Research On Complex Brain Network Based On Persistent Homology

Graph theory index analysis of complex networks is very important for revealing the pathology of certain brain neurological and cognitive diseases,and also provides important biomarkers for the recognition and diagnosis of certain brain diseases.However,the methods of graph theory cannot provide higher-level topological features for complex network research.With the development of algebraic topology,analysis of complex brain networks based on persistent homology has become a new research direction.The latest research on persistent homology shows that changes in the structure and function of the human brain network provide new biomarkers for many neuropsychiatric and neurodegenerative diseases.This paper studies complex brain networks based on the theory of persistent homology.The main work is as follows:(1)Summarize and analyze the complex brain network construction methods based on various image data,construct the metabolic brain network at the whole brain level and the functional brain network at the subnet level.(2)Aiming at the problem that the persistent characteristic changes in the persistent homology theory are complicated and difficult to compare,this paper introduces the kernel method on the basis of the persistent homology theory and proposes a novel univariate network index,which can not only describe Persistence features well but also quantify the differences in persistence graphs.(3)This paper applies the proposed kernel method based on persistent homology to the study of metabolic brain networks.In the metabolic brain network experiment,the fluorodeoxyglucose positron emission tomography imaging data of 140 cases of Alzheimer's disease(AD),280 cases of mild cognitive impairment(MCI)and 280 normal healthy control(NC)from the Alzheimer's Disease Neuroimaging Initiative(ADNI)database were studied.The results show that the kernel method in this paper is superior to the existing persistent feature indexes and graph-based feature indexes in terms of persistence feature description,persistence difference quantification and feature classification.(4)This article is the first to apply the persistent homology method to the functional brain network research of APOE genotype.In the APOE genotype experiment,The imaging data of 16 cases of APOE ?4 homozygous gene carriers(HM),39 cases of APOE ?4 heterozygous gene carriers(HT)and 56 non-carriers(NC)from ADNI was analyzed for persistent homology characteristics.The results show that the method of persistent homology has more significant statistical differences than the graph theory method,indicating that the method of persistent homology is also applicable and robust in the analysis of functional subnetworks.