Probing Surface-to-Volume Ratio of an Anisotropic Medium by Diffusion NMR with General Gradient Encoding

Since the seminal paper by Mitra et al., diffusion MR has been widely used in order to estimate surface-to-volume ratios. In this paper, we generalize Mitra's formula for arbitrary diffusion encoding waveforms, including recently developed q-space trajectory encoding sequences. We show that the surface-to-volume ratio can be significantly misestimated using the original Mitra's formula without taking into account the applied gradient profile. In order to obtain more accurate estimation in anisotropic samples, we propose an efficient and robust optimization algorithm to design diffusion gradient waveforms with prescribed features. Our results are supported by Monte Carlo simulations.