Measurement of peripheral nerve magnetostimulation thresholds of a head solenoid coil between 200 Hz and 88.1 kHz

Abstract

Magnetic fields switching at kilohertz frequencies induce electric fields in the body that can cause peripheral nerve stimulation (PNS). Magnetically induced PNS, i.e. magnetostimulation, has been extensively studied below 10 kHz. It is widely characterized using a hyperbolic strength-duration curve (SDC), where the PNS thresholds monotonically decrease with frequency. The very few studies performed at higher frequencies found significant deviations from the hyperbolic SDC above ~ 25 kHz, however, those measurements are sparse and show large variability. We fill the gap in the data by measuring PNS in the head of 8 volunteers using a solenoidal coil at 16 frequencies between 200 Hz and 88.1 kHz. Contrary to the hyperbolic SDC, PNS thresholds did not decrease monotonically with frequency, but reached a minimum ~ 25 kHz. The thresholds then increased by 39% from 25 kHz to 88.1 kHz on average across subjects. Our measurements can be used for guidance and validation of neurodynamic models and to inform PNS limits of magnetic resonance imaging (MRI) gradient coils and magnetic particle imaging (MPI) systems. The observed deviation of the experimentally measured thresholds from the hyperbolic SDC calls for further study of the underlying biological mechanisms of magnetostimulation beyond 25 kHz.

Keywords: High Frequency Magnetostimulation; MPI Safety; MRI Gradient Safety; Magnetostimulation; Peripheral Nerve Stimulation.

Figure 1

(a) Image of the solenoidal coil used in human head PNS studies. (b) Illustration of coil winding position relative to the subject’s head. (c), (d) Comparison of measured field efficiencies using a 3-axis hall magnetometer and field mapping robot and simulated field efficiencies using FEMM 4.2. Field efficiencies were evaluated radially (at z=0) in (c) and axially (at r=0) in (d).

Figure 2

(a) Image of patient bed used for human head PNS studies, with coil mounted (blue dashed box) and reconfigurable capacitor bank (red dashed box). (b) Image of constructed capacitor bank. (c) Circuit schematic detailing amplifier connection and switchable capacitor bank. Switch S1 allows for bypassing the capacitor bank to operate in untuned configuration. Switches S2, S3… connect additional capacitors in parallel, enabling rapid changing of LC tuning for human studies.

Figure 3

Pulse shaping examples. We shaped current pulses to eliminate differences in pulse rampup times to enforce similar waveform shapes across all frequencies. Each row shows the voltage waveform (left), current waveform (middle), and zoom in of current waveform to show fit function (equation (3)) superimposed in dashed red. (a)Measured 4.04 kHz step voltage input and current response, which has a natural time constant of 12.7 cycles. (b) Shaped 4.04 kHz voltage waveform to achieve a desired time constant of 5 cycles (measured as 5.2 cycles). T_desis marked during the rampup phase for this waveform. (c) Shaped 4.04 kHz voltage waveform to achieve a rampup time constant of 25 cycles (measured 24.9 cycles). (d)Example untuned 200 Hz waveform, modulated by an exponential envelope with 25 cycle rampup time constant (25.05 measured). In the experiments, a time constant of 25 cycles for all resonant and untuned frequencies was chosen.

Figure 4

Example subject responses for threshold determination. Subjects record stimulation via a push button for each pulse over peak amplitude at the coil center. (a) Example of a clear transition between no stim and stim, where there is no overlap in subject response verses field amplitude. (b) Example of a wide transition between no stim and stim with some ambiguity.

Figure 5

All subject titration data versus frequency on a log scale. Field amplitudes represent the peak B-field at the coil center. Each dot represents an applied B-field pulse. Red dots represent subject-reported stimulation at the respective B-field frequency and amplitude. Grey dots represent no reported stimulation. Each vertical set of dots represents a single titration run for a particular frequency.

Figure 6

(a) All subject threshold data on linear frequency scale. Gray traces represent a single subject’s threshold vs. frequency curve. Overlaid are averages across subjects calculated by fitting error functions to a normal CDF (red trace). Error bars indicate standard deviation of the fit CDF. A hyperbolic fit (black trace) modeling the hyperbolic SDC (B__rheo= 5.80 mT, τ_chron=394 μs) to the subject average curve is additionally plotted. (b) Zoom into lower frequency data points on linear scale. (c) Zoom into lower amplitude threshold region, to emphasize deviation from hyperbolic SDC for high frequency data points. (d) All subject data plotted against effective stimulus duration, t_eff, where t_eff=1⁄πf for a sinusoidal stimulation waveform. (e) Zoom into lowest t_eff (highest frequency) points to highlight deviation from the hyperbolic fit.

Figure 7

(a) Comparison of all subject averages (red trace) for constant 256 cycles per sinusoidal pulse, with application of equation (8) to scale thresholds to constant pulse duration (gray trace). Overlaid is the hyperbolic fit from Fig. 6 (black trace). (b)Zoom into lower frequency data points. Note that the duration scaling does not alter thresholds significantly over these frequencies. (c) Zoom into lower amplitude threshold region. Because of the short pulse durations at these frequencies, we see up to 17% lower thresholds at 88.1 kHz in the corrected trace compared to the uncorrected trace. (d) The same data from (a), plotted versus t_eff. (e) Zoom into lowest range of t_eff.