Microcanonical and canonical ensembles for fmri brain networks in alzheimer’s disease

Jianjia Wang*, Xichen Wu, Mingrui Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Article number216
Pages (from-to)1-16
Number of pages16
Issue number2
Publication statusPublished - Feb 2021
Externally publishedYes


  • Brain network entropy
  • Canonical ensemble
  • Microcanonical ensemble


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