Electromagnetic induction, which provides the fundamental principle of biomagnetic stimulation, was discovered by Michael Faraday in 1831. When a pair of coils is situated close to one another and the current flowing in one coil varies, an electromotive force arises in the other coil. The current flowing in the primary coil generates a magnetic field, and a rapid switching of the current causes a steep variation in the magnetic flux linkage. The magnitude of electromotive force in the circuit is proportional to the time rate of change in this flux linkage. The electromotive force is directed so that the magnetic field arising from the secondary coil current inhibits the variation of flux linkage. Because biological tissues and fluids are electrically conductive, the electromagnetic induction occurs also in the body to induce electric fields and resulting currents. When a rapidly varying current is applied to a coil located on the surface of the body, electric fields are induced in nearby tissues owing to the varying magnetic fields. The magnetic stimulation is understood as an electric stimulation mediated by magnetic fields because the resulting biological effects originate from the induced electric fields. Considering that the magnetic permeabilities of biological tissues are nearly equal to that of free space, electric properties of biological tissues play important roles in biological effects of alternating and pulsed magnetic fields. At low frequencies below Activating Function 47 Stimulation Site 48

2.4 Numerical Analyses of Magnetic Field and Eddy Current 48 2.4.1 Numerical Methods 48 Finite Element Method 48 Scalar Potential Finite Difference Method 49

2.4.2 Numerical Model of the Brain 50 2.4.3 Analyses of Transcranial Magnetic Stimulation 51 Comparison of Electroconvulsive Therapy and Magnetic Stimulation 51 Magnetic Stimulation to the Cerebellum 53 2.4.4 Use of Numerical Methods in Coil Design 53

2.5 Summary and Future Prospects 55 References 56

tens of kilohertz, depolarization of excitable membrane is the dominant mechanism of biological effects, and thermal effects are negligible in many cases.