Magnetic Field Stimulation of Bent Neurons




Abdeen, Mohammad

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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.



neural stimulation, magnetic field, electric field, human head