MAGNETIC-FIELD ARISING FROM CURRENT DIPOLES RANDOMLY DISTRIBUTED IN AHOMOGENEOUS SPHERICAL VOLUME CONDUCTOR

Certain types of magnetic noise arising from physical as well as biolo gical sources can be explained by the model of current dipoles randoml y distributed in a volume conductor. The volume conductor investigated in the present study is the homogeneous sphere, which is the model co mmonly used in analyses of the magnetic field of the human brain (magn etoencephalogram). Uniform distributions of random dipoles in three di fferent source spaces are considered: a spherical surface, a spherical shell, and a sphere. The main emphasis is put on the radial component of the magnetic field. It is shown that the expectation value for the product of magnetic fields simultaneously measured at two locations, the covariance, depends on only two parameters of the measurement loca tions: the angular distance and the product of the radii. The formulas derived for the covariance can be expressed in terms of elliptic inte grals of the first and the second kind, so that a very efficient numer ical calculation is possible. For the special case of the variance (tw o identical measurement locations) these formulas reduce to expression s composed of elementary functions. Numerical examples show that the n oise produced by random dipoles in a sphere is similar to the noise ge nerated by random dipoles on a spherical surface having a slightly sma ller radius.