MEASURING THE INDUCED ELECTRICAL FIELDS IN 3-DIMENSIONS WHEN APPLYING MAGNETIC STIMULATION TO A SPHERICAL TARGET

Nafia Al-Mutawaly, Hubert de Bruin
Department of Electrical and Computer Engineering, McMaster University
1280 Main St. West, Hamilton, Ontario, CANADA, L8S 4L7

Abstract: The induced electric fields during magnetic stimulation represent a critical variable in evaluating and quantifying the effectiveness of this technique. A precise measure of these fields in three dimensions is the first step to map and define their spatial distributions. However, measuring these fields is a tedious task due to the field transient pattern and dependability on many variables such as: coil type, pulse configuration, media conductivity, and target shape. Further, these fields are extremely sensitive to coil position and orientation especially within biological tissues.

In this paper a practical approach is presented to measure and map the induced electrical fields, in three dimensions within spherical volumes. The variables considered for the experiment were: coil type (Figure 8 and circular coils), coil current rate of change (di/dt), current direction, and media conductivity.

INTRODUCTION

Previous researchers [1,2,3] conducted many experiments to measure and map the electrical fields in homogeneous and inhomogeneous media. Their measuring apparatus generally consisted of: a positioning device, a tank of saline solution, different types of probes, and an oscilloscope. In these studies, the voltage gradients between the probe(s) tips, assuming that the distance between the tips is negligible, was approximated to represent the electric field as a point source. The experimental procedures were time consuming and required considerable attention to ensure valid measurements. Further, the data could not be retrieved since they were partially stored on a multi channel oscilloscope. As well, these experiments mostly utilized flat surfaces and did not accurately model transcranial stimulation which requires a spherical volume. Weissman et al. [4] conducted a study using multi spherical targets, however,their measurements were limited to specific points and did not map the induced fields through the entire targeted region.

Considering the previous work, a prototype resembling the size of the head was designed and built to measure the electric field. The model consists of three glass half spheres stacked inside each other with adjustable rings to align their position. Each sphere has a spout which allows filling and draining of various types of media. An array of orthogonal pairs of inductors was positioned from the center of the sphere to its parameter. These inductors are attached to a ribbon cable which extends outside the sphere and is terminated by a 15 pin connector. Figure (1) illustrates the experiment setup.

EXPERIMENT HARDWARE AND SOFTWARE

The influence of coil type, coil current rate of change, current direction, and media conductivity were examined for different stimulus intensities. A magnetic stimulator (Dantec MagPro) with a circular coil (outer diameter 12cm consisting of 13 windings) and a Figure 8 coil (outer diameter 10cm consisting of 2x10 windings) were used for this study. The advantage in using the Dantec MagPro is the flexibility in changing the coil current direction, without rotating the coil, by a switch located at the front panel. The stimulus intensities were increased in steps of 10% from 20% to 100% of the maximum stimulator output. For each step 10 consecutive signals were collected and averaged for the orthogonal fields induced in the inductors. To ensure the same energy was supplied for all stimuli within one step the di/dt value, displayed at the front of the panel, was monitored throughout the experiment. The magnitude and the direction of the measured fields were calculated from the orthogonal data. In addition to air, saline solutions with two concentration levels were tested.

The voltages induced in the inductors were collected using a personal computer via a data acquisition board guaranteed for 200 kS/sec (PCI-6024E a 12-bit data acquisition board National Instruments). The common mode rejection ratio (CMMR) of the board is 85 dB for a gain of 100. The fields in two dimensions (plane) were sampled at 100 kHz and acquired by a stand alone algorithm created using Labview software (ver. 5.1 National Instruments) and Matlab software (ver. 5.2 MathWorks Inc.) The algorithm allows the user to acquire a train of signals, calculate the area and the peak to peak amplitude of each pulse, and store the data in ASCII and spreadsheet formats. The algorithm also allows the user to retrieve or reread the data from the stored files, average and post-process the data.

Figure 1. Experiment Setup.

RESULTS

1. Figures (2) and (3) show the measured electric fields generated by a circular coil for bi-phasic and mono-phasic pulses respectively. Using a Figure 8 coil, comparable waveforms in shape with proportional amplitudes were obtained for both types of pulse configurations. Figure (4) shows a comparison between the electric fields measured for different waveforms using different coils.

These results are identical to Niehaus et al. [5], and Kammer et al. [6] findings. In their experiments, they used what is called a “pick up coil” to measure the waveform of the Dantec MagPro stimulator.

2. Changing the current direction for both types of coils did not change the induced field generated by the inductors.

3. The above results were collected using empty spheres. Adding saline solutions with different concentration levels (different conductivity) did not affect the induced fields. This agrees with the study of Maccabee et al. [1] in which they used saline solutions with different concentration levels.

Figure 2. Electric fields generated by bi-phasic waveforms.

Figure 3. Electric fields generated by mono-phasic waveforms.

Figure 4. Electric fields of various waveforms and coils.

DISCUSSION

This paper has outlined a practical approach to measure the induced electrical fields during magnetic stimulation. The results obtained showed that the induced fields are dependent on the coil type and pulse configuration but not on current direction or the media conductivity. It is important to reiterate that the induced fields are very sensitive to the coil position and orientation. Accordingly, it is difficult to use a probe to measure the field precisely within a sphere. However, the proposed prototype ensures minimal movement, consistency in position and orientation and consequently accurate measurements can be achieved. The instrumentation used in this study will allow us to further investigate the electric field induced in a spherical medium by new coil designs. The effect of different media conductivities will also be investigated.

Acknowledgment: This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

REFERENCES

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[4] J.D. Weissman, C.M. Epstein, K.R. Davey, “Magnetic brain stimulation and brain size: relevance to animal studies,” Electroencephalography and Clinical Neurophysiology, vol. 85, pp. 215-219, 1992.

[5] L. Niehaus, B.-U. Meyer, T. Weyh, “Influence of pulse configuration and direction of coil current on excitatory effects of magnetic motor cortex and nerve stimulation,” Clinical Neurophysiology, vol. 111, pp.75-80, 2000.

[6] T. Kammer, S. Beck, A. Thielscher et al., “Motor thresholds in humans: a transcranial magnetic stimulation study comparing different pulse waveforms, current directions and stimulator types,” Clinical Neurophysiology, vol. 112, pp.250- 258, 200.