Apolipoprotein E4 effects on topological brain network organization in mild cognitive impairment

The Apolipoprotein E isoform E4 (ApoE4) is consistently associated with an elevated risk of developing late-onset Alzheimer’s Disease (AD); however, less is known about the potential genetic modulation of the brain networks organization during prodromal stages like Mild Cognitive Impairment (MCI). To investigate this issue during this critical stage, we used a dataset with a cross-sectional sample of 253 MCI patients divided into ApoE4-positive (‛Carriers’) and ApoE4-negative (‘non-Carriers’). We estimated the cortical thickness (CT) from high-resolution T1-weighted structural magnetic images to calculate the correlation among anatomical regions across subjects and build the CT covariance networks (CT-Nets). The topological properties of CT-Nets were described through the graph theory approach. Specifically, our results showed a significant decrease in characteristic path length, clustering-index, local efficiency, global connectivity, modularity, and increased global efficiency for Carriers compared to non-Carriers. Overall, we found that ApoE4 in MCI shaped the topological organization of CT-Nets. Our results suggest that in the MCI stage, the ApoE4 disrupting the CT correlation between regions may be due to adaptive mechanisms to sustain the information transmission across distant brain regions to maintain the cognitive and behavioral abilities before the occurrence of the most severe symptoms.

The regions are listed following the anatomical brain atlas described in Destrieux et al. (2010). The subcortical regions were not included. The short names, as well as the full structure names, are specified. The lobe to which the structure belongs is also included. L: Limbic; I: Insula; P: Parietal; O: Occipital; F: Frontal; T: Temporal. G: gyri; S: sulcus.

Measures of functional brain segregation
Functional segregation: the ability for specialized processing to occur within densely interconnected groups of brain regions

Clustering index
. Nodes are considered neighbors when a connection between them exists, which is not reduced to a physical neighborhood concept.
In anatomical networks, the clusters suggest the potential for functional segregation, while the presence of clusters in functional networks suggests an organization of statistical dependencies indicative of segregated neural processing.

Modularity
Many complex networks, like the brain, consisting of several modules. Modules are derived from a decomposition of the network into subcomponents that are internally strongly coupled but externally only weakly correlated. Each module contains several densely interconnected nodes (brain regions).
Dense connectivity within modules allows brain regions within each module to interact with one another easily. In contrast, sparser connectivity between modules allows each set of brain regions to be relatively independent of one another (specialized functions). Diminished connectivity between communities can result in loss of essential interactions or even disconnection of an entire community. On the other hand, excessive connectivity between modules may result in loss of compartmentalization or specialization of this brain region group. It is the average efficiency of the local This measure reveals how much the Local Efficiency subgraphs brain as a system is fault-tolerant, showing how efficient the communication is among the first neighbors of a node (brain region) when it is removed.

Measures of functional brain integration
Functional integration: is the ability to combine specialized information from distributed brain regions rapidly

Characteristic path length
The path length is the minimum number of edges that must be traversed to go from one node (brain region) to another. It is a measure of the typical separation between two brain regions. The average shortest path length between all pairs of nodes in the the network is known as the characteristic path length of the network. Connection lengths are typically dimensionless and do not represent spatial or metric distance.
Lengths of paths consequently estimate the potential for functional integration between brain regions. Shorter paths are implying a more substantial potential for integration between brain regions. Paths in functional/morphological networks represent statistical associations and may not correspond to information flow on anatomical connections. In this case, paths are less straightforward to interpret in terms of brain functions.

Global efficiency
It is the average inverse of the shortest path length.
The global efficiency es primarily affected by the shorth path length, represents a superior measure of integration.

Global connectivity
It summarizes the interregional correlations coefficients between all possible pairs of nodes (brain regions). Describes the degree to which nodes are connected in a network. It can be quantified based on network metrics such as the relative density, the shortest path, or the diameter of the network.
Previous studies have found strong correlations between regions with no direct structural (white matter tracts) connection. The total interregional morphometric correlations could capture all indirect structural correlations between two brain regions facilitated by a third party, from which diverse factors such as pathologic changes to the connectivity patterns could be detected.

