Sensitivity and resolution of two-dimensional NMR diffusion-relaxation measurements

The performance of 2D NMR diffusion-relaxation measurements for fluid typing applications is analyzed. In particular, we delineate the region in the diffusion - relaxation plane that can be determined with a given gradient strength and homogeneity, and compare the performance of the single and double echo encoding with the stimulated echo diffusion encoding. We show that the diffusion editing based approach is able to determine the diffusion coefficient only if the relaxation time T2 exceeds a cutoff value T2,cutoff, that scales like T2,cutoff∝g(-2/3)D(-1/3). For stimulated echo encoding, the optimal diffusion encoding times (Td and δ), that provide the best diffusion sensitivity, rely only on the T1/T2 ratios and not on the diffusion coefficients of the fluids or the applied gradient strengths. Irrespective of T1, for high enough gradients (i.e. when γ(2)g(2)DT2(3)>10(2)), the Hahn echo based encoding is superior to encoding based on the stimulated echo. For weaker gradients, the stimulated echo is superior only if the T1/T2 ratio is much larger than 1. For single component systems, the diffusion sensitivity is not adversely impacted by the uniformity of the gradients and the diffusion distributions can be well measured. The presence of non-uniform gradients can affect the determination of the diffusion distributions when you have two fluids of comparable T2. In such situations the effective single component diffusion coefficient is always closer to the geometric mean diffusion coefficient of the two fluids.