Brain structural networks are often represented as discrete adjacency matrices with elements summarizing the connectivity between pairs of regions of interest (ROIs). These ROIs are typically determined a-priori using a brain atlas. The choice of atlas is often arbitrary and can lead to a loss of important connectivity information at the sub-ROI level. This work introduces an atlas-free framework that overcomes these issues by modeling brain connectivity using smooth random functions. In particular, we assume that the observed pattern of white matter fiber tract endpoints is driven by a latent random function defined over a product manifold domain. To facilitate statistical analysis of these high dimensional functional data objects, we develop a novel algorithm to construct a data-driven reduced-rank function space that offers a desirable trade-off between computational complexity and flexibility. Using real data from the Human Connectome Project, we show that our method outperforms state-of-the-art approaches that use the traditional atlas-based structural connectivity representation on a variety of connectivity analysis tasks. We further demonstrate how our method can be used to detect localized regions and connectivity patterns associated with group differences.

翻译：大脑结构网络通常表示为离散的邻接矩阵，其元素汇总了感兴趣区域（ROIs）对之间的连接性。这些ROI通常使用大脑图谱预先确定。图谱的选择往往具有任意性，可能导致亚ROI层级上重要连接信息的丢失。本研究引入了一个无图谱框架，通过使用光滑随机函数对大脑连接进行建模，克服了这些问题。具体而言，我们假设观察到的白质纤维束终点模式由一个定义在乘积流形域上的潜在随机函数驱动。为了促进对这些高维功能数据对象的统计分析，我们开发了一种新颖算法，构建了一个数据驱动的降阶函数空间，在计算复杂性和灵活性之间提供了理想的平衡。利用人类连接组项目的真实数据，我们展示了在多种连接分析任务中，该方法优于使用传统基于图谱的结构连接表征的最先进方法。我们进一步演示了如何使用该方法检测与组间差异相关的局部区域和连接模式。