Study of Brain Network in Alzheimers Disease Using Wavelet-Based Graph Theory Method

Alzheimer's disease (AD) is a neurodegenerative disorder marked by memory loss and cognitive decline, making early detection vital for timely intervention. However, early diagnosis is challenging due to the heterogeneous presentation of symptoms. Resting-state fMRI (rs-fMRI) captures spontaneous brain activity and functional connectivity, which are known to be disrupted in AD and mild cognitive impairment (MCI). Traditional methods, such as Pearson's correlation, have been used to calculate association matrices, but these approaches often overlook the dynamic and non-stationary nature of brain activity. In this study, we introduce a novel method that integrates discrete wavelet transform (DWT) and graph theory to model the dynamic behavior of brain networks. By decomposing rs-fMRI signals using DWT, our approach captures the time-frequency representation of brain activity, allowing for a more nuanced analysis of the underlying network dynamics. Graph theory provides a robust mathematical framework to analyze these complex networks, while machine learning is employed to automate the discrimination of different stages of AD based on learned patterns from different frequency bands. We applied our method to a dataset of rs-fMRI images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, demonstrating its potential as an early diagnostic tool for AD and for monitoring disease progression. Our statistical analysis identifies specific brain regions and connections that are affected in AD and MCI, at different frequency bands, offering deeper insights into the disease's impact on brain function.

BDgraph: An R Package for Bayesian Structure Learning in Graphical Models

Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce an R package BDgraph which performs Bayesian structure learning for general undirected graphical models with either continuous or discrete variables. The package efficiently implements recent improvements in the Bayesian literature. To speed up computations, the computationally intensive tasks have been implemented in C++ and interfaced with R. In addition, the package contains several functions for simulation and visualization, as well as two multivariate datasets taken from the literature and are used to describe the package capabilities. The paper includes a brief overview of the statistical methods which have been implemented in the package. The main body of the paper explains how to use the package. Furthermore, we illustrate the package's functionality in both real and artificial examples, as well as in an extensive simulation study.