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Comparison of Maximum Induced Current and Electric Fieldfrom Transcranial Direct Current and Magnetic Stimulations of a

Human Head Model

Mai Lu1, T. Thorlin2, Shoogo Ueno3, and Mikael Persson4

1 Department of Signals and systems, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden2 Department of Neurology, Institute for Clinical Neuroscience, Sahlgrens University Hospital

Bla Straket 7, SE 413 45 Gothenburg, Sweden3 Department of Biomedical Engineering, Graduate School of Medicine

University of Tokyo, Tokyo 113-0033, Japan4 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 cur-rent stimulation (tDCS) and transcranial magnetic stimulation (TMS) have been studied andcompared in this paper by employing impedance method and a 3D human head model. Thequantitative analysis of distributions of current density and electric field by tDCS and TMS havebeen 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. Transcranialmagnetic stimulation uses powerful rapidly changing magnetic fields to induce electric fields inthe brain by electromagnetic induction without the need for surgery or external electrodes. As anon-invasive method to stimulate brain, TMS has attracted considerable interest as an importanttool for studying the functional organization of the human brain as well as a therapeutic tool innumerous clinical trials to improve a variety of psychiatric diseases [1, 2].

Recently another non-invasive method transcranial direct current stimulation has been devel-oped. The tDCS method involves application of low intensity direct current stimulation of cortexthrough large surface scalp electrodes. The principle of how tDCS works in the brain is roughlythe 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’sdisease, it offers new interesting therapeutic option [3, 4].

Although tDCS shows promise in fighting psychiatric disorders, we need to know a lot morebefore it can be accepted as an effective treatment method. To date the spatial distribution ofthe current density and electric field within the volume of the human brain for tDCS is largelyunknown. Also there has been no comparison between the tDSC and TMS methods. This is mainmotivation of the present work. By employing the impedance method, and a 3D human headmodel, this paper provides a quantitative analysis and a comparison of current density and electricfield 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 itis originally obtained from the Visible Human Project. The electrical properties are modeled usingthe 4-Cole-Cole model [5]. Typical sliced layer in the head model and tissue colour palette for partof the tissues are shown in Fig. 1. Conductivities of some important tissues used in the presentpaper 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 smallcubic voxels. Assuming that, in each cell, the electric conductivities are isotropic and constant in

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x [mm]

z [m

m]

cut y=110 mm

0 50 100 150 2000

50

100

150

200

250

x [mm]

y [m

m]

cut z=120 mm

0 50 100 150 2000

50

100

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250

(a) (c)(b)

Figure 1: Typical sliced layers in human head model. (a) cross section at y = 110 mm, (b) cross section atz = 120 mm, (c) Tissue color Palette.

Table 1: Tissue properties used in the calculations.

Tissue Conductivity σ[S/m] Conductivity σ[S/m](TMS case) (tDCS case)

BLOOD 7.00e-01 7.00e-01BONE.MARROW 2.52e-3 5.00e-04CEREB.SPIN.FL 2.00e+00 2.0e+00FAT 2.34e-02 1.00e-02LIGAMENTS 3.85e-01 2.5e-01NERVE.(spine) 3.21e-02 6.00e-03GRAY.MATTER 1.07e-01 2.00e-02WHITE.MATTER 6.55e-02 2.00e-02SKIN-DERMIS 2.01e-4 2.00e-04

all direction, the model is represented as a 3D network of impedances. The impedances for variousdirections can be written as

Zi, j, km =

∆m

∆n∆p(σ + jωε)(1)

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 ε are the conductivity and the electrical permittivity for the voxel(i, j, k). Kirchoff voltagelaw around each loop in this network generates a system of equations for the loop currents. Inthe case of TMS, these loop currents are driven by Faraday induction from the magnetic field ofthe applicator. In the tDCS case, the currents are injected at the electrodes and then distributedaccording to the Kirchoff laws. This system of equations is solved numerically using a standarditerative method. The net induced currents within the head are then calculated from these knownloop currents. The induced electric field is in turn calculated from the net induced currents usingthe 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 thatare placed on the 3D head model in the bilateral position, as shown in Fig. 2(a). A direct currentof 1 mA is injected from right electrode and extracted the same current on the left side. For theTMS calculation, we design a TMS coil with figure of eight shaped and place it near the left sideof head model (Fig. 2(b)). It consists of two circular coils with inner radius of 10 mm, and outerradii 50 mm, and the number of wire turns in each wing is nr = 10. A typical clinic applicationcurrent (sine wave with current amplitude I = 7.66 kA, and working frequency f = 3.6 kHz withrepetition of 20 Hz) was implemented in the calculations.

