Quantitatively analysing the spatial patterns of multifocal lesions on clinical MRI is an important step towards a better understanding of the disease and for precision medicine, which is yet to be properly explored by feature engineering and deep learning methods. Network science addresses this issue by explicitly modeling the inter-lesion topology. However, the construction of the informative graph with optimal edge sparsity and quantification of community graph structures are the current challenges in network science. In this paper, we address these challenges with a novel Dynamic Topology Analysis framework on the basis of persistent homology, aiming to investigate the predictive values of global geometry and local clusters of multifocal lesions. Firstly, Dynamic Hierarchical Network is proposed to construct informative global and community-level topology over multi-scale networks from sparse to dense. Multi-scale global topology is constructed with a nested sequence of Rips complexes, from which a new K-simplex Filtration is designed to generate a higher-level topological abstraction for community identification based on the connectivity of k-simplices in the Rips Complex. Secondly, to quantify multi-scale community structures, we design a new Decomposed Community Persistence algorithm to track the dynamic evolution of communities, and then summarise the evolutionary communities incorporated with a customisable descriptor. The quantified community features are encapsulated with global geometric invariants for topological pattern analysis. The proposed framework was evaluated on both diagnostic differentiation and prognostic prediction for multiple sclerosis that is a typical multifocal disease, and achieved ROC_AUC 0.875 and 0.767, respectively, outperforming seven state-of-the-art persistent homology methods and the reported performance of six feature engineering and deep learning methods.

在临床 MRI 上定量分析多灶性病变的空间模式是更好地了解疾病和精准医学的重要一步，这还有待通过特征工程和深度学习方法进行适当探索。网络科学通过显式建模病变间拓扑来解决这个问题。然而，构建具有最佳边缘稀疏性的信息图和量化社区图结构是网络科学当前面临的挑战。在本文中，我们采用基于持久同源性的新型动态拓扑分析框架来应对这些挑战，旨在研究全局几何形状和多灶性病变局部集群的预测值。首先，提出了动态分层网络，用于在从稀疏到密集的多尺度网络上构建信息丰富的全局和社区级拓扑。多尺度全局拓扑结构是用 Rips 复合体的嵌套序列构建的，从中设计了一个新的 K-simplex 过滤，用于基于 Rips 复合体中 k-simlices 的连通性生成更高级别的拓扑抽象用于社区识别。其次，为了量化多尺度的社区结构，我们设计了一种新的 Decomposed Community Persistence 算法来跟踪社区的动态演化，然后用可定制的描述符对演化的社区进行总结。量化的社区特征用全局几何不变量封装，用于拓扑模式分析。