instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Brain and Mind: Dynamical systems on Networks and Informational Structures
Seminario PHD

In the search for neural signatures of consciousness, several approaches and measures of conscious experiences have been proposed in the literature. Nevertheless, a relationship between these measures and actual neurophysiological activity in the brain remains elusive. With the aim of contributing to the characterization of consciousness (and eventually to the building of a unified theory of consciousness), we propose a whole-brain computational model which can be directly related to the well-known Integrated Information Theory. Assuming a Lotka-Volterra dynamical system, where the growth rate parameter is changing with time, we can compute a directed graph associated with the global attractor of the system, called the Informational Structure, at every time instant. Thus, we can define Dynamical Informational Structures (DISs), a continuous flow of informational structures associated with the dynamics of the system. The informational structure associated with a dynamical system has been recently proposed as a tool to asses the level of integrated information, as it defines the past and future behavior of the system and is related to the topology of the network.

Here, we assume a DTI-constrained whole-brain dynamical model based on the cooperative Lotka-Volterra system, where the activity of each brain area is modeled with one equation and the interaction between areas is regulated by the underlying brain anatomy, described by the structural connectivity matrix obtained from empirical data. We define then the Lotka-Volterra Transform, a mathematical operator which allows us to assess the growth rate function that tracks the time-evolution of BOLD fMRI signals from subjects in two distinct conditions: resting-state and deep sleep (N3). The Lotka-Volterra Transform is defined to exactly reproduce the empirical time-series, and the time-varying informational structure defines an underlying energy landscape that shapes neural activity of the brain, allowing us to distinguish between different brain states.