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The application of FEM technique to electromagnetic models for magnetic neural stimulation Le Pocher, Herve

Abstract

Several aspects of magnetic neural stimulation are investigated by applying an advanced finite-element analysis. The objective is to demonstrate that the finite element method is well suited for realistic bio-electromagnetic modelling. The focus of our research is to explore four factors which affect induced electric fields: 1) magnetic coil diameter, 2) anisotropic tissue conductivity, 3) inhomogeneous tissue conductivity and 4) finite tissue volumes. All results are analyzed in terms of the second space derivative of the potential along the nerve fiber path 82V/82 called the "activation function". If two magnetic coils have the same outer diameter than the one with the larger inner diameter will induce the largest electric field and activation function. This result has direct clinical implications for modern commercial magnetic coil designs which are characterized by small inner diameters. In addition, a magnetic coil was modelled over a semi-infinite planar tissue and a finite cylindrical tissue. The electric field induced in the finite volume was 25% smaller than in the planar volume; however, the activation function magnitude remained essentially constant. The fields generated by two magnetic coil designs were then applied to arms modelled with isotropic and anisotropic conductivities. The results show that the electric field is 13% lower and that the activation function is 24% lower in anisotropic tissue relative to the values seen in the isotropic tissue. These field reductions may be attributable to changes in the distribution of surface charges. The isotropic model results for the arm were compared to previous studies where fields were modelled within a planar isotropic tissue. This analysis indicates that a larger activation function can be induced in the arm due to rapid spatial changes in the electric field magnitude, even though a larger electric field magnitude is present in the planar tissue. Conversely, if the magnetic coil is too large surface charges in the arm will significantly decrease both the activation function and the electric field. A magnetic coil was modelled above the gyrus of the primary motor cortex. The gyrus conductivity was modelled in three ways: 1) homogeneous, 2) inhomogeneous-isotropic and 3) inhomogeneous-anisotropic. Only minor differences in the results could be attributed the anisotropic conductivity parameters. Several features of the modelled electric fields within the inhomogeneous tissue were different from those found in the homogeneous model: 1) the electric fields were not all parallel to the planar air/tissue interface, 2) there was a significant increase in the electric field above the gyrus and within the crest of the gyrus, 3) decreases in the current density were found within the gyrus and 4) large electric field gradients were observed at conductivity interfaces. A typical pyramidal fiber path was then defined within the gyrus andits activation function was calculated. We found two distinct peaks in the activation function, one related to a conductivity interface and the second related to a bend along the fiber path. The magnitude and spatial span of both these peaks are unlike any previously reported for magnetic stimulation. Either of these two peaks may account for both the direct and indirect pyramidal stimulation reported in clinical investigations. These model results indicate the importance of several tissue characteristics which have not been investigated in previous studies, and demonstrate how these characteristics interact with each other and their relationship to effective nerve stimulation.

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