For tDCS case, we know that fat (at x = 69 mm, y = 114 mm, z = 202 mm) and skin-dermis
(at x = 112 mm, y = 137 mm, z = 208 mm) under the right patch exhibit maximum values
of current density: |J| = 1.2 × 104 mA/m2 , and |J| = 1.0 × 104 mA/m2 , respectively. Skindermis (same position as above) and bone marrow (at x = 72 mm, y = 126 mm, z = 197 mm)
under the left patch exhibits maximum values electric field: |E| = 5.2 × 107 mV/m, and |E| =
2.1 × 106 mV/m respectively. This means that the current density and the electric field in tDCS
are mostly distributed in the skull. The distributions of current density |J| and electric field |E|
at the cross sections have been illustrated in Fig. 3. From Table 2, we know that brain tissues,
such as spine nerve has maximum value of current density |J| = 370 mA/m2 and electric field
|E| = 6.2 × 104 mV/m at the position (89, 106, 106). As we know this position is located in
PIERS ONLINE, VOL. 3, NO. 2, 2007
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Table 3: Maximum values of current density J, electric field E and their 95%-CI in different tissues for TMS
case.
Tissue Name
BLOOD..........
BODY.FLUID.....
BONE.MARROW....
CARTILAGE......
CEREB.SPIN.FL..
EYE.(lens).....
FAT............
GLANDS.........
LIGAMENTS......
MUSCOUS.MEMB...
MUSCLE.........
NERVE.(spine)..
GRAY.MATTER....
WHITE.MATTER...
CEREBELLUM.....
SKIN-DERMIS....
|J|
[mA/m2 ]
3.8e+04
1.2e+04
2.7e+04
9.8e+03
4.1e+05
3.6e+04
9.7e+04
5.8e+04
2.9e+05
4.4e+04
1.8e+05
2.2e+04
1.3e+05
2.9e+04
2.2e+04
3.7e+04
95%-CI
[mA/m2 ]
2.0e+03
1.3e+03
2.9e+03
1.0e+03
3.9e+04
4.2e+03
8.7e+03
5.9e+03
3.0e+04
6.1e+03
6.3e+03
2.4e+03
1.1e+04
1.7e+03
1.9e+03
4.8e+03
|E|
[mv/m]
5.5e+04
7.8e+03
1.1e+07
5.6e+04
2.0e+05
1.1e+05
4.2e+06
1.1e+05
7.5e+05
4.2e+07
5.3e+05
6.8e+05
1.2e+06
4.4e+05
1.7e+05
1.8e+08
95%-CI
[mv/m]
2.9e+03
8.8e+02
1.2e+06
5.9e+03
2.0e+04
1.3e+04
3.7e+05
1.1e+04
7.8e+04
5.8e+06
1.9e+04
7.5e+04
1.0e+05
2.6e+04
1.5e+04
2.4e+07
(x, y, z)
(unit: mm)
( 98, 56,155)
(126, 74, 13)
(156,112,144)
(164,137, 82)
(149,113,149)
(135, 48,107)
(158,102,152)
(147, 58,104)
(149,113,147)
(106, 70,111)
(158,103,151)
(124, 65,106)
(151,110,138)
(150,115,130)
(140,159, 82)
(156, 64,100)
the central and deep part of the brain. Since |E| = 6.2 × 104 mV/m can be comparable with
100 mV/mm (the effective fields for electrically induced effects in living cells [9]), we believe tDCS
can also play a role in deep brain stimulation.
(a)
(b)
Figure 3: Current density (|J|) and electrical field (|E|) distributions for tDCS case. (a) |J| at the cross
section y = 114 mm, (b) |E| at the cross section y = 137 mm.
For TMS case, cerebro spinal fluid (at x = 149 mm, y = 113 mm, z = 149 mm), and ligaments (at
x = 149 mm, y = 113 mm, z = 147 mm) at the coil side exhibit maximum values of current density
|J| = 4.1 × 105 mA/m2 , and |J| = 2.9 × 105 mA/m2 , respectively. Electric field exhibits maximum
values |E| = 1.8 × 108 mV/m in skin (at x = 156 mm, y = 64 mm, z = 100 mm) at the coil side,
and |E| = 4.2 × 107 mV/m in muscous membranes (at x = 106 mm, y = 70 mm, z = 111 mm) in
the deep part of the brain. This means during TMS implementation, current density will mostly
distributed in the brain area, because the applied magnetic field can easily penetrate the skull.
While electric field will be distributed in the scalp as well as in the brain. Fig. 4 illustrates the
distribution of current density |J| and electric field |E| in cross sections in TMS case.
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(b)
Figure 4: Current density (|J|) and electrical field (|E|) distributions for TMS case. (a) |J| at the cross
section y = 113 mm, (b) |E| at the cross section y = 64 mm.
In the head model with 1 mm resolution, the thickness of the tissues is often close to the grid
size, and severe staircasing will locally perturb the calculation. A statistical analysis was thus
carried out to estimate the maximum |J| and |E| with a 95% confidence interval (95%-CI). Table
2 and Table 3 summarise 95%-CI in various tissues for tDCS case and TMS case, respectively. For
example, the relative errors of |J| and |E| in skin for tDCS case are 5.8% and 5.6%, respectively,
while in the brain tissue i.e., white matter, the estimated relative errors are 11.4% for |J| and 11.7%
for |E|, which also reveals a fact that tDCS causes large current density and electric field levels in
the skull.
Theoretical studies show that a nerve is activated by the first derivative of the component of an
induced electric field along the nerve, the so called activating function, during magnetic stimulation
[10, 11]. It is important to investigate the activating functions in human brain by tDCS, and TMS,
and the precise study will be reported soon.
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