By employing the impedance method as described in Section 3, the current density J and electric

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(a) (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 tDCScase.

|J| 95%-CI |E| 95%-CI (x, y, z)Tissue Name [mA/m2] [mA/m2] [mv/m] [mv/m] (unit: mm)BLOOD.......... 5.6e+02 4.0e+01 8.0e+02 5.7e+01 (104, 73,174)BODY.FLUID..... 2.4e+01 2.7e+00 1.6e+01 1.8e+00 (126, 74, 13)BONE.MARROW.... 1.1e+03 1.3e+02 2.1e+06 2.7e+05 ( 72,126,197)CARTILAGE...... 1.1e+02 6.3e+00 7.2e+02 4.2e+01 (103, 20, 85)CEREB.SPIN.FL.. 2.5e+03 1.6e+02 1.2e+03 8.0e+01 (144,132,163)EYE.(lens)..... 1.1e+02 1.2e+01 3.8e+02 4.1e+01 (128, 48,110)FAT............ 1.2e+04 7.6e+02 1.2e+06 7.6e+04 ( 69,114,202)GLANDS......... 3.4e+02 6.6e+00 6.9e+02 1.3e+01 ( 90,109,100)LIGAMENTS...... 8.6e+03 1.1e+03 3.4e+04 4.3e+03 ( 71,114,200)MUSCOUS.MEMB... 6.2e+02 9.0e+01 1.6e+06 2.2e+05 ( 98, 69,113)MUSCLE......... 7.8e+03 1.5e+03 3.9e+04 7.6e+03 ( 71,125,202)NERVE.(spine).. 3.7e+02 4.4e+01 6.2e+04 7.4e+03 ( 89,106,106)GRAY.MATTER.... 9.9e+02 8.9e+01 5.0e+04 4.4e+03 (133,137,163)WHITE.MATTER... 3.5e+02 4.0e+01 1.7e+04 2.0e+03 ( 88,133,139)CEREBELLUM..... 2.2e+02 2.0e+01 5.4e+03 4.9e+02 ( 64,147, 91)SKIN-DERMIS.... 1.0e+04 5.8e+02 5.2e+07 2.9e+06 (112,137,208)

For tDCS case, we know that fat (at x = 69mm, y = 114mm, z = 202mm) and skin-dermis(at x = 112mm, y = 137mm, z = 208mm) under the right patch exhibit maximum valuesof current density: |J| = 1.2 × 104 mA/m2, and |J| = 1.0 × 104 mA/m2, respectively. Skin-dermis (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 tDCSare 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| = 370mA/m2 and electric field|E| = 6.2 × 104 mV/m at the position (89, 106, 106). As we know this position is located in

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Table 3: Maximum values of current density J, electric field E and their 95%-CI in different tissues for TMScase.

|J| 95%-CI |E| 95%-CI (x, y, z)Tissue Name [mA/m2] [mA/m2] [mv/m] [mv/m] (unit: mm)BLOOD.......... 3.8e+04 2.0e+03 5.5e+04 2.9e+03 ( 98, 56,155)BODY.FLUID..... 1.2e+04 1.3e+03 7.8e+03 8.8e+02 (126, 74, 13)BONE.MARROW.... 2.7e+04 2.9e+03 1.1e+07 1.2e+06 (156,112,144)CARTILAGE...... 9.8e+03 1.0e+03 5.6e+04 5.9e+03 (164,137, 82)CEREB.SPIN.FL.. 4.1e+05 3.9e+04 2.0e+05 2.0e+04 (149,113,149)EYE.(lens)..... 3.6e+04 4.2e+03 1.1e+05 1.3e+04 (135, 48,107)FAT............ 9.7e+04 8.7e+03 4.2e+06 3.7e+05 (158,102,152)GLANDS......... 5.8e+04 5.9e+03 1.1e+05 1.1e+04 (147, 58,104)LIGAMENTS...... 2.9e+05 3.0e+04 7.5e+05 7.8e+04 (149,113,147)MUSCOUS.MEMB... 4.4e+04 6.1e+03 4.2e+07 5.8e+06 (106, 70,111)MUSCLE......... 1.8e+05 6.3e+03 5.3e+05 1.9e+04 (158,103,151)NERVE.(spine).. 2.2e+04 2.4e+03 6.8e+05 7.5e+04 (124, 65,106)GRAY.MATTER.... 1.3e+05 1.1e+04 1.2e+06 1.0e+05 (151,110,138)WHITE.MATTER... 2.9e+04 1.7e+03 4.4e+05 2.6e+04 (150,115,130)CEREBELLUM..... 2.2e+04 1.9e+03 1.7e+05 1.5e+04 (140,159, 82)SKIN-DERMIS.... 3.7e+04 4.8e+03 1.8e+08 2.4e+07 (156, 64,100)

the central and deep part of the brain. Since |E| = 6.2 × 104 mV/m can be comparable with100mV/mm (the effective fields for electrically induced effects in living cells [9]), we believe tDCScan 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 crosssection 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 (atx = 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 maximumvalues |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) inthe deep part of the brain. This means during TMS implementation, current density will mostlydistributed 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 thedistribution of current density |J| and electric field |E| in cross sections in TMS case.

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(a) (b)

Figure 4: Current density (|J|) and electrical field (|E|) distributions for TMS case. (a) |J| at the crosssection y = 113 mm, (b) |E| at the cross section y = 64 mm.

In the head model with 1mm resolution, the thickness of the tissues is often close to the gridsize, and severe staircasing will locally perturb the calculation. A statistical analysis was thuscarried out to estimate the maximum |J| and |E| with a 95% confidence interval (95%-CI). Table2 and Table 3 summarise 95%-CI in various tissues for tDCS case and TMS case, respectively. Forexample, 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 inthe skull.

Theoretical studies show that a nerve is activated by the first derivative of the component of aninduced 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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