Construction and Analysis of Weighted Brain Networks from SICE for the Study of Alzheimer's Disease

Abstract

Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people, and current drugs, unfortunately, do not represent yet a cure but only slow down its progression. This is explained, at least in part, because the understanding of the neurodegenerative process is still incomplete, being sometimes mistaken, particularly at the first steps of the illness, with the natural aging process. A better identification of how the functional activity deteriorates is thus crucial to develop new and more effective treatments. Sparse inverse covariance estimates (SICE) have been recently employed for deriving functional connectivity patterns from Positron Emission Tomography (PET) of brains affected by Alzheimer's Disease. SICE, unlike the traditional covariance methods, allows to analyze the interdependencies between brain regions factoring out the influence of others. To analyze the effects of the illness, connectivity patterns of brains affected by AD are compared with those obtained for control groups. These comparisons are, however, carried out for binary (undirected and unweighted) adjacency matrices with the same number of arcs. Additionally, the effect of the number of subjects employed or the validity of the regularization parameter used to compute the SICE have been not hitherto analyzed. In this paper, we delve into the construction of connectivity patterns from PET using SICE. In particular, we describe the effect that the number of subjects employed has on the results and identify, based on the reconstruction error of linear regression systems, a range of valid values for the regularization parameter. The amount of arcs is also proved as a discriminant value, and we show that it is possible to pass from unweighted (binary) to weighted adjacency matrices, where the weight of a connection corresponding to the existence of a relationship between two brain areas can be correlated to the persistence of this relationship when computed for different values of the regularization parameter and sets of subjects. Finally, network measures are computed for the connectivity patterns confirming that SICE may be particularly apt for assessing the efficiency of drugs, since it produces reliable brain connectivity models with small sample sizes, and that connectivity patterns affected by AD seem much less segregated, reducing the small-worldness.

Network Disruption in the Preclinical Stages of Alzheimer’s Disease: From Subjective Cognitive Decline to Mild Cognitive Impairment

“…MCI and AD patients also showed clustering reductions in a previous study using sparse inverse covariance estimation with positron emission tomography (PET) 75 which seems to be an optimal and reliable methodology for studying AD. 76 Thus, our results for SCD and MCI are consistent with the previous literature. The increase in transitivity in the alpha band showed by SCD elders reflects an increase in the number of short-range connections in this specific frequency range.…”

Cortical Thickness and Surface Area Networks in Healthy Aging, Alzheimer’s Disease and Behavioral Variant Fronto-Temporal Dementia

“…The partial correlations were calculated as linear, Pearson's correlation coefficient between pairs of x i and x j , after first removing the effects of all other regions m = (i, j) and then adjusting both x i and x j for controlling variables (stored in a separate array S × C, where C represents number of controlling variables). 35 This means that prior to the correlation analysis a linear regression was performed on every x i to remove the effect of age, gender and mean CT (mean cortical thickness of all areas) or total SA (sum of overall surface areas). 19 Selfcorrelations (represented by the main matrix diagonal) were excluded from the analysis and the network measures were calculated on the lower triangular part of the matrix.…”

Novel genetic variants associated with brain functional networks in 18,445 adults from the UK Biobank

“…Here, we address the question of how genetics influences the integrity of functional connectivity as measured by graph theory measures in resting-state fMRI (rs-fMRI) data. We assessed graph theory measures, including global efficiency, characteristic path length, Louvain modularity, transitivity, local efficiency and strength of default, dorsal attention, frontoparietal, limbic, salience, somatomotor, and visual networks, which are typically examined and found to change in aging 6 as well as multiple neuropathological processes 11-13 . A UK Biobank sample comprising 18,445 participants of British ancestry was used in this study.…”