Errors in gradient waveforms used for RF excitation or encoding during signal acquisition can significantly degrade MR image quality. For example, errors in half-pulse (HP) slice selection¹, commonly used in 2D ultrashort echo time (UTE) imaging, can lead to errors in the evaluation of short-T₂ signals present in several tissues, including bone^2,3. In HP-UTE, two acquisitions excited with complementary half pulses are digitally combined to cancel unwanted out-of-slice signal, resulting in the desired excitation profile. However, gradient errors caused by eddy currents or gradient amplifier limitations can cause these two half-pulses to be out of alignment, and out-of-slice signal to be present within 2D-UTE images.

While several methods have been proposed to account for gradient errors, including methods specifically applied to HP-UTE^4-6, these methods usually require careful calibration before imaging. In this abstract, we present an automatic method to perform gradient predistortion to optimize HP-UTE slice selection.

All MRI experiments were collected on a 3T Philips Achieva system with a Philips 8 channel knee coil for reception. After scout images were acquired, a RF waveform and a bipolar slice-select gradient waveform were automatically generated based upon gradient slew and acceleration rate limits. Gradient waveforms were measured⁷, and iterative predistortion was performed using the update rule:

$$ G_{app}^{i+1}=G_{app}^{i}+K\Delta $$

where G_app is the applied gradient waveform, ∆ is the difference between the ideal and measured gradient waveforms, and

$$ K=\kappa\left(A^tA-\lambda I\right)^{-1}A $$

Here, the matrix A represents an estimate of a linear system response, while $$$\kappa$$$ (=1) and $$$\lambda$$$ (=0.5) are regularization parameters⁶. For each iteration, the sequence to measure gradient waveforms lasted 20 s, and feedback was provided to the user stating if the iteration had converged.

Before and after gradient predistortion was applied, HP-excited 2D-UTE was performed within the tibia at 6 echo times, t_e = 0.15, 0.25, 0.4, 0.6, 1.0 and 2.0 ms, with a repetition time, t_r = 10 ms. Three phantoms were included next to the leg, containing T₂s of ≈ 10 ms (one small diameter tube) and ≈ 50 ms (two larger diameter tubes), within a FOV of 230 mm and a 5 mm slice thickness.

Figure 1 shows the nominal ideal gradient waveform and the predistorted gradient waveform optimized to minimize the overall gradient error, which was achieved after 4 iterations. Gradient errors (i.e. the difference between the ideal and measured gradient waveforms) are also shown in Figure 1 when the ideal and predistorted waveforms were applied. The normalized root squared gradient error improved from 0.0413 to 0.0105.

Cropped 2D-UTE images are given in Figure 2 (t_e = 0.15 ms) when the nominal and predistorted gradient waveforms were applied for half-pulse slice selection. In the nominal image, errors in the alignment of the two half-pulses allowed out-of-slice signal to be present. This resulted in an apparent smearing of the image, which is related to the orientation of the leg in the regions outside the desired slice thickness.

Plots of signal vs. t_e are also shown in Figure 2 for an ROI in the cortical bone (yellow), as well as in water phantoms with T₂ = 10 (blue) and 50 ms (red). For signals acquired with the nominal gradient waveform, increases in image intensity with echo time were due to transient gradient errors, which cause out-of-slice signals to come in and out of phase. In the images acquired with predistorted gradient waveforms, the water phantoms decay at a rate similar to their intrinsic T₂ relaxation time-constants. Further, in the cortical bone, the signal exhibits a bi-exponential T₂, where ultrashort and longer T₂ components arise from distinct bound- and pore-water compartments known to exist in cortical bone^2,3.