Investigating time-independent and time-dependent diffusion phenomena using steady-state diffusion MRI.

Diffusion MRI is a leading method to non-invasively characterise brain tissue microstructure across multiple domains and scales. Diffusion-weighted steady-state free precession (DW-SSFP) is an established imaging sequence for post-mortem MRI, addressing the challenging imaging environment of fixed tissue with short T2 and low diffusivities. However, a current limitation of DW-SSFP is signal interpretation: it is not clear what diffusion 'regime' the sequence probes and therefore its potential to characterise tissue microstructure. Building on Extended Phase Graphs (EPG), I establish two alternative representations of the DW-SSFP signal in terms of (1) conventional b-values (time-independent diffusion) and (2) encoding power-spectra (time-dependent diffusion). The proposed representations provide insights into how different parameter regimes and gradient waveforms impact the diffusion sensitivity of DW-SSFP. I subsequently introduce an approach to incorporate existing biophysical models into DW-SSFP without the requirement of extensive derivations, with time dependence estimated via a Gaussian phase approximation representation of the DW-SSFP signal. Investigations incorporating free-diffusion and tissue-relevant microscopic restrictions (cylinder of varying radius) give excellent agreement to complementary analytical models and Monte Carlo simulations. Experimentally, the time-independent representation is used to derive Tensor and proof-of-principle NODDI estimates in a whole human post-mortem brain. A final SNR-efficiency investigation demonstrates the theoretical potential of DW-SSFP for ultra-high field microstructural imaging.