Acquisition of displacement space with NMR, the conjugate of q-space, has many applications including diffusion, dispersion, velocimetry, tortuosity, and surface to volume ratio measurements. Normally, acquisition of q-space data requires a series of scans over which current pulsed through a gradient coil producing a constant magnetic field gradient is varied to step through q-space. Consequently, repetition time for scans in a measurement determines the lower limit of total experimental time and is, in part, governed by T1 relaxation. A series of scans may also pose problems when using hyperpolarised gas, as polarisation levels may fluctuate between scans, causing diffusion related signal attenuation readings to be misinterpreted.
Development of pulse sequences to speed up diffusion measurements using only one scan has led to innovative ‘single-shot’ pulse sequences. Some of these sequences use multiple excitation pulses and exploitation of coherence pathways with multiple echoes (MMME), and multiple recall pulses varying diffusion times with a single excitation pulse (DiffTrain). The single-shot diffusion measurement we propose uses a single excitation with all of q-space acquired in one echo. By applying a second order magnetic field instead of the traditional first order, the gradient value becomes a function of position. This allows q-space to be mapped onto real space and measurement of the apparent diffusion coefficient in a single echo for a homogeneous sample. When this q-space to real space mapping is implemented in DiffTrain, it becomes a single-shot technique for obtaining time dependent diffusion coefficients. Therefore, for the first time, the tortuosity and surface to volume ratio of a sample may be measured with a single scan. We have demonstrated a proof of concept under this second order magnetic field using PGSE and DiffTrain pulse sequences, showing this method to be promising for other q-space based measurements and more complex samples exhibiting restricted diffusion.