Characterization and correction of diffusion gradient-induced eddy currents in second-order motion-compensated echo-planar and spiral cardiac DTI

Abstract

Purpose: Very high gradient amplitudes played out over extended time intervals as required for second-order motion-compensated cardiac DTI may violate the assumption of a linear time-invariant gradient system model. The aim of this work was to characterize diffusion gradient-related system nonlinearity and propose a correction approach for echo-planar and spiral spin-echo motion-compensated cardiac DTI.

Methods: Diffusion gradient-induced eddy currents of 9 diffusion directions were characterized at b values of 150 s/mm² and 450 s/mm² for a 1.5 Tesla system and used to correct phantom, ex vivo, and in vivo motion-compensated cardiac DTI data acquired with echo-planar and spiral trajectories. Predicted trajectories were calculated using gradient impulse response function and diffusion gradient strength- and direction-dependent zeroth- and first-order eddy current responses. A reconstruction method was implemented using the predicted $k$ -space trajectories to additionally include off-resonances and concomitant fields. Resulting images were compared to a reference reconstruction omitting diffusion gradient-induced eddy current correction.

Results: Diffusion gradient-induced eddy currents exhibited nonlinear effects when scaling up the gradient amplitude and could not be described by a 3D basis alone. This indicates that a gradient impulse response function does not suffice to describe diffusion gradient-induced eddy currents. Zeroth- and first-order diffusion gradient-induced eddy current effects of up to -1.7 rad and -16 to +12 rad/m, respectively, were identified. Zeroth- and first-order diffusion gradient-induced eddy current correction yielded improved image quality upon image reconstruction.

Conclusion: The proposed approach offers correction of diffusion gradient-induced zeroth- and first-order eddy currents, reducing image distortions to promote improvements of second-order motion-compensated spin-echo cardiac DTI.

Keywords: EPI; GIRF; cardiac DTI; eddy currents; image reconstruction; spiral imaging.

FIGURE 1

Schematic overview of the trajectory prediction and image reconstruction process using a spiral trajectory example. When taking the nominal trajectory ${\overrightarrow{k}}_{\mathit{nom}}(t)$ (blue), the reconstruction process converts the raw $\overrightarrow{k}$‐space data using the off‐resonance field map, coil sensitivities, and trajectory‐induced concomitant fields into an image with a residual level of blurriness. When including the diffusion gradients (incl. diff) and predicting the trajectory with a GIRF, a distorted trajectory $\overrightarrow{k}(t,\overrightarrow{b})$ (green) with respect to the nominal trajectory is obtained. When excluding the diffusion gradients (excl. diff) in the GIRF prediction, we obtain trajectory $\overrightarrow{k}(t)$ (orange), which differs from the nominal trajectory. Updating the trajectory including diffusion gradient‐induced eddy current effects, $\delta \overrightarrow{k}(t,\overrightarrow{b})$, leads to trajectory ${\overrightarrow{k}}^{\prime }(t,\overrightarrow{b})$. The in vivo protocol additionally registers the initial data from the GIRF (excl. diff) path, extracts the rigid displacements, and performs alignment of the $\overrightarrow{k}$‐space data using the Fourier shift theorem (dashed arrows). GIRF, gradient impulse response function.

FIGURE 2

Schematic overview of the EPI and spiral cDTI sequences. (A) Second‐order MC‐SE ssh 2D EPI sequence, and (B) second‐order MC‐SE ssh 2D spiral sequence. The diffusion gradients are oriented along the gradient system axis (XYZ; yellow), while other gradients are positioned according to the measurement orientation (MPS ; gray). The 90° excitation pulse is in red, and the echo pulse is in green. AQ marks data acquisition (pink). cDTI, cardiac DTI; MC‐SE, motion‐compensated spin‐echo; ssh, single shot; REST, regional saturation; SPIR, spectral presaturation with inversion recovery.

