Complex Network Analysis of MCI and AD Patients

Alireza Fathian |

November, 2020

1. Introduction

In this study, we have investigated the changes in functional brain connectivity of Alzheimer’s Disease (AD), Early Mild Cognitive Impairment (EMCI), and Late Mild Cognitive Impairment (LMCI).

By creating networks that model the functional brain connectivity of different subjects, we have shown that there are topological differences between subjects of each group.

2. Methods

2.1. Subjects

The rs-fMRI and T1w images of 92 subjects from ADNI database were analyzed in this study.

	CN	EMCI	LMCI	AD	ALL
Sample Size	23 08 M 15 F	23 12 M 11 F	23 10 M 13 F	23 11 M 12 F	92 41 M 51 F
Age (Mean±SD)	75.82±9.44	75.29±6.36	72.26±7.05	77.75±3.75	74.78±7.11

2.2 Preprocessing

Preprocessing data was done using fMRIPrep. fMRIPrep is a fMRI data preprocessing pipeline that performs basic processing steps on raw images. Including:

2.3. Denoising

A selection of nuisance variables generated by fMRIPrep were regressed out of the data. These variables are:

6 motion estimates
Mean signal in WM, Mean signal in CSF
Global signal regression

In addition to that, the derivatives, quadratic terms, and squares of derivatives of these variables were also regressed out.

2.4. Parcellation

In this step, the brain were parcellated into 360 regions by the HCP-MMP parcellation. The time series corresponding to each region were computed as the mean of time series of voxels within that region.

2.4. Parcellation

Visual	Somatomotor	Limbic	Default
DorsalAttention	VentralAttention	Frontoparietal

2.5. Correlation Matrix

The correlation among time series corresponding to different brain regions were computed with two different methods, Pearson's correlation coefficient and GLASSO. These correlations then were used to create undirected networks of functional connectivity.

The element within represents the correlation between nodes $i$ and $j$.

2.6. Adjacency Matrix

Adjacency matrices were created by thresholding the correlation matrices. we have choosed the thresholding values that maximizes the global cost efficiency (GCE). \begin{aligned} Threshold & = \underset{-1 \leq t\leq 1}{\mathrm{argmax}}(GCE(t)) = \underset{-1 \leq t\leq 1}{\mathrm{argmax}}(E(t) - PSW(t)) \end{aligned} \begin{aligned} E(t) & = \frac{1}{n}\sum_{i\in N}^{}\frac{\sum_{j\in N,j\neq i}^{ }(\frac{1}{d_{ij}})}{n-1}, PSW(t) = \frac{\sum_{i\in W,i\geq t}^{}i}{\sum_{j\in W}^{}j} \end{aligned}

where $E$ is the global efficiency, $PSW$ is the proportion of the strong weights, $N$ is the set of all nodes, $n$ is the number of nodes, $d_{ij}$ is the shortest path length between nodes $i$ and $j$, and $W$ is the set of all weights

2.7. Network Measures

For each network 10 local and 14 global network measures were computed:

Local Measures:

Density, Average Shortest Path Length, Transitivity, Average Clustering, Local Efficiency, Global Efficiency, Pearson Correlation, Degree Assortativity Coefficient, Diameter, Radius.

Global Measures:

Degree, Eccentricity, Betweenness, Communicability Betweenness, Eigenvector, Katz, Closeness, Current Flow Closeness, Load, Clustering Coefficient, Pagerank, Subgraph, Harmonic, Strength.

2.7. Network Measures

Clustering

Clustering measures the tendency of neighbors of a node to be also neighbors.

Betweenness

2.8. Mean Network

For each subject in a group the mean network were computed as the voxel-wise mean of all subjects within that group.

