起伏结构中随时间变化的扩散：对轴突直径估计的影响
Time-dependent diffusion in undulating structures: Impact on axon diameter estimation
摘要：
扩散MRI可以实现轴突微结构的非侵入性映射。大多数方法通过将轴突建模为直圆柱体来从时间依赖性扩散对扩散加权MR信号的影响推断轴突直径。然而，轴突不以直线轨迹运行，到目前为止，轴突轨迹对直径估计的影响还没有被系统地研究。在这里，我们采用了一个玩具模型的轴突，我们称之为起伏的细纤维模型，来分析起伏的轨迹上的扩散谱所代表的扩散时间依赖性的影响。我们通过其高度（高频扩散率）、宽度（半峰半宽）和低频行为（幂律指数）分析光谱。结果表明，细纤维的微观取向色散是决定扩散谱特征的主要参数。直圆柱体和波状细纤维在较低频率下具有几乎相同的光谱。如果直圆柱假设被用来解释数据从起伏的薄轴突，直径被高估的量成比例的波动幅度和微观取向分散。在高频率（短扩散时间），光谱从圆柱体和起伏的细纤维不同。来自起伏细纤维的光谱也可以通过呈现指数低于2的幂律行为而不同于圆柱体的光谱。总之，我们认为，轴突轨迹的非直线性质不应被忽视时，分析dMRI数据和仔细的实验可能会使扩散分离直圆柱体和扩散在起伏的细纤维。
英文摘要：
Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modelling axons as straight cylinders. Axons do not, however, run in straight trajectories and so far, the impact of the axonal trajectory on diameter estimation has not been systematically investigated. Here, we employ a toy-model of axons, which we refer to as undulating thin-fiber model, to analyze the impact of undulating trajectories on the diffusion-time dependence represented by the diffusion spectrum. We analyze the spectrum by its height (diffusivity at high frequencies), width (half width at half maximum), and low-frequency behavior (power law exponent). Results show that microscopic orientation dispersion of the thin-fibers is the main parameter that determines the characteristics of the diffusion spectra. Straight cylinders and undulating thin-fibers have virtually identical spectra at lower frequencies. If the straight-cylinder assumption is used to interpret data from undulating thin axons, the diameter is overestimated by an amount proportional to the undulation amplitude and the microscopic orientation dispersion. At high frequencies (short diffusion times), spectra from cylinders and undulating thin-fibers differ. The spectra from the undulating thin-fibers can also differ from that of cylinders by exhibiting power law behaviors with exponents below two. In conclusion, we argue that the non-straight nature of axonal trajectories should not be ignored when analyzing dMRI data and that careful experiments may enable separation of diffusion within straight cylinders and diffusion in undulating thin-fibers.
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