Integrated Information Theory (IIT) has become nowadays the most sensible general theory of consciousness. In addition to very important statements, it opens the door for an abstract (mathematical) formulation of the theory. Given a mechanism in a particular state, IIT identifies a conscious experience with a conceptual structure, an informational object which exists, is composed of identified parts, is informative, integrated and maximally irreducible. This paper introduces a space-time continuous version of the concept of integrated information. To this aim, a graph and a dynamical systems treatment is used to define, for a given mechanism in a state for which a dynamics is settled, an Informational Structure, which is associated to the global attractor at each time of the system. By definition, the informational structure determines all the past and future behavior of the system, possesses an informational nature and, moreover, enriches all the points of the phase space with cause-effect power by means of its associated Informational Field. A detailed description of its inner structure by invariants and connections between them allows to associate a transition probability matrix to each informational structure and to develop a measure for the level of integrated information of the system.
Electroencephalography (EEG) monitors -by either intrusive or noninvasive electrodes-time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during both rest periods and specific events in which the subject is under stimulus. This is a useful tool to explore brain behavior, as it complements imaging techniques that have a poorer temporal resolution. We here approach the understanding of EEG data from first principles by numerical simulating and studying a networked model of excitatory and inhibitory neurons which generates a variety of comparable waves. In fact, we thus numerically reproduce oscillatory behavior similar to α, β, γ and other rhythms as observed by EEG recordings, and identify the details of the respectively involved complex phenomena, including a precise relationship between an input and the collective response to it. It ensues the potentiality of our model to better understand actual brain oscillatory activity in normal and pathological situations, and we also describe kind of stochastic resonance phenomena which could be useful to locate main qualitative changes of brain activity in (e.g.) humans.
The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between interconnected brain regions. Until now, most efforts of capturing the causal mechanistic generating principles have supposed underlying stationarity, being unable to describe the non-stationarity of brain dynamics, i.e. time-dependent changes. Here, we present a novel framework able to characterise brain states with high specificity, precisely by modelling the time-dependent dynamics. Through describing a topological structure associated to the brain state at each moment in time (its attractor or ‘information structure’), we are able to classify different brain states by using the statistics across time of these structures hitherto hidden in the neuroimaging dynamics. Proving the strong potential of this framework, we were able to classify resting-state BOLD fMRI signals from two classes of post-comatose patients (minimally conscious state and unresponsive wakefulness syndrome) compared with healthy controls with very high precision.
The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between interconnected brain regions. Until now, all efforts of capturing the causal mechanistic generating principles have proven elusive, since they have been unable to describe the non-stationarity of brain dynamics, i.e. time-dependent changes. Here, we present a novel framework able to characterise brain states with high specificity, precisely by modelling the time-dependent dynamics. Through describing the topological structure of the brain at each moment in time (its ‘information structure’), we are able to classify different brain states by using the statistics across time of these exact ‘information structures’ hitherto hidden in the neuroimaging dynamics. Proving the strong potential of this framework, we were able to classify the neuroimaging data from two classes of comatose patients (minimally conscious state and unresponsive wakefulness syndrome) compared with healthy controls with very high precision.
The dynamical activity of the human brain describes an extremely complex energy landscape changing over time and its characterisation is central unsolved problem in neuroscience. We propose a novel mathematical formalism for characterizing how the landscape of attractors sustained by a dynamical system evolves in time. This mathematical formalism is used to distinguish quantitatively and rigorously between the different human brain states of wakefulness and deep sleep. In particular, by using a whole-brain dynamical ansatz integrating the underlying anatomical structure with the local node dynamics based on a Lotka-Volterra description, we compute analytically the global attractors of this cooperative system and their associated directed graphs, here called the informational structures. The informational structure of the global attractor of a dynamical system describes precisely the past and future behaviour in terms of a directed graph composed of invariant sets (nodes) and their corresponding connections (links). We characterize a brain state by the time variability of these informational structures. This theoretical framework is potentially highly relevant for developing reliable biomarkers of patients with e.g. neuropsychiatric disorders or different levels of coma. of the phase space described by a set of selected invariant global solutions of the associated dynamical system, such as stationary points (equilibria), connecting orbits among them, periodic solutions and limit cycles. The informational structure of the GA is defined as a directed graph composed of nodes associated with those invariants and links establishing their connections (see Methods and Supplementary Information for a formal rigorous definition). Informational Structure has been used to show the dependence between the topology, the value of the parameters and the state with respect to its level of integration 14 , as such pointing for the small world configuration of the brain 16 (although see recent controversies 17 ).Previous research has applied Informational Structure to population dynamics in complex networks 18,19 . Equally used for modelling mutualistic systems in Theoretical Ecology and Economy 20, 21 , Informational Structure can relate the topology of complex networks and their dynamics. In mutualistic systems when achieving robustness and life abundance -the so-called architecture of biodiversity 22, 23 -the dynamics is determined not only by the topology 24 but also by modularity 25 and the strength of the parameters 26 .These kinds of relationships are also at the heart of many important open questions in neuroscience 27,28 . Informational Structures and their continuous time-dependence on the strength of connections can allow to understand the dynamics of the system as a coherent process, whose information is structured, and potentially providing new insights into sudden bifurcations 29 .Here, we were interested in characterising human sleep, which is traditionally subdivided into different stages that alternate in the course...
Contemplative neuroscience has increasingly explored meditation using neuroimaging. However, the brain mechanisms underlying meditation remain elusive. Here, we implemented a causal mechanistic framework to explore the spatiotemporal dynamics of expert meditators during meditation and rest. We first applied a model-free approach by defining a probabilistic metastable substate (PMS) space for each state, consisting of different probabilities of occurrence from a repertoire of dynamic patterns. Different brain signatures were mainly found in the triple-network model (i.e., the executive control, salience, and default-mode networks). Moreover, we implemented a model-based approach by adjusting the PMS of the resting state to a whole-brain model, which enabled us to explorein silicoperturbations to transition to the meditation state. Consequently, we assessed the sensitivity of different brain areas regarding their perturbability and their mechanistic local-global effects. Using a synchronous protocol, we successfully transitioned from the resting state to the meditative state by shifting areas mainly from the somatomotor and dorsal attention networks. Overall, our work reveals distinct whole-brain dynamics in meditation compared to rest, and how the meditation state can be induced with localized artificial perturbations. It motivates future work regarding meditation as a practice in health and as a potential therapy for brain disorders.
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