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Codice  QDD 190 
Titolo  A Mathematical Model for Evaluating the Functional Connectivity Strongness in Healthy People 
Data  20150113 
Autore/i  Finotelli, P.;Dulio, P. 
Link  Download full text 
Abstract  The human brain is a really complex organization of connectivity whose principal elements are neurons,
synapses and brain regions. Up to now this connectivity is not fully understood, and recent impulse
in investigating its structure has been given by Graph Theory. However, some points remain unclear,
mainly due to possible mismatching between the Mathematical and the Neuroscientic approach. It
is known that neural connectivity is classied into three categories: structural (or anatomical) connectivity,
functional connectivity and eective connectivity. The point is that these categories demand
dierent kinds of graphs, except in the case of the resting state, and sometimes topological and metrical
parameters are involved simultaneously, without a specic distinction of their roles.
In this paper we propose a mathematical model for treating the functional connectivity, based
on directed graphs with weighted edges. The function W(i; j; t), representing the weight of the edge
connecting nodes i; j at time t, is obtained by splitting the model in two parts, where dierent parameters
have been introduced step by step and rigorously motivated. In particular, there is a double role
played by the notion of distance, which, according to the dierent parts of the model, assumes a
discrete or an Euclidean meaning. Analogously, the time t appears both from a local and from a global
perspective. The local aspect relates to a specic task submitted to an health volunteer (in view of
possible future applications also to subjects aected by neurological diseases), while the global one
concerns the dierent periods in the human life that characterize the main changes in the neural brain
network. In the particular case of the resting state, we have shown that W reduces to the usually
employed probabilistic growth laws for the edge formation. We tested the correctness of our model by
means of synthetic data, where the selection of all involved parameters has been motivated according
to what is known from the available literature. It turns out that simulated outputs t well with the
expected results, which encourages further analysis on real data, and possible future applications to
neurological pathologies. 
