Stimulation threshold comparison of time‐varying magnetic pulses with different waveforms

Abstract

Purpose: To clarify whether sinusoidal pulses possess lower thresholds than rectangular ones at perception threshold, a statement often made that contradicts the theory of stimulation. Materials and Methods:The results of a nerve stimulation study with 65 volunteers and with trapezoidal and sinusoidal gradient pulses were used to apply the combination of the electric field, induced in the tissue of the human body, with the "Fundamental Law of Electrostimulation." This law claims that the waveshape of a pulse is not essential as long as the amplitude of the pulse does not decrease below rheobase (rheobase condition). Results:If the rheobase condition is applied to sinusoidal waveforms and the pulse duration and amplitude is corrected accordingly, both trapezoidal and sinusoidal gradient pulses have identical threshold amplitudes as a function of pulse duration. Conclusion:The "Fundamental Law of Electrostimulation," including the "rheobase condition," proved to be a good basis for describing magnetic field stimulation (magnetostimulation) and that application of it to magnetostimulation is suitable as the basis for describing magnetic field stimulation with various waveforms. For nonrectangular pulses, pulse durations and pulse amplitudes must be corrected according to the "rheobase condition." The exponential Blair Equation is less suited to be applied in magnetostimulation. NATIONAL AND INTERNATIONAL BODIES have discussed possible hazards due to gradient switching in magnetic resonance imaging (MRI) systems and have formulated limiting exposure levels of magnetic fields (1). KeyHowever, there is still interest in understanding the process of stimulation in human subjects exposed to timevarying magnetic fields as they are used in MRI. The need to avoid painful peripheral nerve stimulation (PNS) or, even worse, cardiac stimulation, due to rapidly switched magnetic fields sets an upper limit on the magnetic field gradient strengths that can be employed in fast MRI. It is generally recognized that in whole-body imaging the ygradient coil causes PNS at the lowest rates of gradient change (2,3). A search of the literature of which electric fields can stimulate the heart revealed that the rheobase field strength of the heart for single monophasic stimuli is Ϸ60 V/m (4), and thus, 10 times higher than the lowest assumed threshold for 20 m diameter nerves with 6.2 V/m (5). Due to the fact that cardiac magnetostimulation has not yet been reported in humans and is not expected with the hardware currently available, the following considerations are focused on PNS, the first sensations that appear in whole-body MRI.Since publication of our first article on electrostimulation by time-varying magnetic fields (4), it is mostly accepted in the MRI literature that it is the electric field and not the current density that is responsible for magnetostimulation and that there is a hyperbolic relationship between pulse duration and the electric field characterized by the terms rheobase and chronaxie as they were introduced by Lapicq...

Magnetostimulation Limits in Magnetic Particle Imaging

“…Equation (11) is therefore an accurate estimation for the fundamental law of magnetostimulation for frequencies in the kHz range and above. APPENDIX ACCURACY OF THE FUNDAMENTAL LAW OF MAGNETOSTIMULATION As explained in [40], the fundamental law of magnetostimulation given in (11) is not exact. This is because the relation given in (5) assumes that the E-field is larger than at all times , which is not true for an electric field generated by a sinusoidal magnetic field.…”

A Model of Electrostimulation Based on the Membrane Capacitance as Electromechanical Transducer for Pore Gating

“…must be based on the effective pulse duration. The result, then, is equal to the threshold of a rectangular pulse of equal duration . Taking simply the period of the haversine would reduce the averaged amplitude thereby suggesting that sinusoidal pulses are more efficient than rectangular pulses.…”

“…We believe that this theory can be extended to nonrectangular waveforms . The fundamental equation (FE4) demands that the “effective pulse duration” ends where the rheobase is reached.…”

“…The fundamental equation (FE4) demands that the “effective pulse duration” ends where the rheobase is reached. This condition (FE4) is suited to determine the “effective pulse duration” of a nonrectangular pulse shape . The procedure is explained with Figure for a haversine pulse.…”

Predicting Magnetostimulation Thresholds in the Peripheral Nervous System using Realistic Body Models

“…It is well documented that for a given peak B-field strength, the trapezoidal waveform has increased PNS thresholds compared to a sinusoidal waveform 50, 51 . Furthermore, it has been observed that the PNS thresholds increase linearly with the pulse duration (ramp rise-time) 3 .…”