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, which can cause peripheral nerve stimulation (PNS). Although magnetostimulation has been extensively studied below 10 kHz, the behavior of PNS at higher frequencies remains poorly understood. This study aims to investigate PNS thresholds at frequencies up to 88.1 kHz and to explore deviations from the widely accepted hyperbolic strength-duration curve (SDC).PNS thresholds were measured in the head of 8 human volunteers using a solenoidal coil at 16 distinct frequencies, ranging from 200 Hz to 88.1 kHz. A hyperbolic SDC was used as a reference to compare the frequency-dependent behavior of PNS thresholds.Contrary to the predictions of the hyperbolic SDC, PNS thresholds did not decrease monotonically with frequency. Instead, thresholds reached a minimum near 25 kHz, after which they increased by an average of 39% from 25 kHz to 88.1 kHz across subjects. This pattern indicates a significant deviation from previously observed behavior at lower frequencies.Our results suggest that PNS thresholds exhibit a non-monotonic frequency dependence at higher frequencies, diverging from the traditional hyperbolic SDC. These findings offer critical data for refining neurodynamic models and provide insights for setting PNS safety limits in applications like MRI gradient coils and magnetic particle imaging (MPI). Further investigation is needed to understand the biological mechanisms driving these deviations beyond 25 kHz. Clinical impact -These findings call for further basic research into biological mechanisms underlying high frequency PNS threshold trends, and supports refinement of safety guidelines for MRI and MPI systems for clinical implementation.

Keywords: High frequency magnetostimulation; MRI gradient safety; magnetic particle imaging (MPI); magnetic resonance imaging (MRI); 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). is 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 B-field frequency and amplitude. Grey dots represent no subject 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. The black curve is a hyperbolic strength-duration curve fit of the subject-averaged thresholds ( mT, s). Note that the hyperbolic fit was performed using frequency points below 10 kHz but extrapolated at all frequencies. (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, , where for a sinusoidal stimulation waveform. (e) Zoom into lowest (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 . (e) Zoom into lowest range of .