Optimized Diffusion‐Weighting Gradient Waveform Design (ODGD) formulation for motion compensation and concomitant gradient nulling

Purpose To present a novel Optimized Diffusion‐weighting Gradient waveform Design (ODGD) method for the design of minimum echo time (TE), bulk motion‐compensated, and concomitant gradient (CG)‐nulling waveforms for diffusion MRI. Methods ODGD motion‐compensated waveforms were designed for various moment‐nullings M n (n = 0, 1, 2), for a range of b ‐values, and spatial resolutions, both without (ODGD‐M n ) and with CG‐nulling (ODGD‐M n ‐CG). Phantom and in‐vivo (brain and liver) experiments were conducted with various ODGD waveforms to compare motion robustness, signal‐to‐noise ratio (SNR), and apparent diffusion coefficient (ADC) maps with state‐of‐the‐art waveforms. Results ODGD‐M n and ODGD‐M n ‐CG waveforms reduced the TE of state‐of‐the‐art waveforms. This TE reduction resulted in significantly higher SNR ( P < 0.05) in both phantom and in‐vivo experiments. ODGD‐M 1 improved the SNR of BIPOLAR (42.8 ± 5.3 vs. 32.9 ± 3.3) in the brain, and ODGD‐M 2 the SNR of motion‐compensated (MOCO) and Convex Optimized Diffusion Encoding‐M 2 (CODE‐M 2 ) (12.3 ± 3.6 vs. 9.7 ± 2.9 and 10.2 ± 3.4, respectively) in the liver. Further, ODGD‐M 2 also showed excellent motion robustness in the liver. ODGD‐M n ‐CG waveforms reduced the CG‐related dephasing effects of non CG‐nulling waveforms in phantom and in‐vivo experiments, resulting in accurate ADC maps. Conclusions ODGD waveforms enable motion‐robust diffusion MRI with reduced TEs, increased SNR, and reduced ADC bias compared to state‐of‐the‐art waveforms in theoretical results, simulations, phantoms and in‐vivo experiments.