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TitoloA Mathematical Proposal to Evaluate Functional Connectivity Strongness in Complex Brain Networks
Autore/iFinotelli, P.; Dulio, P.
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AbstractThe brain is a really complex organization of connectivity whose principal elements are neurons, synapses and brain regions. To date this connectivity is not fully understood. Graph Theory represents a powerful tool in the study of brain networks. Though the complex organization of connectivity in human and animal brain has found a great impulse by the use of Graph Theory, some points result to be not very clear and needed to be clarified, the weakness lies in the mismatching between the mathematical and neuroscientific approach. In this paper we focus, in particular, on two points: the concept of distance and a mathematical approach in treating functional and structural connectivity by means of the introduction of the parameter time. One of the most relevant remark we point out concerns the concept of graph in the inter-field crossing Mathematics and Neuroscience. In detail, when talking about Graph Theory in brain connectivity, it should be clear that we are considering two basic categories: one static, relative to the anatomical connectivity, and the other, dynamical, concerning the functional connectivity. We believe that in order to describe them it is fundamental to introduce the concept of time, which, at present, seems to be a lack in the theory of this area of research. For example, the static category regards the anatomical neural network in particular range of the life of human beings (and animals), i.e. the synaptic connections or directed anatomical pathways derived from neural tract tracing, can be retained static only in absence of injuries or cerebral illnesses, or far from the childhood and one’s old age. The dynamical approach is involved in the other cases, in particular it is linked to the functional connectivity, i.e. the temporal correlations between remote neurophysiological events as reaction to well specific external stimuli (e.g. social paradigms, social cognitive functions or other specific tasks), it interests cerebral areas not necessarily close each other (in the sense of Euclidean distance). Aside we emphasize that the functional connectivity is very distinctive from effective connectivity, i.e. the influence one neural system exerts over another [26]. The point is that these categories demand different kinds of graphs,except the case of resting state. The integration between these two different approaches is a topic of present interest. In this paper we formalize in a mathematical way this concept and we speculate the existence of a function which can give the weight of the edges composing the graph representing the functional connectivity. This function W(i, j, t) depends on the position of nodes i, j and on the time t at which a specific task is submitted to an health volunteer (and in prospective to a subject affected by a neurological disease). Interestingly this function, in particular cases, comes down to the probability of edge formation. Basically these particular cases are the resting state and when a particular task do not affect the cerebral region to which the nodes belong to. This second case is rare since when performing a task the region of interest, ROI, are well known.

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