2.8. Mean Network

CN EMCI LMCI AD

2.8. Mean Network

CN EMCI LMCI AD

2.8. Mean Network

CN EMCI LMCI AD

2.8. Mean Network

CN EMCI LMCI AD

3. Results

3.1 Pearson Correlation Coefficient Among Mean Networks

3.2 Analyzing Measures: Global Measures of Mean Networks

3.2 Analyzing Measures: local Measures of Mean Networks

3.2 Analyzing Measures: Histogram of Strength

3.4 Symmetric Links

The mean of the correlation coefficients of pairs of nodes that are symmetrical to each other.

Group	Mean	SD
CN	0.708	0.060
EMCI	0.696	0.073
LMCI	0.613	0.148
AD	0.533	0.154

3.5 Long and Short Links

We have classified links as short and long links based on the spatial location of its nodes on the brain.

	Short Links		Long Links
Group	Mean	SD	Mean	SD
CN	1.128	1.896	0.441	1.309
EMCI	1.114	1.950	0.454	1.360
LMCI	1.114	1.915	0.455	1.340
AD	1.065	1.910	0.501	1.403

3.6 Assortativity

The tendency of nodes to connect to other nodes with similar degree.

Measuring Assortativity: The average nearest neighbors degree of a vertex $i_{k}$: \begin{aligned} k_{nn,i} & = \frac{1}{k_{i}}\sum_{j\in V(i)}^{}k_{j} \end{aligned} The average degree of the nearest neighbors, $k_{nn}(k)$, for vertices of degree $k$: \begin{aligned} k_{nn}(k) & = \frac{1}{N_{k}}\sum_{i/k_{i}=k}^{}k_{nn,i} \end{aligned} Where $k_{i}$ is the degree of node $i$, $V(i)$ is the set of neighbours of node $i$, and $N_{k}$ is the number of nodes with degree $k$.

3.6 Assortativity

Group	Pearson assortativity coefficient
CN	0.708
EMCI	0.696
LMCI	0.613
AD	0.533

3.7 CL(k)-Knn Plot

Group	Slope of the fitted line
CN	0.00723
EMCI	0.00726
LMCI	0.00729
AD	-0.00080

3.8 Rich-Club

Rich-club measures the tendency of high degree nodes, to be connected to each other, forming subgraphs more easily than low degree nodes. \begin{aligned} \phi(k) = \frac{2 E_{>k}}{N_{>k}(N_{>k}-1)}, \rho_{ran}(k)=\frac{\phi(k)}{\phi_{ran}(k)}, \scriptscriptstyle where \begin{gather} E_{>k}\, is\, the\, number\, of\, edges\, among\, the\, N>k\, nodes \\ N_{>k}\, is\, the\, number\, of\, vertices\, with\, degree\, larger\, than\, k \end{gather} \end{aligned}

3.9 Small-world Property

A network has a small-world property if it is possible to go from one vertex to any other in the network passing through a very small number of intermediate vertices.

$M(l)$ the average number of nodes within a distance less than or equal to from any given vertex.
In small-world networks this quantity follows an exponential or faster increase.

3.10 Classifying Nodes

We have classified nodes into 7 modules based on the 7-ROI parcellation by Yeo et al., (2011).

	weights of inter-ROI links		weights of intera-ROI links
Group	Mean	SD	Mean	SD
CN	0.197	0.171	0.003	0.120
EMCI	0.182	0.155	0.007	0.107
LMCI	0.173	0.156	0.012	0.114
AD	0.153	0.166	0.014	0.128

3.10 Classifying Nodes

CN EMCI LMCI AD

3.10 Classifying Nodes

CN EMCI LMCI AD

3.10 Classifying Nodes

CN EMCI LMCI AD

3.10 Classifying Nodes

CN EMCI LMCI AD

3.11 Hubs

Given a scoring system for nodes, network hubs are defined as nodes with score larger than the mean + the standard deviation of the scores of each node in the network.

Here we applied 3 different scores: Strength, Betweenness, and Clustering.

The network hubs are then the nodes which are hub based on one of these scores.