Feasibility of phase-locked transcranial magnetic stimulation of cerebellum for the treatment of essential tremor

Objective.Cerebellar transcranial magnetic stimulation (TMS) has been proposed to suppress limb tremors in essential tremor (ET), but mixed results have been reported so far, both when pulses are applied repetitively TMS (rTMS) and in bursts. We aim to investigate the cellular effects of TMS on the cerebellum under ET through numerical simulations.Approach.A computational model of the olivo-cerebello-thalamocortical pathways exhibiting the main neural biomarkers of ET (i.e. circuit-wide tremor-locked neural oscillations) was expanded to incorporate the effects of TMS-induced electric field (E-field) on Purkinje cells. TMS pulse amplitude, frequency, and temporal pattern were varied, and the resultant effects on ET biomarkers were assessed. Four levels of cellular response to TMS were considered, ranging from low to high cell recruitment underneath the coil, and three stimulation patterns were tested, i.e. rTMS, irregular TMS (ir-TMS, pulses were arranged according to Sobol sequences with average frequency matching rTMS), and phase-locked TMS (PL-TMS).Main results.rTMS can suppress ET oscillations, but its efficacy depends on tremor frequency and recruitment level, with these factors shaping a narrow range of effective settings. The ratio between tremor and rTMS frequencies also affects the neural response and further narrows the span of viable settings, while ir-TMS is ineffective. PL-TMS is highly effective and robust against changes to cell recruitment level and tremor frequency. Across all scenarios, PL-TMS provides a rapid (i.e. within seconds) suppression of tremor oscillations and, when both PL-TMS and rTMS are effective, the time to tremor suppression decreases by 50% or more in PL-TMS versus rTMS. At the cellular level, PL-TMS operates by disrupting the synchronization along the olivo-cerebellar loop, and the preferred phases map onto the mid-region of the silent period between complex spikes of the Purkinje cells.Significance.Cerebellar PL-TMS can provide robust suppression of ET oscillations while operating within safety boundaries.