Magnetic Field Stimulation of Bent Neurons
Date
2014-06-25
Authors
Abdeen, Mohammad
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Abstract
Magnetic neural stimulation of straight neurons with bends (1) in a semi-infinite volume
conductor with a planar interface and (2) in the model of the human head is analyzed. Two
stimulating coils, namely the double-square and the double circular, producing the magnetic
field for the neuron stimulation are considered. The results indicate that the stimulating
coil characteristics (size, shape and location) and the neuron shape affect the magnitude and
location of the stimulation. The activating function, defined as the electric field derivative
along the neuron, has two components. One component depends on the derivative of the
electric field along the straight section of the neuron, and the other on the field magnitude.
For bent neurons in a semi-infinite volume conductor, an analytical expression of the activating
function (the stimulus) of the neuron was derived. The maximal stimulation point is
at the bend of the nerve and its position depends on the nerve shape and coil parameters.
The analysis also shows a better performance (a stronger stimulus) for a double-circular
(figure eight) coil than for a double-square coil of comparable size.
Stimulating bent neurons in the human head is also analyzed. The head model consists
of an outer sphere representing the skull and scalp and two inner spheres such that
each represents one half of the brain. The 3D-impedance method was used to obtain the
induced electric fields by the double-square and double-circular coils. Quasi-static conditions
are assumed. The geometry of the neuron in this model approximates the normal
configuration of motor neurons in the human head. The analysis shows that the stimulation
occurs almost at the highest point on the nerve (the closest point to the coil) with the
coil positioned in such a way that its center is directly over the highest point on the nerve.
It is also shown that the double-square coil produces a stronger stimulus than the double-circular
coil. This result is in contradiction with that for a bent neuron in a semi-infinite
volume conductor, however, it agrees with the results obtained for a straight neuron [1].
The analysis of bent neurons represents a more realistic approximation of the
actual anatomy. The results of this analyses confirms the conclusions and, therefore, usefulness
of simplified analyses of straight neurons. The results are expected to be of some
use in clinical applications where non-invasive neural stimulation is desired and location
of stimulation needs to be known.
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Keywords
neural stimulation, magnetic field, electric field, human head