Sparse Solution of Fiber Orientation Distribution Function by Diffusion Decomposition

Fang-Cheng Yeh,Wen-Yih Isaac Tseng,Pedro Antonio Valdes-Sosa

doi:10.1371/journal.pone.0075747

Abstract

Fiber orientation is the key information in diffusion tractography. Several deconvolution methods have been proposed to obtain fiber orientations by estimating a fiber orientation distribution function (ODF). However, the L 2 regularization used in deconvolution often leads to false fibers that compromise the specificity of the results. To address this problem, we propose a method called diffusion decomposition, which obtains a sparse solution of fiber ODF by decomposing the diffusion ODF obtained from q-ball imaging (QBI), diffusion spectrum imaging (DSI), or generalized q-sampling imaging (GQI). A simulation study, a phantom study, and an in-vivo study were conducted to examine the performance of diffusion decomposition. The simulation study showed that diffusion decomposition was more accurate than both constrained spherical deconvolution and ball-and-sticks model. The phantom study showed that the angular error of diffusion decomposition was significantly lower than those of constrained spherical deconvolution at 30° crossing and ball-and-sticks model at 60° crossing. The in-vivo study showed that diffusion decomposition can be applied to QBI, DSI, or GQI, and the resolved fiber orientations were consistent regardless of the diffusion sampling schemes and diffusion reconstruction methods. The performance of diffusion decomposition was further demonstrated by resolving crossing fibers on a 30-direction QBI dataset and a 40-direction DSI dataset. In conclusion, diffusion decomposition can improve angular resolution and resolve crossing fibers in datasets with low SNR and substantially reduced number of diffusion encoding directions. These advantages may be valuable for human connectome studies and clinical research.

Highlights

Crossing fiber problem is still under active research in the field of diffusion MRI, and a method that offers accurate fiber orientation is the cornerstone of human connectome studies since it can facilitate fiber tracking and provide better mapping of neuronal connections [1,2]
We extended the L1 regularization paradigm to diffusion ODF (dODF) obtained from q-ball imaging (QBI), diffusion spectrum imaging (DSI), or generalized q-sampling imaging (GQI), aiming to get a sparse solution of fiber ODF (fODF) and to provide better resolving power for crossing fibers
This paper proposes a sparse fODF estimation method called diffusion decomposition, which obtains fODF by decomposing the dODF acquired from DSI, QBI, or GQI

Summary

Introduction

Crossing fiber problem is still under active research in the field of diffusion MRI, and a method that offers accurate fiber orientation is the cornerstone of human connectome studies since it can facilitate fiber tracking and provide better mapping of neuronal connections [1,2]. To further extend the applicability, Yeh et al [7] proposed generalized q-sampling imaging (GQI), which can be applied to a variety of diffusion sampling schemes to obtain dODFs, and the results are consistent with those from QBI and DSI. These dODF methods have been used to determine fiber orientations, their accuracy is limited by the blurred contour of dODF. This problem is demonstrated, an example of two fiber populations crossed at right angles (Fig. 1A). The fiber orientations can be resolved by the peak orientations of the dODF (Fig. 1B), but the blurred contour of the dODF may fail to resolve crossing fibers if the crossing angle is sufficiently small

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