UCLA, Los Angeles, CA, USA.
Neuroinformatics. 2012 Jan;10(1):5-17. doi: 10.1007/s12021-011-9113-2.
Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore enabling interactive probabilistic tractography: the user can quickly modify the seed region if he is not satisfied with the output without having to wait on average 7 min.
许多不同的概率追踪方法已经在文献中被提出，以克服经典确定性追踪的局限性：（i）缺乏定量连通性信息；和（ii）对噪声、部分体积效应和种子区域选择的鲁棒性。然而，这些方法依赖于计算上非常耗费的蒙特卡罗采样技术。本研究提出了一种近似随机追踪算法（FAST），可以交互使用，而不需要在标记种子区域后等待几分钟才能获得输出。在 FAST 中，追踪被表述为一个马尔可夫链，该链依赖于一个转移张量。该张量旨在模拟基于随机游走模型和蒙特卡罗采样的一种著名的概率追踪方法的特征，但也可以适应其他传播规则。与基线算法相比，我们的方法绕过了采样过程，并以部分牺牲亚像素精度为代价提供了确定性解决方案。因此，该方法严格来说不是随机的，但在随机追踪方法的精神下提供了概率输出。FAST 与随机游走模型使用来自 10 名患者的真实数据进行了两种比较：1. 两种方法在五个已知纤维束上生成的概率图直接使用图像配准文献中的度量进行比较；和 2. 两种方法给出的大脑不同区域之间的连通性测量使用相关系数 ρ 进行比较。结果表明，两种算法提供的连通性测量值相关性很好（ρ=0.83），概率图也是如此（归一化互相关 0.818±0.081）。图谱在质量上（即视觉上）也非常相似。与蒙特卡罗采样方案相比，该方法实现了 60 倍的加速（7 秒对 7 分钟），从而实现了交互式概率追踪：如果用户对输出不满意，可以快速修改种子区域，而无需平均等待 7 分钟。
