3-D tomographic reconstruction of the average propagator from MRI data

The measurement of the 3-D "average propagator", P(r) from diffusion-weighted (DW) NMR or MRI data has been a "holy grail" in materials science and biomedicine, as P(r) provides detailed microstructural information, particularly about restriction, without assuming an underlying diffusion model. While Callaghan proposed a 3-D Fourier transform relationship between P(r) and the DW signal attenuation, E(q), using it to measure P(r) from E(q) data is not currently feasible biologically or clinically, owing to the staggering amount of DW data required. To address this problem, we propose that computed tomography principles can be applied to reconstruct P(r) from DW signals. Moreover, this reconstruction can be performed efficiently using many fewer DW E(q) data as compared to conventional 3-D q-space MRI or diffusion spectrum imaging (DSI) by employing a priori information about E(q) and P(r)