Pre-excitation gradients for eddy current nulled convex optimized diffusion encoding (Pre-ENCODE)

Abstract

Purpose: To evaluate the use of pre-excitation gradients for eddy current-nulled convex optimized diffusion encoding (Pre-ENCODE) to mitigate eddy current-induced image distortions in diffusion-weighted MRI (DWI).

Methods: DWI sequences using monopolar (MONO), ENCODE, and Pre-ENCODE were evaluated in terms of the minimum achievable echo time (TE ${}_{\min }$ ) and eddy current-induced image distortions using simulations, phantom experiments, and in vivo DWI in volunteers ( $N=6$ ).

Results: Pre-ENCODE provided a shorter TE ${}_{\min }$ than MONO (71.0 $\pm$ 17.7ms vs. 77.6 $\pm$ 22.9ms) and ENCODE (71.0 $\pm$ 17.7ms vs. 86.2 $\pm$ 14.2ms) in 100 $\%$ of the simulated cases for a commercial 3T MRI system with b-values ranging from 500 to 3000 s/mm ${}^2$ and in-plane spatial resolutions ranging from 1.0 to 3.0mm ${}^2$ . Image distortion was estimated by intravoxel signal variance between diffusion encoding directions near the phantom edges and was significantly lower with Pre-ENCODE than with MONO (10.1 $\%$ vs. 22.7 $\%$ , $p=6^{-5}$ ) and comparable to ENCODE (10.1 $\%$ vs. 10.4 $\%$ , $p=0.12$ ). In vivo measurements of apparent diffusion coefficients were similar in global brain pixels (0.37 [0.28,1.45] $\times 10^{-3}$ mm ${}^2$ /s vs. 0.38 [0.28,1.45] $\times 10^{-3}$ mm ${}^2$ /s, $p=0.25$ ) and increased in edge brain pixels (0.80 [0.17,1.49] $\times 10^{-3}$ mm ${}^2$ /s vs. 0.70 [0.18,1.48] $\times 10^{-3}$ mm ${}^2$ /s, $p=0.02$ ) for MONO compared to Pre-ENCODE.

Conclusion: Pre-ENCODE mitigated eddy current-induced image distortions for diffusion imaging with a shorter TE ${}_{\min }$ than MONO and ENCODE.

Keywords: diffusion; eddy currents; time‐optimal.

FIGURE 1.

Eddy currents, characterized as $ϵ(\lambda ,t)$ (black lines) from Eq. 10, shown for (A) MONO, (B) MONO with pre-excitation gradients (Pre-MONO), and (C) Pre-ENCODE for b-value=1000s/mm². MONO results in non-zero values of $ϵ(\lambda ,t)$ during the EPI readout (gray region). Pre-excitation gradient lobes (green region) can be used to null $ϵ(t)$ using ${\lambda }_{null}=100\mathrm{m}\mathrm{s}$. While Pre-MONO demonstrates eddy current mitigation, it is not a time-optimal solution owing to inherent sequence dead time (pink region) representing inefficient periods of gradient inactivity. The deadtime is eliminated with Pre-ENCODE to produce the shortest ${\mathrm{T}\mathrm{E}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$. The RF excitation and refocusing pulses are indicated in gray.

FIGURE 2.

(A) Pre-ENCODE gradient waveforms using the protocol parameters outlined in Table 1 designed for various singular values of ${\lambda }_{null}$ (20–100 ms, $\mathrm{\Delta }{\lambda }_{null}=20\mathrm{m}\mathrm{s}$). The EPI readout duration is indicated by the gray shaded region while the RF excitation and refocusing pulses are indicated by gray lines. (B) Pre-ENCODE minimizes $ϵ(\lambda ,t)$ for the given value of ${\lambda }_{null}$. A wider range of ${\lambda }_{null}$ values are shown in Figure S4.

FIGURE 3.

