To implement and clinically evaluate Convex Optimized Diffusion Encoding (CODE) DWI for motion compensated and minimum TE Diffusion Weighted MRI (DWI) of the liver.Spin echo EPI (SE-EPI) DWI is frequently used to characterize cancerous lesions in the liver[1]. However, sensitivity to cardiac and respiratory bulk motion frequently contributes to large signal losses during diffusion encoding that confound DWI-based measurements. Hepatic bulk motion artifacts can be largely eliminated with cardiac triggering and respiratory management[2], but this significantly increases acquisition duration. Bipolar diffusion encoding gradient waveforms with velocity compensation (i.e. first moment, M₁=0) improve ADC measurements without the need for cardiac triggering [3], but also increase TE, which limits SNR. Convex Optimized Diffusion Encoding (CODE) was used to design a time-optimal, velocity compensated DWI sequence with shorter TEs than bipolar encoding.

Gradient Design: Convex optimization was used to determine the M₁ nulled diffusion encoding gradient waveform (CODE-M₁) that minimizes TE while conforming to hardware (G_Max=74mT/m and SR_Max=50T/m/s) and pulse sequence (b-value, spatial resolution) constraints[4, 5].

Healthy Volunteer Imaging: Healthy volunteers (N=10) were scanned on a 3.0T scanner (Siemens Prisma) after providing written informed consent. Breath held axial DWI were acquired in the liver with: b=500s/mm² along three orthogonal gradient directions, 2x2x7mm spatial resolution and TR=1000ms using both monopolar (MONO) (TE=67ms) and CODE-M₁ (TE=72ms) diffusion encoding. Multiple slices were acquired in separate breath holds to cover the whole liver (10-15 slices with gaps) and three averages were included to improve SNR (scan time: 15s per slice).

Clinical Imaging: Patients (N=3) undergoing routine liver MRI exams were scanned after providing written informed consent. Free breathing, axial, whole volume, 31 slice-interleaved DWI were acquired with b=100,500,1000s/mm² along three orthogonal gradient directions, 2.5x2.5x5mm spatial resolution (2.5mm gap) and TR=7000ms using both MONO (TE=65ms) and CODE-M₁ (TE=70ms) encoding with three averages to improve SNR and reduce respiratory motion artifacts (total scan time: 4.5min).

Reconstruction and Data Analysis: ADC maps were reconstructed for all acquisitions using linear least squares. Mean ADCs were calculated in four manually defined regions of interest (ROI) in homogeneous liver regions in the lateral left lobe (ADC_LL), medial left lobe (ADC_ML), superior right lobe (ADC_SR) and inferior right lobe (ADC_IR). Mean ADCs were compared between ROIs to identify motion corruption.

In healthy subjects CODE-M₁ achieved velocity compensation with a 7% TE increase compared to MONO and with a 23% shorter TE than bipolar (TE=93ms) (Fig. 1). CODE-M₁ resulted in spatially homogeneous DWI and ADC maps (Fig. 2A-B) with no significant differences between mean ADCs across the four ROIs (P=N.S.). MONO encoding resulted in large bulk motion signal dropouts in portions of the liver closest to the heart (Fig. 2A) that lead to large overestimates of ADC (Fig. 2B). With MONO, ADC_LL and ADC_ML were significantly higher than ADC_IR (both p<0.003). Mean ADC varied by as much as 48±28% between ROIs for MONO and only 12±12% for CODE-M₁.

Clinical DWI were consistent with volunteer scans (Fig. 3), with less signal dropout near the heart and more homogeneous ADC maps with CODE-M1. Mean ADC varied between ROIs by as much as 54±12% for MONO and only 2±2% for CODE-M₁.

The improved homogeneity of the CODE-M₁ ADC maps and measured ADC values are consistent with Ozaki et al.[3] for bipolar gradients. Note that CODE-M₁ should have higher SNR than bipolar due to the shortened TE. In volunteers, CODE-M₁ reported significantly lower ADC values than MONO in all regions, even in ROIs distal from the heart and ostensibly free of bulk motion. This discrepancy is likely due to the perfusion sensitivity in MONO acquisitions that is reduced with CODE-M₁.

While volunteers scans were breath held, patients were imaged during free breathing with averaging to match clinical workflow. Similarity of the results indicates that cardiac motion is a larger factor in DWI corruption than respiratory motion. Future work will involve investigating whether CODE-M₁ can effectively reduce the number of signal averages required in free breathing liver DWI.

CODE-M₁ DWI achieved M₁ compensation with little TE increase compared to MONO. MONO encoding led to regions of elevated ADC caused by bulk motion artifact while CODE-M₁ yielded spatially homogeneous ADC maps in healthy volunteers and clinical subjects.