[论文解读] Spatially regularized reconstruction of fibre orientation distributions in the presence of isotropic diffusion

Quan Zhou, Oleg Michailovich+1 more|arXiv (Cornell University)|Jan 23, 2014

Advanced Neuroimaging Techniques and Applications参考文献 29被引用 4

一句话总结

本文提出了一种空间正则化的球面反卷积（SCSD）方法，用于在高角分辨率扩散成像（HARDI）中重建纤维方向分布（fODFs），该方法结合了白质纤维束的空间连续性与各向同性扩散。该方法在中到严重噪声和部分容积效应条件下，提升了方向分辨率与鲁棒性，在模拟与在体实验中均优于现有方法。

ABSTRACT

The connectivity and structural integrity of the white matter of the brain is nowadays known to be implicated into a wide range of brain-related disorders. However, it was not before the advent of diffusion Magnetic Resonance Imaging (dMRI) that researches have been able to examine the properties of white matter in vivo. Presently, among a range of various methods of dMRI, high angular resolution diffusion imaging (HARDI) is known to excel in its ability to provide reliable information about the local orientations of neural fasciculi (aka fibre tracts). Moreover, as opposed to the more traditional diffusion tensor imaging (DTI), HARDI is capable of distinguishing the orientations of multiple fibres passing through a given spatial voxel. Unfortunately, the ability of HARDI to discriminate between neural fibres that cross each other at acute angles is always limited, which is the main reason behind the development of numerous post-processing tools, aiming at the improvement of the directional resolution of HARDI. Among such tools is spherical deconvolution (SD). Due to its ill-posed nature, however, SD standardly relies on a number of a priori assumptions which are to render its results unique and stable. In this paper, we propose a different approach to the problem of SD in HARDI, which accounts for the spatial continuity of neural fibres as well as the presence of isotropic diffusion. Subsequently, we demonstrate how the proposed solution can be used to successfully overcome the effect of partial voluming, while preserving the spatial coherency of cerebral diffusion at moderate-to-severe noise levels. In a series of both in silico and in vivo experiments, the performance of the proposed method is compared with that of several available alternatives, with the comparative results clearly supporting the viability and usefulness of our approach.

研究动机与目标

• 解决低b值下HARDI因部分容积效应与噪声导致的方向分辨率有限的问题。
• 提升球面反卷积（SD）在重建纤维方向分布（fODFs）时的稳定性和准确性。
• 将神经纤维的空间连续性与各向同性扩散整合进SD框架，实现更具生物学合理性的重建。
• 开发一种凸优化方法，计算上可处理，且在信噪比低的情况下仍能保持空间一致性。
• 在真实噪声环境与复杂纤维构型下，证明该方法优于现有SD与ODF重建方法。

提出的方法

• 该方法将球面反卷积表述为一个凸优化问题，包含假设高斯噪声的数据保真项与采用总变差（TV）正则化项以强制fODFs的空间连续性。
• 通过在球面谐波基中引入常数项来建模各向同性扩散，从而实现各向同性与各向异性扩散成分的分离。
• 利用频域方法高效求解优化问题，将问题转化为具有有限冲激响应（FIR）滤波器的频域滤波操作。
• FIR滤波器由方向差分算子的频率响应的逆推导而来，并截断至7×7×7体素以提高计算效率。
• 采用分裂Bregman算法求解非光滑TV正则化问题，实现高效且稳定的收敛。
• 该方法在多壳HARDI框架中实现，即使在低b值（如1000 s/mm²）下也能实现稳健重建。

实验结果

研究问题

• RQ1 在存在噪声与部分容积效应的情况下，球面反卷积中的空间正则化是否能提升fODF估计的准确性和稳定性？
• RQ2 将各向同性扩散整合进SD框架，对复杂纤维构型的重建有何影响？
• RQ3 通过总变差强制空间连续性，是否能生成比标准SD方法更一致且更具生物学合理性的fODF图？
• RQ4 与传统QBI和SD技术相比，该方法在低b值下是否能实现更优的方向分辨率？
• RQ5 该方法的计算复杂度是否适合临床与研究场景中的实际应用？

主要发现

• 所提出的SCSD方法在低b值（如1000 s/mm²）下显著提升了fODF重建的方向分辨率，而传统方法在此条件下失效。
• 在模拟实验中，SCSD在60°交叉纤维角度下实现了更高的角分辨率，并更优地恢复了交叉纤维，优于标准SD与QBI方法。
• 该方法对中到严重噪声水平表现出鲁棒性，保持了空间一致性，并减少了虚假fODF主瓣的出现。
• 在体实验中，纤维束追踪质量得到改善，且在复杂纤维结构区域，fODF图在不同受试者间表现出更高的稳定性。
• 使用截断FIR滤波器实现了高效、线性复杂度的滤波，误差低于1%，使该方法适用于大规模数据处理。
• 在定量指标（如fODF主瓣锐度与角误差）方面，该方法在模拟与真实数据中均优于最先进的替代方法。