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

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.