Calculating so the functional as the structural relations between different cerebral areas and align those links to the personal differences in cognitive, behavioral and affective domains seems to be a crucial step for the understanding of human connectome . As the resolution of the accurate brain imaging increases, the number of these links also increases, generating more complex networks, elevating the connectivity research to a big data problem. This alongside with the restricted computational resources indicates the urgent need for developing new models and new approaches in order to solve and visualize this big-data problem. Graph theory is widely used for mathematical modeling of complex networks. According to graph theory, a graph is defined as a pair between a set of vertices and a set of edges. Graphs can be described so by the existence of directionality in their edges (directed/undirected), as by their weight (weighted/unweighted-binary). As Although undirected binary graphs can be used to reduce the complexity of the networks, much of the information is lost due to arbitrary thresholding [2,3] leading to the disconnection syndrome , with negative implications so for the computation of several graph theoretical parameters as for the cohesion of the network , while there is also an introduction of several biases . One way to reduce the complexity of the network overcoming the aforementioned biases  is by modeling our weighted graphs using Minimum Spanning Tree (MST) methodology. A MST is a loopless subgraph of the original graph connecting all nodes , and it can be used to reduce the dimensionality of the graph, because by it’s definition it has n-1 edges, while the initial graph has n*(n-1)/2 edges. The goal of the MST is to minimize the cost (increase the weights) of the graph and preserve only the most important edges , and it is assumed to be the backbone of the initial graph. Another approach to reduce the complexity of the brain connectome, is by employing linear or non-linear dimension reduction techniques. One non-linear technique, called diffusion mapping , which has recently draw the attention of the neuroscientific community , is based on the principles of spectral graph theory. A typical example of the aligned mean diffusion map extracted by the resting state fMRI correlation networks (468 subjects) is depicted in Figure 1. Each node is colored according to it’s connectivity profile, meaning that two nodes with the same color (red, green, blue, etc.) are connected similarly to the rest of the brain, while they are also strongly interconnected. On the other hand, as far the difference of two nodes in diffusion spectrum increases, the dissimilarity of these nodes also increases, and moreover the transition from one node to another becomes more difficult. Another important application of diffusion mapping is the visualization of functional connectivity in a much easier and more interpretable way. Indeed, a great challenge for neuroscientists today is to visualize connectivity networks incorporating so the functional as the anatomical information, and produce easily interpretable images. Currently the most common approach is the graph-like visualization overlaid in head/cortex. In this context, the nodes bear all the anatomical information by denoting a point in an anatomical space (e.g. MNI, IS 10/20, etc.), so the graph is aligned to head’s/cortex’s anatomy. Although this approach seems as a straightforward solution for the visualization of functional networks, it only works with a low number of edges. When the number of edges increases dramatically, this methodology will lead to the obfuscation of the underlying anatomical space . Several other methods have been proposed so far for the illustration of human connectome , however still a lot of work should be done in order to visualize dense connectivity matrices. Concluding, we should again remark that as the neuroimaging resolution increases, and the human connectome becomes even more computationally demanding, either in terms of analysis or for visualization purposes, we need to pay more attention in dimensionality reduction techniques, so as to ensure that we maintain the greatest possible portion of the information hidden in our connectome.
|Publication status||Published - 9 Oct 2016|