Network Optimization of Functional Connectivity Within Default Mode Network Regions to Detect Cognitive Decline

The rapid aging of the world's population is causing an increase in the prevalence of cognitive decline and degenerative brain disease in the elderly. Current diagnoses of amnestic and nonamnestic mild cognitive impairment, which may represent early stage Alzheimer's disease or related degenerative conditions, are based on clinical grounds. The recent emergence of advanced network analyses of functional magnetic resonance imaging (fMRI) data taken at cognitive rest has provided insight that declining functional connectivity of the default mode network (DMN) may be correlated with neurological disorders, and particularly prodromal Alzheimer's disease. The goal of this paper is to develop a network analysis technique using fMRI data to characterize transition stages from healthy brain aging to cognitive decline. Previous studies primarily focused on inter-nodal connectivity of the DMN and often assume functional homogeneity within each DMN region. In this paper, we develop a technique that focuses on identifying critical intra-nodal DMN connectivity by incorporating sparsity into connectivity modeling of the k-cardinality tree (KCT) problem. Most biological networks are efficient and formed by sparse connections, and the KCT can potentially reveal sparse connectivity patterns that are biologically informative. The KCT problem is NP-hard, and existing solution approaches are mostly heuristic. Mathematical formulations of the KCT problem in the literature are not compact and do not provide good solution bounds. This paper presents new KCT formulations and a fast heuristic approach to efficiently solve the KCT models for large DMN regions. The results in this paper demonstrate that traditional fMRI group analysis on DMN regions cannot detect any statistically significant connectivity differences between normal aging and cognitively impaired subjects in DMN regions, and the proposed KCT approaches are more sensitive than the state-of-the-art regional homogeneity approach in detecting significant differences in both left and right medial temporal regions of the DMN.