Computation of Diffusion Function Measures in $q$ -Space Using Magnetic Resonance Hybrid Diffusion Imaging

The distribution of water diffusion in biological tissues may be estimated by a 3-D Fourier transform (FT) of diffusion-weighted measurements in q-space. In this study, methods for estimating diffusion spectrum measures (the zero-displacement probability, the mean-squared displacement, and the orientation distribution function) directly from the q-space signals are described. These methods were evaluated using both computer simulations and hybrid diffusion imaging (HYDI) measurements on a human brain. The HYDI method obtains diffusion-weighted measurements on concentric spheres in q-space. Monte Carlo computer simulations were performed to investigate effects of noise, q-space truncation, and sampling interval on the measures. This new direct computation approach reduces HYDI data processing time and image artifacts arising from 3-D FT and regridding interpolation. In addition, it is less sensitive to the noise and q-space truncation effects than conventional approach. Although this study focused on data using the HYDI scheme, this computation approach may be applied to other diffusion sampling schemes including Cartesian diffusion spectrum imaging.