Bayesian Analysis for Quantitative NMR Flow and Diffusion Imaging

Abstract This study demonstrates the use of a Bayesian statistical method for data analysis in practical flow and diffusion measurements based on pulsed-held-gradient magnetic-resonance imaging. In addition to providing estimates of both the velocity and the diffusion coefficient at each voxel, the technique produces reliable fitting errors for these measurements. Bayesian analysis is especially useful, compared to the Fourier transform method, for treating noisy data which are truncated and/or sparsely and nonuniformly sampled in q , the wavevector for motion encoding. Nonuniform sampling in q is shown to be more efficient than uniform sampling for velocity and diffusion measurement; it can result in smaller fitting errors for the estimated parameters corresponding to fewer q samples and hence less data-acquisition time. The specific example of laminar flow of water in a straight cylindrical tube is illustrated with experimental and simulated data.