Network construction: a graph spectrum approach
Understanding network features of brain pathology is essential to reveal underlying pathological mechanisms of neurodegenerative diseases. We developed a novel graph regression model (GRM) for learning structural brain connectivity from neuroimaging datasets. The proposed GRM regards neuroimaging data as smooth signals defined on an unknown graph. This graph is then estimated through an optimization framework, which fits the graph to the data with an adjustable level of uniformity of the connection weights. Under the assumed data model, results based on simulated data illustrate that our approach can accurately reconstruct the underlying network, often with better reconstruction than those obtained by both sample correlation and L1-regularized partial correlation estimation. We applied our GRM approach to an Alzheimer’s Disease (AD) positron emission tomography (PET) dataset and evaluations performed upon neuroimaging data demonstrate that the connectivity patterns revealed by the GRM are easy to interpret and consistent with known pathology. Moreover, the hubs of the reconstructed networks match the cortical hubs given by functional MRI. The discriminative network features including both global connectivity measurements and degree statistics of specific nodes discovered from the AD and NC amyloid-beta networks provide new potential biomarkers for preclinical and clinical AD.
Hu, Chenhui, et al. “A spectral graph regression model for learning brain connectivity of alzheimer’s disease.” PloS one 10.5 (2015): e0128136.
Matched subspace detection: theory and application to brain imaging data classification
Motivated by recent progress in signal processing on graphs, we developed a novel matched signal detection (MSD) theory for signals with intrinsic structures described by weighted graphs. First, we regard graph Laplacian eigenvalues as frequencies of graph-signals and assume that the signal is in a subspace spanned by the first few graph Laplacian eigenvectors associated with lower eigenvalues. The conventional matched subspace detector can be applied to this case. Furthermore, we study signals that may not merely live in a subspace. Concretely, we consider signals with bounded variation on graphs and more general signals that are randomly drawn from a prior distribution. For bounded variation signals, the test is a weighted energy detector. For the random signals, the test statistic is the difference of signal variations on associated graphs, if a degenerate Gaussian distribution specified by the graph Laplacian is adopted. We evaluate the effectiveness of the MSD on graphs both with simulated and real data sets. Specifically, we apply MSD to the brain imaging data classification problem of Alzheimer’s disease (AD) based on two independent data sets: 1) positron emission tomography data with Pittsburgh compound-B tracer of 30 AD and 40 normal control (NC) subjects, and 2) resting-state functional magnetic resonance imaging (R-fMRI) data of 30 early mild cognitive impairment and 20 NC subjects. Our results demonstrate that the MSD approach is able to outperform the traditional methods and help detect AD at an early stage, probably due to the success of exploiting the manifold structure of the data.
Hu, Chenhui, et al. “Matched signal detection on graphs: Theory and application to brain imaging data classification.” NeuroImage 125 (2016): 587-600.
Prediction of neurodegeneration based on network diffusion model
Pinpointing the sources of dementia is crucial to the effective treatment of neurodegenerative diseases. We propose a diffusion model with impulsive sources over the brain connectivity network to model the progression of brain atrophy. To reliably estimate the atrophy sources, we impose sparse regularization on the source distribution and solve the inverse problem with an efficient gradient descent method. We localize the possible origins of Alzheimer’s disease (AD) based on a large set of repeated magnetic resonance imaging (MRI) scans in Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. The distribution of the sources averaged over the sample population is evaluated. We find that the dementia sources have different concentrations in the brain lobes for AD patients and mild cognitive impairment (MCI) subjects, indicating possible switch of the dementia driving mechanism. Moreover, we demonstrate that we can effectively predict changes of brain atrophy patterns with the proposed model. Our work could help understand the dynamics and origin of dementia, as well as monitor the progression of the diseases in an early stage.
Hu, Chenhui, et al. “Localizing Sources of Brain Disease Progression with Network Diffusion Model.” IEEE Journal of Selected Topics in Signal Processing 10.7 (2016): 1214-1225.
