Fig. 1.
Schematic drawing of the imaging sequence for mapping time-dependent magnetic field changes induced by an arbitrary sequence of gradient pulses. Greadout – reading gradient, Gphase – phase encoding gradient, Gslice – slice selective gradient, RF – radiofrequency pulses, Signal – acquisition, τ – time interval used to minimize residual effects of eddy currents induced by the gradient during the second excitation pulse.
Fig. 2.
Ring-down sequence. rd – is the time interval for unblanking the receiver, and ad – is the interval from receiver unblanking to signal acquisition. In our case, both were set to 1 μs.
Fig. 3.
Gradient ring-down experiment for gradient in the x-direction. (a) Measured FID signal for different delays dj (shown in the title of each subplot) sorted in ascending order: (blue) real part and (red) imaginary part. The signal is shown in arbitrary units. (b) Imaginary value of the FFT of the measured FID signal for each delay dj (shown in the legend) sorted in ascending order: the maximal peak (marked with “*”), along with its half-height boundaries (marked with “<” and “>”) that define the peak width wj for each delay, is shown.
Fig. 4.
Peak width vs. delay dependence is shown as (dj,wj) points for j = 1, … , m (m = 19), fitted with function (5) using n = 5 and the least-squares method. The (dj,wj) points are obtained from the data in Fig. 3.
Fig. 5.
Simplified model of eddy current effects and gradient pre-emphasis compensation: (a) Eddy current model, where . (b) Gradient pre-emphasis compensation of the eddy current model, where . (c) Comparison of the (a) and (b) models with the magnetic flux density field over time for an ideally switching gradient, and their relative errors. Parameters used in the simulations are shown in Table 1.
Table 1.
Values of parameters for simulations and experiments.
| Description | Symbol | Value | Unit |
|---|---|---|---|
| Common parameters: | |||
| Time step size | ∆t | 50 | μs |
| Gradient ramp time | tramp | 900 | μs |
| Gradient plateau time | tplato | 2 | ms |
| Gradient strength in GRD experiment | GrGRD | 20 | % |
| Gradient strength in GS experiment | GrGS | 2 | % |
| Peak width in GS experiment | wGS | 1191.1 | Hz |
| Number of EC sources | n | 5 | 1 |
| Simplified model of ECs effects gradient PE compensation: | |||
| Gradient max magnetic flux density | max (Bideal) | 1 | T |
Fig. 6.
Measured eddy current effect gradient pre-emphasis compensation in the gradient ring-down experiment: the ° indicates uncompensated data, (blue) fitting function, and the * indicates gradient pre-emphasis compensated data with fitting function (yellow).