Department of Medical Physics, University of Wisconsin School of Medicine and Public Health, Madison, WI 53705, USA.
Med Phys. 2012 May;39(5):2499-511. doi: 10.1118/1.3700166.
Diffusion magnetic resonance imaging (MRI) in combination with functional MRI promises a whole new vista for scientists to investigate noninvasively the structural and functional connectivity of the human brain-the human connectome, which had heretofore been out of reach. As with other imaging modalities, diffusion MRI data are inherently noisy and its acquisition time-consuming. Further, a faithful representation of the human connectome that can serve as a predictive model requires a robust and accurate data-analytic pipeline. The focus of this paper is on one of the key segments of this pipeline-in particular, the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond.
The authors propose a novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and a novel and effective semistochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. The goal of the optimality criteria is threefold: first, to maximize uniformity of the diffusion measurements in each shell, which is equivalent to maximal incoherence in angular measurements; second, to maximize coverage of the diffusion measurements around each radial line to achieve maximal incoherence in radial measurements for multiple-shell acquisition; and finally, to ensure maximum uniformity of diffusion measurement directions in the limiting case when all the shells are coincidental as in the case of a single-shell acquisition. The approach taken in evaluating the stability of various acquisition designs is based on the condition number and the A-optimal measure of the design matrix.
Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general-e.g., in the order of 10(232) for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI).
A novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and an effective search strategy for finding the best configuration have been developed. The results are very promising, interesting, and practical for diffusion MRI acquisitions.
扩散磁共振成像（MRI）与功能 MRI 相结合，为科学家们提供了一个全新的视角，使他们能够无创地研究人类大脑的结构和功能连接——人类连接组，这在此前是遥不可及的。与其他成像方式一样，扩散 MRI 数据本身存在噪声，采集时间较长。此外，要构建一个能够作为预测模型的真实人类连接组，需要一个稳健、准确的数据分析管道。本文的重点是该管道的关键环节之一——特别是扩散 MRI 多壳层采集及更高层次的稀疏和最优采集（SOA）设计的开发。
作者提出了一种新的扩散 MRI 稀疏多壳层采集和准多壳层设计的最优性准则，以及一种新颖而有效的半随机和适度贪婪组合搜索策略，并结合模拟退火来定位最优设计或配置。最优性准则的目标有三个：首先，最大化每个壳层中扩散测量的均匀性，这等效于角度测量的最大不相关性；其次，最大化每个径向线周围扩散测量的覆盖范围，以实现多壳层采集的径向测量的最大不相关性；最后，在所有壳层都重合的极限情况下（例如单壳层采集的情况），确保扩散测量方向的最大均匀性。在评估各种采集设计的稳定性时，采用的方法是基于条件数和设计矩阵的 A 最优度量。
尽管对于给定的扩散梯度方向集，不同的配置数量通常非常大，例如对于 144 个扩散梯度方向的集合，其数量高达 10(232)，但所提出的搜索策略被发现能够有效地找到最优配置。研究发现，在许多具有相同样本大小的其他设计中，方形设计是最稳健的（即在不同的实验条件下，条件数和 A 最优度量稳定）。在相同的性能评估下，方形设计比广泛使用的采样方案更稳健，这些方案类似于 3D 径向 MRI 和扩散谱成像（DSI）的采样方案。
本文提出了一种新的扩散 MRI 稀疏多壳层采集和准多壳层设计的最优性准则，以及一种用于寻找最佳配置的有效搜索策略。这些结果对扩散 MRI 采集非常有前途、有趣且实用。
