We derive from first principles that confinement of cortical electric fields to a thin slab yieldsa hardening Duffing oscillator with backbone frequency ω0 = πvTW/d set by cortical thickness dand traveling-wave velocity vTW. The geometry produces a phase-dependent threshold asymme-try in transcranial magnetic stimulation (TMS): stimulation aligned with the confinement-inducedpreferred direction requires less amplitude than stimulation opposing it. The magnitude of theasymmetry depends on the chiral coupling κ, which is not fixed by the present theory; we treatit as a calibration parameter. If κ is calibrated to reproduce the ∼ 15% asymmetry reported inexisting phase-locked TMS experiments, the model makes two additional falsifiable predictions—avelocity-resonance condition and a geometric orientation dependence—that are independent of κand testable with existing TMS–EEG protocols.
David B Smith (Fri,) studied this question.
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