30th Annual International IEEE EMBS Conference Vancouver, British Columbia, Canada, August 20-24, 2008
The numeric calculation of eddy current distributions in transcranial magnetic stimulation Seichi Tsuyama, Akira Hyodo, Masaki Sekino, Takehito Hayami, Shoogo Ueno and Keiji Iramina
Abstract—Transcranial magnetic stimulation (TMS) is a method to stimulate neurons in the brain. It is necessary to obtain eddy current distributions and determine parameters such as position, radius and bend-angle of the coil to stimulate target area exactly. In this study, we performed FEM-based numerical simulations of eddy current induced by TMS using three-dimentional human head model with inhomogeneous conductivity. We used double-cone coil and changed the coil radius and bend-angle of coil. The result of computer simulation showed that as coil radius increases, the eddy current became stronger everywhere. And coil with bend-angle of 22.5 degrees induced stronger eddy current than the coil with bendangle of 0 degrees. Meanwhile, when the bend-angle was 45 degrees, eddy current became weaker than these two cases. This simulation allowed us to determine appropriate parameter easier.
I.
spatial resolution of 5mm. Currently there are so little ways to stimulate brain directly that TMS is expected to develop in the field where it use this advantage. For example, a tool for studying plasticity of the brain or medical treatment of mental disease. It is necessary to obtain eddy current distributions and determine parameter such as position, radius and bend-angle of coil to stimulate target area for these applications of TMS. However, it was difficult to guess eddy current distribution because human head is composed of various tissues which have various conductivity. In this study, we created three-dimensional human head model with inhomogeneous conductivity and obtained eddy current distribution by numerical simulation based on the finite-element method (FEM).
INTRODUCTION
II. MATERIAL AND METHOD
T
ranscranial magnetic stimulation (TMS) is one of the methods for stimulating neurons in the brain [1],[2], which is applied to study of neuronal physiology and medical care. It is necessary to apply high voltage to stimulate brain by electroconvulsive therapy (ECT) due to high electric resistance of skull. Therefore ECT involves severe pain so it may hurt subject and it is difficult to apply to medical care. Meanwhile, TMS has advantages such as painless and noninvasive and can stimulate deep area of head. TMS made study and medical care easier. In TMS, a time-variable current is applied to a coil placed on the skalp. It produces a time-variable magnetic field which induces an eddy current in the brain. The eddy current stimulates neurons and induces action potential, which facilitate or inhibit particular brain function. Circular coil or double-cone coil are used for stimulation. Though circular coil couldn't stimulate locally, the invention of double-cone coil enabled us to stimulate with
Manuscript received April 16, 2008. S. Tsuyama is with the Graduate School of Information Science and Electrical Engineering, Kyushu University , Japan. phone: 81-92-802-3767; fax: 81-92-802-3581; e-mail:
[email protected] kyushu-u.ac.jp). A. Hyodo is with the Graduate School of Systems Life Sciences, Kyushu University, Japan. M. Sekino is with the Graduate School of Frontier Sciences, Tokyo University , Japan. T. Hayami is with the Digital Medicine Initiative, Kyushu University, Japan. S. Ueno is with Graduate School of Engineering, Kyushu University, Japan K. Iramina is with the Graduate School of Information Science and Electrical Engineering, Kyushu University , Japan.
978-1-4244-1815-2/08/$25.00 ©2008 IEEE.
In this simulation, we obtained an eddy current using the FEM. The simulation model was a three-diminsional human head model composed of cubes 3mm on the size [3]-[7]. The numbers of nodes and elements were 177649 and 189975. Conductivities of the tissues were based on Cole-Cole model [8] by Brooks Air Force Labolatory, which represents human body with 49 tissues. Relative magnetic permeabilities of all the tissues were 1.0. Though the original data had a spatial resolution of 1mm, we reconstructed the data with a resolution of 3 mm to reduce amount of calculation. The coil for stimulation was a double-cone coil and consisted of a pair of circular coil elements. Each coil elements was represented by 72 line currents approximately. Linear time-variable electric currents were applied to each coil element in opposite directions. We use commercial software for electromagnetic computation based on the FEM, PHOTO-Series by PHOTON Co., Ltd.. We changed coil radius in four ways, 30, 40, 50 and 60 mm, and the bend-angle of coil element in three ways 0, 22.5, 45 degrees. We set the coil center at 30 degrees left from inion, as close as possible to the head. Fig. 1 shows the numerical model. The magnetic field B was calculated using the Biot-Savart's law
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B=
m 0 I (t ) t (r' ) ´ (r - r' ) 3 4p ò r - r'
Fig. 1 Axial cross section of the numerical model of transcranial magnetic stimulation. The bend-angle of coil elements were changed in three ways, 0, 22.5 and 45 degree. Coil radius is 60 mm in this figure.
