Peripheral Nerve Stimulation Thresholds Based on Waveform Shape and Implications for Guideline Limits

Abstract

The objective of this paper is to derive basic restrictions for induced internal electric field and reference levels for external magnetic flux density for a class of periodic non-sinusoidal waveforms as multiples of the existing limits applicable to sinusoidal waveforms in current exposure standards. The Law of Electrostimulation and the Spatially Extended Nonlinear Node computational model were used to derive peripheral nerve stimulation thresholds of the internal electric field for both non-sinusoidal and sinusoidal waveforms. Threshold ratios (non-sinusoidal to sinusoidal) permitted basic restrictions and reference levels to be derived as multiples of the sinusoidal ones. Intercomparisons of threshold ratios from both models suggest that they are in agreement for flat-topped flux density waveforms with fast rise-times relative to the period but showed a discrepancy for the continuous sinusoid. Results from the computational model were used to establish the threshold ratios used in the conversion. Resulting non-sinusoidal basic restrictions and reference levels were found to have the same functional relationship with frequency as the sinusoidal ones, consisting of two ranges: a flat rheobase and a frequency-dependent (basic restriction) or inverse frequency-dependent (reference level) portion that intersects the rheobase at a transition frequency that is waveform-dependent. Above the transition frequency, the non-sinusoidal basic restriction was found to be inversely related to the flux density rise-time, resulting in an increased limit for fast-rising waveforms. The transition frequencies of fast-rising waveforms were found to be lowered relative to the sinusoidal one. Above the same transition frequency, the non-sinusoidal reference level is flat with frequency and was found to be approximately 79% lower than the sinusoidal one.

Fig. 1

(a) The three waveforms of B(t) all having peak amplitude B_pk. (b) The corresponding waveforms of E(t) = C_i dB/dt, evaluated for their relative thresholds (scale factors relating to B_pk are indicated in the legend).

Fig. 2

Examples of monophasic single pulses of E(t) consisting of sinusoid, exponential, and rectangular shapes for demonstration of the LOE and comparison with the SENN model.

Fig. 3

Threshold SD curves for single monophasic pulses (sinusoidal, rectangular, and exponential shapes) computed using the LOE and the rheobase and chronaxie values indicated. Also shown is the result of the SENN analysis for the rectangular pulse.

Fig. 4

Comparison of SENN and LOE-derived SD curves of single monophasic sinusoidal and exponential pulses. LOE curves were computed using a rheobase of 5.90 V m⁻¹ and chronaxie of 0.1248 ms.

Fig. 5

Results of SENN threshold calculations for the ramp waveform with phase factors β = 1, 3, 5, and 7 and the continuous sinusoid. Also shown are the low-frequency asymptote (rheobase) and high-frequency asymptotes (where thresholds have linear frequency dependence).

Fig. 6

Results of SENN threshold calculations for the exponential waveform with phase factors α = 1, 5, 10, 15, and 20. Also shown are the low-frequency asymptote (rheobase) and high-frequency asymptotes (where thresholds have linear frequency dependence).

Fig. 7

Magnetic flux density waveform with sinusoidal leading edge (SLE) and its associated E(t) waveform consisting of biphasic sine pulses separated by a dead space of length T/2−d.