| Περίληψη: | The human brain is an extremely complex organ for which the knowledge we have so far is minimal. This complexity is due to the vast number of nerve cells it contains. The brain neurons compose an enormous electric circuit in which ionic currents of biochemical origin flow. The presence of primary and induced electric currents in stimulated areas within the brain, leads to the generation of an electromagnetic field that can be detected externally. In particular, the weak external magnetic field is measured by the Magnetoencephalography method.
In the present work, the brain, together with the scull which surrounds it, is considered as a single, homogeneous and isotropic conductor, while the source of the externally measured electromagnetic field is modeled as a single dipole located at a specific point inside the conductor. At this point it is noted that the size of the human brain and the values of the physical parameters describing the propagation of the electromagnetic wave within the brain, allow the use of the quasi – static theory of Maxwell’ s equations to describe the propagation of the electromagnetic field, that is generated by the brain’s function.
The geometric model used for the conductor, in this work, is the spherical and the ellipsoidal one. The spherical geometry is based on spherical symmetry and although it is not a realistic description of the brain, it is widely used for the interpretation of encephalographs. On the other hand, the ellipsoidal geometry embodies the anisotropy of the three – dimensional space and better fits to the brain anatomy, but leads to significantly more complicated equations.
Taking into account the above assumptions and using certain vector analysis techniques, the forward Magnetoencephalography problem is solved. Namely, the magnetic field generated outside the brain, is calculated. In the case of the spherical conductor, the magnetic field can be calculated analytically as an expansion of spherical harmonic functions, but also in a closed form, whereas in the case of the ellipsoidal conductor, the magnetic field is calculated as an expansion of ellipsoidal harmonic functions. The result for the ellipsoidal conductor can produce, with the help of certain techniques, the result obtained for the spherical conductor, indicating that the ellipsoid is a superset of the sphere. In addition, the results reveal the effect that each geometry has on the exterior magnetic field and provide information for it, which can contribute to the solution of the inverse Magnetoencephalography problem.
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