title: Estimation of Bounded and Unbounded Trajectories in Diffusion MRI.
abstract: Disentangling the tissue microstructural information from the diffusion magnetic resonance imaging (dMRI) measurements is quite important for extracting brain tissue specific measures. The autocorrelation function of diffusing spins is key for understanding the relation between dMRI signals and the acquisition gradient sequences. In this paper, we demonstrate that the autocorrelation of diffusion in restricted or bounded spaces can be well approximated by exponential functions. To this end, we propose to use the multivariate Ornstein-Uhlenbeck (OU) process to model the matrix-valued exponential autocorrelation function of three-dimensional diffusion processes with bounded trajectories. We present detailed analysis on the relation between the model parameters and the time-dependent apparent axon radius and provide a general model for dMRI signals from the frequency domain perspective. For our experimental setup, we model the diffusion signal as a mixture of two compartments that correspond to diffusing spins with bounded and unbounded trajectories, and analyze the corpus-callosum in an ex-vivo data set of a monkey brain.
authors.affiliation: Harvard Medical School, Brigham and Women's Hospital Boston, MA, USA.
authors.forename: Lipeng
authors.initials: L
authors.lastname: Ning
authors.affiliation: Harvard Medical School, Brigham and Women's Hospital Boston, MA, USA.
authors.forename: Carl-Fredrik
authors.initials: CF
authors.lastname: Westin
authors.affiliation: Harvard Medical School, Brigham and Women's Hospital Boston, MA, USA.
authors.forename: Yogesh
authors.initials: Y
authors.lastname: Rathi
keywords: Ornstein-Uhlenbeck model; autocorrelation function; diffusion MRI; single-pulsed field gradient