Structure-function relation in a stochastic whole-brain model at criticality

Understanding the relation between brain architecture and function is one of the central issues in neuroscience nowadays. In the last few years, important efforts have been devoted to map the large-scale structure of the human cortex, the so-called "connectome". An example is the neuroanatomical connectivity matrix of the entire human brain obtained through MR diffusion tractography. Recent studies proposed a stochastic model built on top of this connectivity matrix that displays a phase-transition and is able to reproduce several aspects of brain functioning when tuned to its critical point. This master thesis is aimed to review recent results on this subject and to get a deeper insight into the model by studying the distribution of the avalanches, the dynamical range and to investigate how the use of simulated connectivity matrices affects the dynamics. Furthermore, a theoretical description of the dynamics is proposed by introducing a master equation in order to understand the nature of the phase transition and the role of stochasticity.