Structure-Function Relationship of the Brain: A comparison between the 2D Classical Ising model and the Generalized Ising model

There is evidence that the functional patterns of the brain observed at rest using fMRI are sustained by a structural architecture of axonal fiber bundles. As neuroimaging techniques advance with time, the relationship between structure and function has become the object of many studies in neuroscience. As recently suggested, the well-defined connectivity structure found in the brain can be used to understand the self organization of the brain at rest, as well as to infer the functional connectivity patterns of the brain using different models. These models include the Kuramoto model, which studies synchronization, and the two-dimensional classical Ising model, which studies the global dynamics of the brain at the critical temperature. These models have been successful in capturing the underlying properties of the brain. To extend this understanding, our objective is to develop the generalized Ising model, following the lesson from the two-dimensional Ising model, as the generalized Ising model could be simulated using the anatomical structure of the brain. This model can then be used to study functional information integration and segregation in the brain at rest. Thus, the primary research question would be: can the generalized Ising model explain the functional behaviour of the resting brain at the critical temperature? Preliminary analyses were carried out to determine the critical temperature of the models and to compare the correlation distributions. Further analyses were carried out using graph theory considering the brain as a network. By observing the results obtained from our simulations, it can be inferred that there is a temperature that is different from the critical temperature of the model at which the generalized Ising model shows a match with the empirical functional connectivity. At that temperature, the generalized Ising model could be used to study the global dynamics, as well as the local dynamics of the brain.