Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry

Understanding the functional brain is one of the top challenges of contemporary science. The challenge is connected with the fact that we are trying to understand how an organized structure works and the only means available for this task is the structure itself. Therefore an extremely complicated scientific problem is combined with a hard philosophical problem. Under the given conditions it comes as no surprise that so many, apparently simple, physical and mathematical problems in neuroscience are not generally solved today. One of this problems is the electromagnetic problem of a current field inside an arbitrary conductor. We do understand the physics of this problem, but it is very hard to solve the corresponding mathematical problem if the geometry of the conducting medium diverts from the spherical one. Mathematically, the human brain is an approximately 1.5 L of conductive material in the shape of an ellipsoid with average semiaxes of 6, 6.5 and 9 cm [47]. On the outermost layer of the brain, known as the cerebral cortex, most of the 1011 neurons contained within the brain are distributed. The neurons are the basic elements of this complicated network and each one of them possesses 10 4 interconnections with neighboring neurons. At each interconnection, also known as a synapse, neurons communicate via the transfer of particular ions, the neurotransmitters [38]. Neurons are electrochemically excited and they are able to fire instantaneous currents giving rise to very weak magnetic fields which can be measured with the SQUID (Superconducting QUantum Interference Device). The SQUID is the most sensitive apparatus ever built. It can measure magnetic fields as small as 10-14 T, a sensitivity that is necessary to measure the 10-15 to 10-13 T fields resulting from brain activity. For comparison we mention that the magnetic fields due to brain activity are about 10-9 of the Earth's average magnetic field, 10-5 of the fluctuations of the Earth's magnetic field, and about 10-3 of the maximum magnetic field generated by the beating heart. © 2009 Springer-Verlag Berlin Heidelberg.