Pulse sequence diagrams and $ϵ(t)$ for an eddy current time constant of 100ms (${\lambda }_{null}=100\mathrm{m}\mathrm{s}$) for (A) MONO, (B) ENCODE, and (C) Pre-ENCODE using the protocol parameters outlined in Table 1. MONO results in non-zero values of $ϵ(t)$ during the EPI readout (gray region). ENCODE uses the diffusion gradient waveforms and Pre-ENCODE uses pre-excitation gradients (green region) to null $ϵ(t)$ during the EPI readout. Pre-ENCODE provides the shortest ${\mathrm{T}\mathrm{E}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, 11.7% shorter than MONO and 6.4% shorter than ENCODE. The EPI readout duration is indicated by the gray shaded region while the RF excitation and refocusing pulses are indicated by gray lines.

FIGURE 4.

${\mathrm{T}\mathrm{E}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ for various choices of b-value and in-plane spatial resolution for (C) MONO as well as (A) ENCODE and (B) Pre-ENCODE with ${\lambda }_{null}=100\mathrm{m}\mathrm{s}$. Differences in ${\mathrm{T}\mathrm{E}}_{\text{min}}$ for (D) ΔENCODE=MONO-ENCODE and (E) ΔPre-ENCODE=MONO-Pre-ENCODE. ENCODE had a shorter ${\mathrm{T}\mathrm{E}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ than MONO in 28% of the tested cases whereas Pre-ENCODE had a shorter ${\mathrm{T}\mathrm{E}}_{\text{min}}$ than ENCODE and MONO in 100% of the tested cases.

FIGURE 5.

(A) Maps of Coefficient of variation (CoV) from the phantom DWI experiments. CoV was calculated across all diffusion-encoding directions for MONO, ENCODE, and Pre-ENCODE. (B) Mean CoV values, expressed as a percent, measured within each of the 13 phantom vials, ${\mathrm{C}\mathrm{o}\mathrm{V}}_{\text{Global}}$ (red), and within edge voxels, ${\mathrm{C}\mathrm{o}\mathrm{V}}_{\text{Edge}}$ (blue). A high CoV indicates large differences in signal intensity between diffusion directions, indicative of eddy current–induced image distortions. The CoV was largest with the MONO sequence and reduced with ENCODE and Pre-ENCODE, especially for the edge voxels. (C) An example masked image showing the segmented regions used for the analysis. A corresponding animation cycling through the different diffusion encoding directions is provided in Video S2.

FIGURE 6.

(A) Maps of Coefficient of variation (CoV) from the in vivo DWI experiments calculated across all diffusion encoding directions for MONO and Pre-ENCODE. (B) Mean CoV values, expressed as a percent, measured within segmented regions of the brain, ${\mathrm{C}\mathrm{o}\mathrm{V}}_{\text{Global}}$ (red), and ithin edge voxels, ${\mathrm{C}\mathrm{o}\mathrm{V}}_{\text{Edge}}$ (blue). A high CoV indicates large differences in signal intensity between diffusion directions, indicative of eddy current–induced image distortions. The CoV was largest with the MONO sequence and reduced with Pre-ENCODE, especially for the edge voxels. (C) An example masked image showing the segmented regions of the brain used for the analysis. A corresponding animation cycling through the different diffusion encoding directions is provided in Video S3.

FIGURE 7.

Representative in vivo DWI experimental results comparing MONO and Pre-ENCODE for (A) mean diffusivity images, (B) ADC maps, and (C-D) ADC histograms compared in edge ${\mathrm{A}\mathrm{D}\mathrm{C}}_{\text{Edge}}$ and global ${\mathrm{A}\mathrm{D}\mathrm{C}}_{\text{Global}}$ pixels. The edge and global pixels were defined using the mask shown in Figure 6C. Qualitatively, both the mean diffusivity images and ADC maps look comparable between MONO and Pre-ENCODE. The histograms show similar median and 95%-CIs for ${\mathrm{A}\mathrm{D}\mathrm{C}}_{\text{Global}}$ for MONO vs. Pre-ENCODE (0.37 [0.28,1.45]×10⁻³mm²/s vs. 0.38 [0.28,1.45]×10⁻³mm²/s, p=0.25) and increased ${\mathrm{A}\mathrm{D}\mathrm{C}}_{\text{Edge}}$ values for MONO vs. Pre-ENCODE (0.80 [0.17,1.49]×10⁻³mm²/s vs. 0.70 [0.18,1.48]×10⁻³mm²/s, p=0.02).