Estimation of Bounded and Unbounded Trajectories in Diffusion MRI

Lipeng Ning,Yogesh Rathi,Carl-Fredrik Westin

doi:10.3389/fnins.2016.00129

Lipeng Ning, Yogesh Rathi + Show 1 more

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https://doi.org/10.3389/fnins.2016.00129

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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.

Highlights

Diffusion MRI is an important clinical tool for non-invasive investigation of tissue microstructure
A bi-exponential model has been used in Niendorf et al (1996) to fit the Diffusion MRI (dMRI) measurements; the kurtosis of the diffusion propagator was estimated in Jensen et al (2005) for investigating the non-Gaussianity of the ensemble average propagator (EAP); and the time-varying feature of the covariance was shown to be closely related to the microstructural arrangement of axons in brain
Using dMRI data from an ex-vivo monkey brain, we show that the proposed model provides a much more accurate fit of the measured dMRI signals, compared to the fits shown for the same data set in Alexander et al (2010) and Huang et al (2015)

Summary

Introduction

Diffusion MRI (dMRI) is an important clinical tool for non-invasive investigation of tissue microstructure It can identify brain tissue abnormalities and provide useful image-based biomarkers for diagnosing several neurological and psychiatric disorders. Diffusion tensor imaging (DTI) is a classical method for modeling dMRI signals (Basser et al, 1994), where the probability distribution of the displacements of water molecules, referred to as the ensemble average propagator (EAP), is assumed to be Gaussian. This assumption is not satisfied in practice due to the restrictions and hindrances from cellular and axonal membranes. A bi-exponential model has been used in Niendorf et al (1996) to fit the dMRI measurements; the kurtosis of the diffusion propagator was estimated in Jensen et al (2005) for investigating the non-Gaussianity of the EAP; and the time-varying feature of the covariance was shown to be closely related to the microstructural arrangement of axons in brain

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