Abstract- Magnetic stimulation is the process of inducing eddy-currents in excitable tissue by a time varying magnetic field. Time varying gradient fields in high ...
IEEE TRANSACTIONS ON MAGNEl’ICS, VOL. 29, NO. 6, NOVEMBER 1993
3355
Magnetic Stimulation of Excitable Tissue: Calculation of Induced Eddy-Currents With a Three-Dimensional Finite-Element Model G.A. Mouchawar’, J.A. Nyenhuist, J.D. Bourlandt, L.A. Geddest, D.J. Schaefer’, and M.E. Riehl’ *Siemens Pacesetter, 15900 Valley View Ct., Sylmar, CA 91392 USA +Hillenbrand Biomedical Engineering Center, Purdue University, West Lafayette, Indiana 47907 USA ‘GE Medical Systems, 3200 Grandview, Waukesha, WI 53188 USA
Abstract- Magnetic stimulation is the process of inducing eddy-currents in excitable tissue by a time varying magnetic field. Time varying gradient fields in high speed Magnetic Resonance Imaging (MRI) may be of sufficient intensity to stimulate the patient. In this work, the eddy-current distribution in a 3D inhomogeneous model of the dog’s thorax due to time varying fields in MRI x, y and z-gradient coils and pair of coplanar coils are calculated. From experimental data of cardiac threshold from a z-gradient coil for a 540 p rectangular pulse, a current density of 21.5 A/m3 was calculated. For a co-planar coil pair, the threshold current density for cardiac stimulation is 19.2 A/mZ at duration 640 p. The different conductivities of tissues in the thorax have a significant influence on the eddy-current flow. Calculations combined with measurements will help identify safe levels of pulsed gradient fields in future MRI systems.
I. Introduction Magnetic stimulation [ 1,2] is the process of stimulating excitable tissue by application of a time varying, high intensity magnetic field, which induces an electric field. If the resulting eddy-currents are of sufficient intensity and duration, stimulation of the tissue will occur. By suitable coil geometry, some focusing of the induced eddy-currents can be achieved [3-51. In Magnetic Resonance Imaging (MRI). pulsed magnetic fields are applied to the patient in order to alter the frequency and phase of the precessing nuclei. Three pairs of gradient coils are present in the typical imager to produce field gradients G , E aB,/ax, G , = aB,/ay, G, = aB,/az, where the z-direction is defined to be in the direction of the static field. Coils used to generate these gradient fields in an imager with the static field along the bore of the magnet are depicted in Fig. 1.
High speed MRI will use gradient field strengths in excess of those presently used, and these fields may be of sufficient intensity to stimulate the patient [6-81. This stimulation may merely be sufficient to elicit sensation, which is not likely to he harmful but may disturb the tranquillity of the patient. Sufficiently large pulsed field intensities wiIl disturb the rhythm of the heart, which is to be avoided. Potential hazards of the stimulatory effects on excitable tissues by the trapezoidal gradient magnetic fields which are typically used have been reported by Ueno et al. [9] We have undertaken a number of experimental studies to assess what intensities of pulsed field gradients will result in peripheral nerve stimulation in human volunteers [7] and in peripheral nerve and cardiac stimulation in the dog.[lO,ll] Figure 2 depicts the geometries we used to study stimulation in the dog. The transverse coil model is very similar to an actual MRI coil. The inductive coupling between the two MRI z-coils in Fig. i(a) is small and thus the single z-coil in Fig. 2 induces an eddy-current pattern similar to that which is produced in the vicinity of one of the coils in Fig. l(a). In order to interpret the data from stimulation experiments and to predict the stimulating effects of various gradient coil configurations, it is important to know the distribution of the currents induced in the body by the pulsed gradient coils. Simplified geometries have been used to calculate the induced eddy-currents in the patient resulting from MRI gradient fields [ 121. The simple models do not account for the inhomogeneities in the electrical properties of the body. We calculated the induced eddycurrents with a three-dimensional (3D) finite element model (FEM). 11. Numerical Methods The electric field Etbuc in the tissue is given by 01
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rr-,
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where @ is the electrostatic potential and A is the magnetic vector potential. For the waveforms used in MRI and considered here, the electrical skin depth is several meters, much greater than the dimensions of the patient Consequently, we need to consider only the current in the coil in the calculation of A. The electrostatic potential arises from electric charge that accumulates in regions where the conductivity ts is non-uniform. Making the assumption of a linear and isotopic conductivity, the current density J t b e is
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Magnetic Field for x=O
0
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Fig. 1. Geometries of z and transverse gradient coils and the corresponding magnetic field maps. The arrow lengths are proportional to the magnitude of the field and the arrow direction gives the direction of the magnetic field. The y-axis on both field maps extends from -0.25 m to 0.25 m.
fi.
where w is the angular frequency, E is the permeability and j = The displacement current in the body will he small compared to the conduction current, Le. mats. In steady state. we have V * ( C & , ~ ~=)0 and combining this result with Eq. 1 yields aA V*(OV@)= -vw(3) at We multiply Eq. 3 by an arbitrary test function v(x,y,z) and integrate over the volume domain D. Application of Green’s Theorem results in
Manuscript received February 15, 1993. l l i s work was supported in part by GE Medical Systems and by the Fetzer Foundation. Technical a5sistance w a provided by J.T. Jones, K.S.Foster, G.P. Graber and W.E.Schoenlein.
0018-9464/93$03.00 Q 1993 IEEE
3356 13
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Fig. 2. Geometry of experiments for measurement of cardiac stimulation thresholds in the dog by coils which produce stimulating fields similar to those of the gradient coils shown in Fig. 1.
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