  Transcranial static magnetic stimulation is a novel noninvasive method of
reduction of the cortical excitability in certain neurological diseases that,
unlike ordinary transcranial magnetic stimulation, makes use of static magnetic
fields generated by permanent magnets. The physical principle underlying
transcranial magnetic stimulation is well known, that is, the Faradays law. By
contrast, the physical mechanism that explains the interaction between neurons
and static magnetic fields in transcranial static magnetic stimulation remains
unclear, which makes it difficult to improve and fine tune the treatment. In
the present work it is discussed the possibility that this mechanism might be
the Lorentz force exerted on the ions flowing along the membrane channels of
neurons. To support this hypothesis, a dimensional analysis it is carried out
to compare the Larmor radius of the ions in the presence of a static magnetic
field with the dimensions of the cross section of human axons and membrane
channels in neurons. This analysis shows that whereas a moderate static
magnetic field is not expected to affect the ion flux through axons,
nevertheless it can affect the ion flux along membrane channels. The overall
effect of the static magnetic field would be to introduce an additional
friction between the ions and the walls of the membrane channels, thus reducing
its conductance. Calculations performed by using a Hodgkin-Huxley model
demonstrate that even a slight reduction of the conductance of the membrane
channels can lead to the suppression of the action potential, thus inhibiting
neuronal activity.
