Normal and aberrant cognitive functions are the result of the dynamic interplay between large-scale neural circuits. Describing the nature of these interactions has been a challenging task yet important for neurodegenerative disease evolution. Graph theory has been the standard tool to provide biomarkers in imaging connectomics showing the Alzheimer’s disease (AD). We propose a novel concept - graph signal processing - to analyze the evolution of disease graphs leading from mild cognitive impairment (MCI) to AD and derive frequency-based biomarkers representative for this disease. We show that high oscillations derived from the graph Fourier decomposition can provide important discriminatory information. To quantify the qualitative intuition of high oscillations, we use two concepts from signal theory: (1) zero crossings and (2) total variations. We apply these concepts on functional and structural brain connectivity networks for control (CN), mild cognitive impairment (MCI) and Alzheimer’s disease (AD) subjects. Our results applied to functional brain networks suggest that graph signal processing can accurately describe the frequencies of brain networks, and explain how AD is associated with low frequency and localized averaging confirmed by clinical results.
Normal and aberrant cognitive functions are the result of the dynamic interplay between large-scale neural circuits. Describing the nature of these interactions has been a challenging task yet important for neurodegenerative disease evolution. The origin of Alzheimer’s disease lies in the hippocampus and subsequently diffuses to the temporal, parietal and prefrontal cortices. Determining the sources of dementia is crucial to the prediction of the disease evolution and choice of treatment. State-of-the-art method for determining dementia progression are network diffusion models derived from the heat equation without diffusion sources. We propose a different research avenue based on epidemic modeling to localize the disease sources. These models may better characterize the empirical spread of dementia through brain regions. We explore an estimation algorithm based on a susceptible-infected (SI) epidemic algorithm and a network diffusion model for comparison purposes emulating the disease evolution from sources (susceptible) to non-recovered (atrophy, infected) areas. The goal is to identify the probable disease diffusion sources, which we accomplish via a ranking heuristic based upon steady-state convergence times. Graph centrality measures are employed to provide a baseline for further comparison. Our results applied on structural brain networks in dementia suggest that epidemic models are able to accurately describe the different node roles in controlling trajectories of brain networks comparably to the existing diffusion approach.
Statistical learning and decision theory play a key role in many areas of science and engineering. Some examples include time series regression and prediction, optical character recognition, signal detection in communications or biomedical applications for diagnosis and prognosis. This paper deals with the topic of learning from biomedical image data in the classification problem. In a typical scenario we have a training set that is employed to fit a prediction model or learner and a testing set on which the learner is applied to in order to predict the outcome for new unseen patterns. Both processes are usually completely separated to avoid over-fitting and due to the fact that, in practice, the unseen new objects (testing set) have unknown outcomes. However, the outcome yields one of a discrete set of values, i.e. the binary diagnosis problem. Thus, assumptions on these outcome values could be established to obtain the most likely prediction model at the training stage, that could improve the overall classification accuracy on the testing set, or keep its performance at least at the level of the selected statistical classifier. In this sense, a novel case-based learning (c-learning) procedure is proposed which combines hypothesis testing from a discrete set of expected outcomes and a cross-validated classification stage.
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