Normalized betweenness centrality
The centrality of a node (brain region) measures how many of the shortest paths between all other brain regions pairs in the network pass through it. Bridging nodes that connect disparate parts of the network have a high betweenness centrality.
A node (brain region) with high centrality is thus crucial to efficient communication. It is based on the idea that central nodes participate in many short paths within a network, and consequently, act as essential controls of information flow. Their loss is particularly disruptive to the brain network. Several regions in the frontal and parietal cortex have high centrality in the human brain, particularly the posterior cingulate and precuneus. These are areas of the brain defined as transmodal or heteromodal. They are involved in integrating processing across several cognitive modalities. Some of these regions overlap with the DMN, while others coincide with the frontoparietal system.
Hubs are nodes with a high degree or Hubs often interact with many other

Sample Biomarkers Characteristics
Cerebrospinal fluid (CSF) samples at baseline were collected from 192 MCI subjects as part of the ADNI-1 protocol. The overlap between this sample and the one selected for the present study corresponds to 132 subjects (67 MCI-Carriers and 65 MCI non-Carriers areas, facilitate functional integration, and play a vital role in the brain network resilience to insult. Hubs are a cost-efficient solution to increase network efficiency to support cognitive processes without requiring many metabolically expensive connections.
Hubs are suggested to be essential for cognition because they are located along the shortest paths in the network, and therefore are likely to play a critical role in distributed patterns of communication.
This location is evident both by their high degree and by their tendency to connect, forming a core or "rich-club" that boosts inter-hub communication's robustness and promotes efficient communication across the brain. Damage to brain hubs is expected to have critical consequences for cognitive function in terms of the severity and pervasiveness of cognitive deficits.

Targeted Attack
The importance of an individual node to network efficiency can be assessed by deleting it and estimating the the efficiency of the 'lesioned' network. It is an indirect measure of resilience that reflects network vulnerability to insult. Complex networks like the brain are highly vulnerable to disruptions of the central node (hubs).
Robustness refers either to the network's structural integrity following the deletion of nodes or edges or to the effects of perturbations on local or global network states. Direct measures of network resilience generally test the network before and after a presumed insult by computationally simulated targeted removal of nodes and links. The effects of such lesions on the brain network may then be quantified by characterizing changes in the resulting brain connectivity.

Graph Theory Metrics
The following group theoretical metrics were computed in the present study: Clustering index ( C ). The clustering index of a node 'i' is defined as the number of existing connections between the node's neighbors divided by all possible connections. It is a measure of the inherent tendency to cluster nodes into strictly connected neighborhoods. Nodes are considered neighbors when a connection between them exists, which is not reduced to a physical neighborhood concept. The clustering index for the whole graph G is defined as the average clustering around each node: Represent the number of nodes. Clearly, 0 < C < 1; and C= 1 if and only if the network is fully connected, that is, each node is connected to all other nodes.
Characteristic path length ( L ). The characteristic path length L of the graph G is the smallest number of connections required to connect one node to another, averaged over all pairs of nodes.
It is a measure of the typical separation between two nodes (structures) i and j   , i j N  , and it is defined as the mean of geodesic lengths ij d over all pairs of nodes.
In the unweighted network context, the geodesic length dij is defined as the number of edges along the shortest path connecting nodes i and j.
This measure reflects how efficiently the information can be exchanged over the network, considering a parallel system in which each node sends information concurrently through the network. On the other hand, the loc E of G is defined as the average efficiency of the local subgraphs: Where i G is the subgraph of the neighbors of 'i'. This measure reveals how much the system is fault-tolerant, showing how efficient the communication is among the first neighbors of i when it is removed. As above, nodes are considered neighbors when a connection between them exists, which is not reduced to a physical neighborhood concept.
Global and Homologous regional connectivity. We assessed the global connectivity and homologous region connectivity. First, the absolute correlation coefficient values were converted to z using Fisher's r-to-z transformation, followed by taking the mean and transforming back to correlations through the inverse Fisher's z-to-r transformation. All anatomical regions were used to estimate the global connectivity, whereas only the correlation values between homologous regions were used in the mean homologous region connectivity.

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Nodal centrality: normalized betweenness centrality (NBC). The 'betweenness centrality' Bi of a node i is defined as the number of shortest paths between any two nodes that run through node i.
We measured the normalized betweenness centrality as bi= Bi /<B>, where <B> was the average betweenness of the network. bi is a global centrality measure that captures a node's influence over information flow between other nodes in the network. In our case, betweenness centrality bi could be used to reflect the effects of ApoE4 on the global roles of regions in the cortical thickness covariance networks. Hubs were selected as those with bi superior to 1.5, similar to previous investigations.

Modularity.
A complex network module is a subset of nodes that are densely connected within the modules but sparsely connected between the modules. Here we have adopted Newman's metric as a modularity measure to compare our results with previous studies that used this method in other neuroimaging modalities.