Limits to neural stimulation in echo-planar imaging

Simple electrical circuits are used to model neural stimulation. The stimulation current is evaluated for a variety of magnetically induced waveforms and for sinusoidal stimulation as a function of frequency. Experimental results obtained using a small scale magnetic stimulator show that the transient response rather than the steady-state behavior determines the stimulation characteristics thus suggesting a nonlinear model. We show that a nonlinear circuit changes a steady-state current solution into a repeated transient solution and thereby better explains our experimental results. Our model also shows that for very short times and high frequencies, contrary to the current widely held view, neural stimulation is independent of the magnetic field switching rate dB/dt, but depends on the final magnetic field value, Bm. At lower frequencies and rise-times, there may be a small advantage in using square wave over sine wave gradient modulation for whole body echo-planar imaging (EPI). It is found that the peak stimulation fields Bm, for both sinusoidal and trapezoidal waveforms are equal for equal risetimes. This means that for a given image array size and imaging time, trapezoidal modulation EPI ultimately can be made to operate below the neural triggering threshold while the equivalent sine modulation EPI version transcends the threshold.