Hole Detection in Metabolic Connectivity of Alzheimer’s Disease Using k −Laplacian

  • Hyekyoung Lee
  • Moo K. Chung
  • Hyejin Kang
  • Dong Soo Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8675)


Recent studies have found that the modular structure of functional brain network is disrupted during the progress of Alzheimer’s disease. The modular structure of network is the most basic topological invariant in determining the shape of network in the view of algebraic topology. In this study, we propose a new method to find another higher order topological invariant, hole, based on persistent homology. If a hole exists in the network, the information can be inefficiently delivered between regions. If we can localize the hole in the network, we can infer the reason of network inefficiency. We propose to detect the persistent hole using the spectrum of k −Laplacian, which is the generalized version of graph Laplacian. The method is applied to the metabolic network based on FDG-PET data of Alzheimer disease (AD), mild cognitive impairment (MCI) and normal control (NC) groups. The experiments show that the persistence of hole can be used as a biological marker of disease progression to AD. The localized hole may help understand the brain network abnormality in AD, revealing that the limbic-temporo-parietal association regions disturb direct connections between other regions.


Mild Cognitive Impairment Simplicial Complex Brain Network Connectivity Matrix Functional Brain Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hyekyoung Lee
    • 1
  • Moo K. Chung
    • 2
  • Hyejin Kang
    • 1
  • Dong Soo Lee
    • 1
  1. 1.Dept. of Nuclear MedicineSeoul National UniversityRepublic of Korea
  2. 2.Depart. of Biostatistics and Medical InformaticsUniversity of WisconsinMadisonUSA

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