To design and implement a minimum echo time (TE) Spin-Echo EPI Diffusion Weighted MRI (SE-EPI DWI) pulse sequence with or without bulk motion compensation using Convex Optimized Diffusion Encoding (CODE).SE-EPI DWI typically uses a diffusion encoding gradient waveform (G_Diff) with two identical gradients on either side of the 180° pulse. The component of G_Diff after the 180° in combination with the temporal footprint of the EPI readout results in dead time between the 90° and 180° pulses. This dead time can be used for additional diffusion encoding which can, in turn, reduce TE (improving SNR) and/or be used to null the first (velocity, M₁=0) and/or second (acceleration, M₂=0) gradient moments for bulk motion compensated diffusion encoding. The latter is critical for eliminating bulk motion artifacts in cardiac and abdominal DWI. The convex optimization framework for gradient waveform design[1, 2] was implemented to eliminate dead times and minimize TE for DWI with and without motion compensation.

Optimization - The G_Diff that minimizes TE subject to hardware (G_Max and SR_Max), sequence (EPI duration), and diffusion encoding constraints (b-value, M₀, M₁, M₂) was designed using the CODE framework for a target b-value (b_target) (Fig. 1). Optimizations were performed using the CPLEX linear solver (IBM, Armonk NY) with a gradient timestep (∆t) of 100µs.

Sequence Timing Comparison - To compare sequence timing with traditional DWI, diffusion encoding waveforms were generated using CODE for a range of b-values (100-1000s/mm²), and EPI readout durations (T_EPI=20-120ms; corresponding to roughly 0.5-3.0mm in plane resolution. The designs used full Fourier (symmetric) k-space coverage, G_max≤74mT/m, and SR_max≤50T/m/s along a single gradient axis (to limit PNS) for:

1. MONO (Monopolar, M₀=0, Fig. 2A)

2. CODE (M₀=0, Fig. 2B)

3. BIPOLAR (Bipolar, M₀=M₁=0 Fig. 2C)

4. CODE-M₁ (CODE with M₀=M₁=0, Fig. 2D)

5. MOCO (Modified bipolar[3], M₀=M₁=M₂=0, Fig. 2E)

6. CODE-M₁M₂ (CODE with M₀=M₁=M₂=0, Fig. 2F).

Sequence Evaluation - CODE DWI was then implemented on a 3.0T clinical scanner (Siemens Prisma) for three applications:

1. CODE for neuro DWI with b=1000s/mm² and 1.6x1.6x3mm spatial resolution

2. CODE-M₁ for liver DWI with b=500s/mm² and 2x2x7mm spatial resolution

3. CODE-M₁M₂ for cardiac DWI with b=350s/mm² and 1.5x1.5x5mm spatial resolution.

The sequences were validated in a polyvinylpyrrolidone diffusion phantom (High Precision Devices, Boulder, CO) containing thirteen diffusivities. In vivo evaluation was performed in healthy volunteers (N=10 for each application) after obtaining informed consent. Conventional MONO DWI with matched sequence parameters were also acquired for comparison.

CODE has shorter TEs than conventional encoding strategies over the entire range of b-values and EPI durations examined (Fig. 2). Phantom experiments showed excellent linear fits and correlation between ADC values reported by each CODE sequence with the corresponding MONO acquisitions (Table 1). The neuro CODE sequence reduced TE by 11% (75ms to 67ms), which resulted in DWI with higher apparent SNR than MONO (Fig. 3). CODE-M₁ enabled velocity insensitive encoding for more homogeneous ADC maps in the liver (Fig. 4), a simultaneous 23% TE reduction compared to BIPOLAR encoding (72ms vs. 93ms) and only a 7% increase in TE compared to MONO (72ms vs. 67ms). CODE-M₁M₂ resulted in more robust cardiac DWI than MONO (Fig. 4) with only a 17% increase in TE (76ms vs. 65ms) and a 22% shorter TE than MOCO (76ms vs. 97ms).

CODE shortened the TE in all cases examined compared to waveforms with equivalent moment nulling. The benefit was largest for motion compensated encoding (CODE-M₁ and CODE-M₁M₂) and long EPI readouts (e.g high spatial resolution, full-Fourier imaging). Applications using partial Fourier imaging, large parallel imaging factors and/or coarse spatial resolutions will benefit less from the CODE framework. CODE may reduce the TE penalty for full Fourier imaging.

Our findings echo the results of previous studies in which: 1) M₁ nulled bipolar encoding removed ADC heterogeneity caused by cardiac motion in the liver[4]; and 2) M₁+M₂ nulled encoding improved bulk motion robustness for cardiac DWI [3, 5]; but CODE resulted in shorter TEs than these existing methods. Eddy current induced distortions were not exacerbated with CODE.

The CODE framework shortened TEs for DWI with and without motion compensation for all b-values resulting in improved SNR and the potential for motion robustness with limited increases in TE.