Optimal monophasic, asymmetric electric field pulses for selective transcranial magnetic stimulation (TMS) with minimised power and coil heating

TL;DR

The paper addresses the high energy cost and coil heating of monophasic, directionally selective TMS pulses. It introduces a minimally constrained optimisation framework that jointly enforces neuron-activation constraints and allows flexible pulse asymmetry, yielding highly energy-efficient, near-rectangular asymmetric waveforms. Experimental validation shows up to $92\%$ reductions in energy loss and a clear $1.79\pm0.41$ ms MEP-latency difference between AP and PA directions for OUR pulses, indicating directional selectivity. Collectively, the approach enables selective, rapid-rate TMS with reduced power needs and heating, potentially enhancing precision and throughput of neuromodulation therapies.

Abstract

Transcranial magnetic stimulation (TMS) with asymmetric electric field pulses, such as monophasic, offers directional selectivity for neural activation but requires excessive energy. Previous pulse shape optimisation has been limited to symmetric pulses or heavily constrained variations of conventional waveforms without achieving general optimality in energy efficiency or neural selectivity. We implemented an optimisation framework that incorporates neuron model activation constraints and flexible control of pulse asymmetry. The optimised electric field waveforms achieved up to 92 % and 88 % reduction in energy loss and thus coil heating respectively compared to conventional monophasic pulses and previously improved monophasic-equivalent pulses. In the human experiments, OUR pulses showed similar motor thresholds to monophasic pulses in both AP and PA directions with significantly lower energy loss, particularly in the AP direction. Moreover, there was a significant MEP latency difference of (1.79 +/- 0.41) ms between AP and PA direction with OUR pulses, which suggests directional selectivity. Our framework successfully identified highly energy-efficient asymmetric pulses for directionally-selective neural engagement. These pulses can enable selective rapid-rate repetitive TMS protocols with reduced power consumption and coil heating, with potential benefits for precision and potency of neuro-modulation.

Figures (8)

• Figure 1: An optimised and conventional current waveforms. (A) Optimised current waveforms typically have four distinct phases, specifically a leading phase, a rising phase, a falling phase, and a decay phase. The shown waveform has voltage limits of $V_\textrm{max}=2000$ and $V_\textrm{min}=-250$. (B) The current waveform of conventional monophasic pulses has no leading phase and the falling and decay phases are not differentiated as in the optimised waveform. This waveform was computed by integrating the electric field waveform recorded from a MagPro X100 device (MagVenture A/S, Farum, Denmark). Both current waveforms are normalised to 1 at their peak amplitude.
• Figure 2:
• Figure 3: Energy loss versus pulse duration (A) and voltage ratio (B) of the optimised pulses. Marker shape and colour correspond to specific positive and negative voltage limits, respectively. $\mathcal{W}$ represents simulated energy loss in joules. The high coefficients of determination (${R}^\textrm{2} = 0.96$) suggest that the regression curve accurately describes the trends.
• Figure 4: Relationships between the parameters of the optimised waveforms. (A) Duration of the rising (top) and falling (bottom) phases of the current waveform, respectively, versus the positive and negative voltage limits. (B) Maximum (top) and minimum (bottom) current amplitudes versus the pulse duration. (C) Current asymmetry ratio $r_\textrm{I}$ versus the pulse duration. The generation of symmetric current pulses (though still asymmetric in voltage and electric field) can have technological advantages. The high coefficients of determination ($R^\textrm{2} \geq 0.94$) suggest that the regression curves accurately describe the trends.
• Figure 5: Experimental coil current and voltage traces of the optimised waveforms generated by MPS-TMS. For visualisation purposes, both current and voltage waveforms in each $V_\textrm{min}$ group were filtered to remove measurement noise and proportionally scaled according to the amplitude ratio between them.