Human Brain Anatomical Connections to Graph Theory
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The brain is a complex organ of soft nervous tissue in the skull of vertebrates. It is one of the largest and most complex organs in the body. Information is continuously being processed and transferred between interdependent regions within the brain. The anatomical connection probabilities (ACP) between cortical and subcortical brain gray matter areas are estimated from diffusion-weighted magnetic resonance imaging (DWMRI) techniques to assess the probability of any given two areas being connected. Those areas are connected by at least a single nerve fiber, which conducts nerve impulses. Current resting-state functional magnetic resonance imaging (fMRI) studies have correlated the inter-regional functional connectivity exhibiting a small-world topology, signifying an arrangement in the brain which is a profound construction of clustered subnetworks. I have collected published data from 15 different cases studies that have examined the sub-network connections to small-world topology. One particular research study examines the clustered sub-networks of the brain by using resting-state data of 28 healthy subjects conducted at the Institute of Clinical and Experimental Neurosciences in Amsterdam. The individual connectivity graphs were developed out of all cortical and sub-cortical voxels with the connections showing inter-voxel functional connectivity. Voxels are a unit of graphic data that characterizes a point in three-dimensional space that relates to a pixel in an image. The components of the nervous system and their interactions are characterized as networks and are mainly represented as graphs where thousands of nodes are interconnected. Graph theory is a mathematical framework that helps put the interconnection of the human brain anatomical network into perspective. This theory provides a viewpoint that helps provide new insights in the discovery of small-world topology, scale-free networks and the data on anatomical and functional properties of magnetic resonance imaging (MRI) studies using artificial and actual human data. In my recent studies, I investigated diffusion weighted MRI scans of patients that have suffered from either a severe stroke or brain trauma. Using graph theoretical analysis of functional brain networks, I was able to assess the functional connectivity of the brain of the patients, one of the patients being my father. The purpose of this thesis is to examine the connectivity distribution of the number of inter-voxel connections and how a combined small-world and scale-free organization can help identify the functionally connected regions of the human brain.