MAGNETIC NERVE STIMULATION: A COMPARISON BETWEEN MONO-PHASIC AND BI-PHASIC WAVEFORMS

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

Abstract: Magnetic nerve stimulation is a non-invasive method of exciting neural tissues. In previous work we proposed two types of stimulating coils: an air core coil and a magnetic core coil [1]. The objective of our design was to generate a magnetic field that is strong enough to excite the targeted nerve with no (or minimum) affect to the surrounding nerves.

This paper represents a continuation to our previous work. It outlines the simulation results when applying different pulse configurations (bi-phasic vs mono-phasic) to the stimulating coil. The induced electric fields generated by the two waveforms were calculated using the finite element method along with a three dimensional transient solver. The coils considered for this analysis were: Figure 8 coil and the two proposed coils. A comparison between the three coils was constructed based on the induced electric field spatial distribution.

INTRODUCTION

A magnetic stimulator operates on the concept of charging a capacitor with high voltage and discharging this voltage into a stimulating coil. The result is a high current pulse (in the range of kilo amps) over a short period of time (in the range of 100s of micro seconds). The current pulse is bounded by the time of nerve depolarization (0.1-0.5 msec for peripheral nerve [2]) and the fundamental law of excitation embodied in the strength duration relation (S-D curve [3]). Accordingly, the current pulse configuration represents a crucial variable in magnetic stimulation as it defines the electrical field induced in the excitable tissues.

To model and calculate the electrical field within biological tissues during magnetic stimulation are not easy tasks. The difficulties encountered are due to the transient state of the supply, the regions of interest complex shapes, and the heterogeneous and non linear electrical characteristics of these regions. The finite element method was chosen to solve this problem as it has the flexibility of handling complex geometry for various regions with different types of boundaries and electrical characteristics [4].

Theory

Equation (1) represents a general formula for the electric field induced during magnetic stimulation.

It shows that the electric field consists of two components. The first component (- ∇Φ ) is the electrostatic potential (electric scalar potential) that arises from a fixed electric charge, while the second component (- ∂/ ∂t) represents the contribution of the coil transient magnetic field due to magnetic induction. The first component (- ∇Φ )generates an electric field ζ_Φ which is relatively small when compared to ζ_A (work in progress). Therefore, for this study when calculating the electric field the assumption is the total electric field is defined by the second component only. The software Magnet (which is based on finite element analysis) combined with a three dimensional transient solver were used to calculate the magnetic vector potential ( )[5].

METHOD

Three problems were constructed in three dimensions to simulate the following coils: Figure-8 coil, and the two proposed coils (air core and magnetic core). In each problem, the coil was positioned above a model that represents the upper limb at the junction of the proximal and middle thirds of the humerus. As the median nerve is well defined within its surrounding tissue and provides distinctive boundaries, it was selected as the targeted area in these simulations [1]. Careful mesh distribution was considered with high node densities applied around the nerve and the interface between the coil and the arm. Assuming that the magnetic flux diminishes at the boundary, Dirichlet boundary conditions were applied to this analysis. After applying the mesh, the regions electrical characteristics, number of coils, and their forcing functions (supplies) were defined for each problem. An algorithm was written using the software MatLab to generate the currents required to supply the coils. The same energy per pulse was used for both waveforms. Figure 1 shows the current and the current rate of change waveforms (mono-phasic and bi-phasic) when using a Figure-8 coil. These waveforms were constructed based on monitoring the current pulses generated by a commercial system (Dantec Magpro).

For the Figure-8 coil, the current was divided equally between the two coils, while for the proposed coils, the current was divided into three equal parts. Two parts were divided between fourteen windings while the third part was supplying the three perpendicular windings [1].

Figure 1: Current and current rate of change waveforms.

RESULTS

Figures (2,3) illustrate the electric fields induced at the nerve by the three coils when using a mono-phasic pulse and a bi-phasic pulse respectively. Figures (4,5) show the magnetic flux densities along the nerve for bi-phasic pulses. Comparable results were obtained for mono-phasic pulses.

From figures (2,3) it is clear that the induced electric fields for bi-phasic waveforms are higher than mono-phasic ones. Also, it can be noted (especially figure 3) that the area under the curve of the proposed magnetic core coil is larger than that for the other two coils. This is due to the energy stored in the magnetic core. Figures (4,5) show that the flux densities across and along the nerve produced by the magnetic core coil is higher than that generated by the other two coils. This is valid for both pulse types.

Figure 2. Electric fields induced by mono-phasic pulses.

Figure 3. Electric fields induced by bi-phasic pulses.
 

Figure 4. Magnetic flux densities across the nerve.

Figure 5. Magnetic flux densities along the nerve.

DISCUSSION