Microcanonical and Canonical Ensembles for fMRI Brain Networks in Alzheimer’s Disease

Jianjia Wang

Abstract:

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of
Alzheimer’s disease and identify stages in the disease progression. We employ methods of network
neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for
network construction and analysis. In network construction, we vary thresholds in establishing
BOLD time series correlation between nodes, yielding variations in topological and other network
characteristics. For network analysis, we employ methods developed for modelling statistical
ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical
ensemble are analogous to two different fMRI network representations. In the former case, there is
zero variance in the number of edges in each network, while in the latter case the set of networks
have a variance in the number of edges. Ensemble methods describe the macroscopic properties of
a network by considering the underlying microscopic characterisations which are in turn closely
related to the degree configuration and network entropy. When applied to fMRI data in populations
of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for
clinical purposes in both identifying brain regions undergoing pathological changes and in revealing
the dynamics of such changes.