IEEE Trans Med Imaging. 2021 Jan;40(1):419-430. doi: 10.1109/TMI.2020.3029063. Epub 2020 Dec 29.
Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, their spatial patterns follow large-scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanisms of neuropathological events as they spread through the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework that provides enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves. This algebra overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic differences are measured by a set of common harmonic waves learned from a population of individual Eigen-systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves, which reside at the center of the Stiefel manifold. To that end, the common harmonic waves constitute a new set of neurobiological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuropathological burden spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns than Euclidean methods.
越来越多的证据表明，与疾病相关的大脑改变并非随机出现在大脑的任意位置，而是遵循着大规模的大脑网络。在这种情况下，一种具有数学基础的强大网络分析方法对于理解神经病理事件在大脑中的传播机制是不可或缺的。实际上，每个大脑网络的拓扑结构都由其固有谐波决定，这些谐波是从基础拉普拉斯矩阵的特征系统中导出的一组正交基。为此，我们提出了一种新的连接体谐波分析框架，通过检测与大脑疾病相关的基于频率的改变，提供了增强的数学见解。我们框架的核心是一种新的流形代数，适用于在谐波上进行推理。这种代数克服了在不规则数据结构上使用经典欧几里得操作的局限性。个体谐波差异通过一组从个体特征系统群体中学习到的常见谐波来测量，其中每个固有特征系统被视为从斯蒂夫尔流形中抽取的样本。具体来说，一个流形优化方案被定制来寻找常见的谐波，它们位于斯蒂夫尔流形的中心。为此，常见的谐波构成了理解疾病进展的一组新的神经生物学基础。每个谐波都表现出一种独特的神经病理负担在大脑网络中传播的模式。我们的新型连接体谐波分析方法的统计能力通过识别与阿尔茨海默病相关的基于频率的改变来评估，其中我们基于学习的流形方法发现了比欧几里得方法更显著和可重复的网络功能障碍模式。
