Section on Tissue Biophysics and Biomimetics, PPITS, NICHD, National Institutes of Health, Bethesda, MD 20892, USA.
Neuroimage. 2013 Sep;78:16-32. doi: 10.1016/j.neuroimage.2013.04.016. Epub 2013 Apr 13.
Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.
扩散加权磁共振（MR）信号反映了组织微观结构和细胞结构的信息。我们提出了一种定量、高效、稳健的数学和物理框架，用于表示在“q 空间”中获得的扩散加权磁共振成像（MRI）数据，以及相应的“平均表观扩散算子（MAP）”，用于描述“r 空间”中的分子位移。我们还定义并映射了可以使用这种 MAP-MRI 框架稳健计算的扩散的新定量描述符。我们描述了在基函数级数展开中对三维 q 空间 MR 信号的有效分析表示，该展开准确地描述了许多复杂几何形状中的扩散。该展开中的最低阶项包含一个扩散张量，该张量表征了高斯位移分布，相当于扩散张量 MRI（DTI）。包含更高阶项可以重建真实的平均扩散算子，该算子在单位“位移”球上的投影提供了一个方位分布函数（ODF），该函数仅包含扩散过程的方位依赖性。该表示表征了扩散各向异性的新特征以及三维扩散过程的非高斯特征。该表示提供的其他重要度量包括返回到原点的概率（RTOP），以及其在一维和二维扩散中的变体——返回到平面的概率（RTPP）和返回到轴的概率（RTAP）。这些零净位移概率分别测量了孤立孔分布中的平均隔室（孔）体积和横截面面积，而与孔形状无关。MAP-MRI 代表了一种新的综合框架，用于对三维 q 空间信号进行建模，并将其转换为扩散算子。在切除的狨猴大脑标本上进行的实验表明，MAP-MRI 提供了几个新的、可量化的参数，这些参数捕获了神经组织微观结构以前被掩盖的固有特征。这对于研究正常和病理神经组织的功能组织应该很有帮助。
