Yang Jianfei, Poot Dirk H J, van Vliet Lucas J, Vos Frans M
Quantitative Imaging Group, Department of Imaging Physics, Delft University of Technology, The Netherlands. Department of Radiology, Academic Medical Center, Amsterdam, The Netherlands.
Phys Med Biol. 2015 Dec 7;60(23):9123-44. doi: 10.1088/0031-9155/60/23/9123. Epub 2015 Nov 12.
Diffusion-weighted magnetic resonance imaging permits assessment of the structural integrity of the brain's white matter. This requires unbiased and precise quantification of diffusion properties. We aim to estimate such properties in simple and complex fiber geometries up to three-way fiber crossings using rank-2 tensor model selection. A maximum a-posteriori (MAP) estimator is employed to determine the parameters of a constrained triple tensor model. A prior is imposed on the parameters to avoid the degeneracy of the model estimation. This prior maximizes the divergence between the three tensor's principal orientations. A new model selection approach quantifies the extent to which the candidate models are appropriate, i.e. a single-, dual- or triple-tensor model. The model selection precludes overfitting to the data. It is based on the goodness of fit and information complexity measured by the total Kullback-Leibler divergence (ICOMP-TKLD). The proposed framework is compared to maximum likelihood estimation on phantom data of three-way fiber crossings. It is also compared to the ball-and-stick approach from the FMRIB Software Library (FSL) on experimental data. The spread in the estimated parameters reduces significantly due to the prior. The fractional anisotropy (FA) could be precisely estimated with MAP down to an angle of approximately 40° between the three fibers. Furthermore, volume fractions between 0.2 and 0.8 could be reliably estimated. The configurations inferred by our method corresponded to the anticipated neuro-anatomy both in single fibers and in three-way fiber crossings. The main difference with FSL was in single fiber regions. Here, ICOMP-TKLD predominantly inferred a single fiber configuration, as preferred, whereas FSL mostly selected dual or triple order ball-and-stick models. The prior of our MAP estimator enhances the precision of the parameter estimation, without introducing a bias. Additionally, our model selection effectively balances the trade-off between the goodness of fit and information complexity. The proposed framework can enhance the sensitivity of statistical analysis of diffusion tensor MRI.
扩散加权磁共振成像可用于评估脑白质的结构完整性。这需要对扩散特性进行无偏且精确的量化。我们旨在使用秩-2张量模型选择来估计简单和复杂纤维几何结构（直至三向纤维交叉）中的此类特性。采用最大后验（MAP）估计器来确定约束三重张量模型的参数。对参数施加先验条件以避免模型估计的退化。该先验条件使三个张量的主方向之间的差异最大化。一种新的模型选择方法量化了候选模型（即单张量、双张量或三重张量模型）的合适程度。模型选择可防止对数据的过度拟合。它基于由总库尔贝克-莱布勒散度（ICOMP-TKLD）测量的拟合优度和信息复杂度。将所提出的框架与三向纤维交叉的体模数据上的最大似然估计进行比较。还将其与FMRIB软件库（FSL）中的球棒方法在实验数据上进行比较。由于先验条件，估计参数的离散度显著降低。使用MAP可以精确估计分数各向异性（FA），直至三根纤维之间的角度约为40°。此外，可以可靠地估计0.2至0.8之间的体积分数。我们的方法推断出的构型在单纤维和三向纤维交叉中均与预期的神经解剖结构相对应。与FSL的主要差异在于单纤维区域。在这里，ICOMP-TKLD主要推断出首选的单纤维构型，而FSL大多选择双阶或三阶球棒模型。我们的MAP估计器的先验条件提高了参数估计的精度，且不会引入偏差。此外，我们的模型选择有效地平衡了拟合优度和信息复杂度之间的权衡。所提出的框架可以提高扩散张量MRI统计分析的灵敏度。
