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 co-efficient (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.