Fig. 2 Distribution of eddy current intensity on the surface of the brain when the bend-angle was 0 degree. Coil radius was changed in four ways, 30, 40, 50 and 60 mm.
where m 0 is the magnetic permeability of free space, I(t) is the electric current applied to the coil, r' is the position on the coil, and t(r') is the unit vector tangent to the coil at the position r'. The vector potential P of the eddy curents j was defined as
j = Ñ´P The eddy current distribution was obtained by solving the following equation
Ñ 2P = s
¶B(r, t ) ¶t
The boundary condition for the surface of the model was
P=0 The boundary conditions for the boundaries between tissues were
j1 × n = j2 × n j1 × t j2 × t =
s1
Fig. 3 Distribution of eddy current intensity on the horizontal cross section of the brain under the same condition as Fig.2.
s2
where j1 and j2 are current densities in each tissue, s 1 and s 2 are conductivities, and n and t are the unit normal vector and the unit tangent vector of the boundary.
III. RESULTS AND DISCUSSIONS Fig. 2 to 7 shows distributions of eddy current density. In these figures, the intensity of eddy current were normalized based on the maximum value obtained using coil with radius
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Fig. 2 and 3 show distribution of eddy current density on the surface and the horizontal cross section of the brain when the bend-angle was 0 degrees. Maximum intensity was obtained under the intersecting point of coil elements. As coil radius increases, the maximum value of eddy current became higher and eddy current was widely distributed throughout the brain. Fig. 4 and 5 show distribution of eddy current density when the bend-angle was 22.5 degrees. In comparison with the case of 0 degrees, it shows similar trend. That is to say, as coil radius increases, the eddy current became stronger. However, the intensity of eddy current was higher everywhere. The maximum value was also higher. The result shows that coil with bend-angle of 22.5 degrees can stimulate approximately 5 mm deeper than one with 0 degrees. Fig. 6 and 7 show distribution of eddy current density when the bend-angle was 45 degrees. The eddy current was totally weaker than above two cases and the point where maximum intensity was obtained was not under the intersecting point but under each coil element. We considered that it's because the root of coil elements was far from the head, because the another advance simulation showed that the eddy current induced by this coil was concentrated near the root. Fig. 8 shows the relation between maximum eddy current and coil radius, bend-angle. We concluded that coil with small bend-angle (such as 22.5 degrees) was efficient to stimulate deeper area compared to one with no bending. But there wasn't great difference. Meanwhile, the coil with large bend-angle (such as 45 degrees) was inefficient because its bend didn't let the coil fit over the head. Like this, it had became easy to determine appropriate parameters by this simulation.
Fig. 4 Distribution of eddy current intensity on the surface of the brain when the bend-angle was 22.5 degree. Coil radius was changed in four ways, 30, 40, 50 and 60 mm.
Fig. 5 Distribution of eddy current intensity on the horizontal cross section of the brain under the same condition as Fig.4.
of 60 mm and bend-angle of 22.5 degrees. The intensity of eddy current is determined by temporal differentiation of current adapted to the coil, but the configuration stays constant. So we didn't represent the specific value in these figures. 4288
Fig. 8 The graph of relation between maximum eddy current intensity and coil radius, bend-angle.
Fig. 6 Distribution of eddy current intensity on the surface of the brain when the bend-angle was 45 degree. Coil radius was changed in four ways, 30, 40, 50 and 60 mm.
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Fig. 7 Distribution of eddy current intensity on the horizontal cross section of the brain under the same condition as Fig.6.
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