Dynamic Topology Analysis for Spatial Patterns of Multifocal Lesions on MRI

Abstract 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 network 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.