Magnetic Field Stimulation - the Brain as a Conductor
The brain is an inhomogeneous conductor consisting of white matter, grey matter, and cerebral spinal fluid with conductivities, 0.48 S/m, 0.7 S/m, and 1.79 S/m respectively. The skull is essentially a zero current density region since its conductivity about 100 times smaller, 32-80 mS/m. Analysis shows that for the purposes of magnetic stimulation, the brain can be treated as a homogeneous conductor; differences in the computations of the induced electric field for the homogeneous and inhomogeneous models are insignificant. The currents induced in the brain are induced by a changing magnetic field, but they are too small to influence that field. The induction is a one way coupling, and thus the problem is not a true eddy current problem. Faraday and Ampere’s laws are easily applied to predict the induced current subject to the condition that the normal component of current density go to zero at the scalp interface. Iron core stimulators constructed as tape cores are more efficient than air core stimulators. With both air and iron core stimulators, the field will always be higher on the scalp than within the white and grey matter. The higher induced surface fields are the cause of pain in some patients. This effect can be mitigated by shields and stimulator topologies that spread out the field, but it can never be eliminated. No inversion can ever be realized wherein the induced field is larger at depth than at all places on the scalp. A properly designed brain stimulation system starts with the target stimulation depth, and it should incorporate the neural strength – duration response characteristics. Higher frequency pulses require stronger electric fields. At the heart of the process is the transfer of charge across the nerve membrane commensurate to raise its intracellular potential about 30-40 mV. Think of this membrane as a capacitance that behaves more like a short circuit at high frequency. A nerve’s chronaxie and rheobase values can be used to dictate the electric field required for stimulation as a function of frequency. The system’s parameters can then be chosen to minimize stimulator energy and size. Changes to TMS stimulators are not likely to come from the superconducting community, or the ultracapacitor and supercapacitor community. Because of the large air gaps involved, 3% grain oriented steels and vanadium cores are about as suitable for standard C cores as one might expect. The malleability offered by powdered cores might, however, offer interesting penetration and flexibility options for the TMS market.