FIGURE 3

Schematic overview of the diffusion gradient‐induced ECM sequence. (A) Second‐order MC‐SE 3D diffusion gradient‐induced ECM sequence. With the ECM sequence, a 7 × 7 × 7 grid was measured with standard and inverted diffusion gradient polarity. Phase‐difference data is fitted to third‐order spherical harmonics to obtain zeroth‐ and first‐order diffusion gradient‐induced eddy current contributions for each diffusion direction. The light‐blue area in (A) highlights the position of the 3D phase encode gradients. Light‐yellow colored gradients indicate inverted diffusion gradients. The diffusion gradients are oriented along the gradient system axis (XYZ; yellow), whereas other gradients are positioned according to the measurement orientation (MPS; gray). The 90° excitation pulse is in red, and the echo‐pulse is in green. AQ marks data acquisition (pink). (B) Schematic overview of 3D encoding of the diffusion gradient‐induced eddy currents. A silicon oil sphere (16 cm in diameter) is imaged using a 7 × 7 × 7 3D voxel grid with a FOV of 21 × 21 × 21 cm³. MC‐SE, motion‐compensated spin‐echo; ECM, eddy current measurement.

FIGURE 4

Overview of zeroth‐ and first‐order diffusion gradient‐induced phase evolutions for 3 orthogonal diffusion directions recorded for $b$ values of 150 s/mm² and 450 s/mm². The dashed black line represents the TE.

FIGURE 5

Example of sequential compensation of trajectory and/or magnetic field imperfections for a single diffusion direction acquired with a spiral readout. Starting with the nominal $k$‐space trajectory, the effect of sequentially adding the GIRF‐prediction (excluding diffusion gradients), off‐resonance correction, trajectory‐induced concomitant field correction, and correction of diffusion gradient‐induced eddy current effects is shown

FIGURE 6

MD and FA maps of the structure phantom acquired with spiral and EPI readouts. The top row displays the maps obtained using the reference reconstruction approach. The bottom row shows the maps using the proposed reconstruction approach. The ROI is indicated with the dashed black line. The phase encoding direction of the EPI data is shown with black (in MD maps) and white (in FA maps) arrows. Inset values indicate ROI values expressed in mean ± SDFA, fractional anisotropy; MD, mean diffusivity; ROI, region of interest.

FIGURE 7

Ex vivo porcine heart acquired with EPI and spiral cDTI protocols. For EPI and spiral trajectories, the reference and proposed reconstructions are shown with their respective mean DWI, HA, TA, E2A, MD, and FA maps. Inset values display the mean ± SD values in the LV. For the HA maps, the HAG values in °/%‐transmural depth are shown. The white arrows indicate the phase encoding direction for EPI. The red arrow indicates the endocardial septal wall area. E2A, absolute sheetlet angle; HA, helix angle; HAG, helix angle gradient; TA, transverse angle; MD, mean diffusivity; FA, fractional anisotropy.

FIGURE 8

Example k‐space trajectories of the proposed reconstruction for EPI and spiral (top row) and their relative differences with respect to the reference reconstruction (bottom row). Trajectories are taken from in vivo cDTI data for diffusion direction 8 (Supporting Information Figure S8). Note the presence of a dedicated y‐axis for the $k_0$ component with a different scale and unit. prop, proposed; ref, reference; rel., relative.

FIGURE 9

Example in vivo cDTI data acquired using spiral and EPI readouts and reconstructed using the reference and proposed approach. EPI (top rows) and spiral (bottom rows) are shown with their respective reconstruction cases and display mean DWI, HA, TA, E2A, MD, and FA maps. Inset values display the mean ± SD values in the LV. For the HA maps, the transmural HAG values in °/%‐transmural depth are shown. The white arrows indicate the phase encode direction for EPI. E2A, absolute sheetlet angle; HA, helix angle; HAG, helix angle gradient; TA, transverse angle; MD, mean diffusivity; FA, fractional anisotropy; LV, left‐ventricular.

FIGURE 10

In vivo cDTI metric overview of all volunteers. LV mean and SD are plotted for each volunteer for the ref and prop approaches for EPI and SPI. SPI, spiral imaging; MD, mean diffusivity; FA, fractional anisotropy; HAG, helix angle gradient; E2A, absolute sheetlet angle; TA, transverse angle; ref, reference; prop, proposed.