Effects of mesoscopic susceptibility and transverse relaxation on diffusion NMR

Measuring molecular diffusion is based on the spatial encoding of spin-carrying molecules using external Larmor frequency gradients. Intrinsic variations of the Larmor frequency and of the local relaxation rate, commonly present in structurally complex samples, interfere with the external gradients, confounding the NMR-measured diffusion propagator. Here we consider, analytically and numerically, the effects of the mesoscopic magnetic structure (local susceptibility and transverse relaxation rate) on the NMR-measured "apparent" diffusion coefficient (ADC). We show that in the fast diffusion regime, when molecules spread past the correlation length of the magnetic structure, the deviation of ADC from the genuine diffusion coefficient increases as a power law of diffusion time. The effect of mesoscopically varying transverse relaxation rate is sequence-independent and always leads to the decrease of ADC with time, whereas the effect sign for the mesoscopic Larmor frequency variations depends on the presence of refocussing pulses in the diffusion sequence. We connect this unexpectedly diverging with time ADC discrepancy to the spatial statistics of the mesocopic magnetic structure. Our results establish a novel kind of NMR contrast tied to the microstructural complexity, and can be applied to discern the mesoscopic effects of hindrances to molecular diffusion, susceptibility variations, and varying local relaxation rate, on the measured diffusion propagator. In particular, we numerically show that the susceptibility effect of a microvascular network is sufficient to explain the observed ADC decrease due to superparamagnetic iron-oxide contrast injection in monkeys.