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Introduction

An important but outstanding issue in contemporary cognitive neuroscience is understanding the organizational properties of neural activity. For instance, is there a fundamental structure to the spatial–temporal patterns neural brain activity across different conditions? One common approach used to address this question is to examine the brain at “rest”. Measures such as functional connectivity, independent component analysis and graph theoretic metrics, have been applied to data recorded using different imaging techniques (e.g., functional magnetic resonance imaging (fMRI) and electroencephalography (EEG)), to cluster brain areas that exhibit similar activity patterns. Numerous studies have shown that brain activity during “rest” can be grouped into distinct networks across; such as sensory (visual and auditory), default mode, executive, salience, and attentional (ventral and dorsal) networks that have been reliably reproduced across thousands of participants, and are predictive of phenotypic measures like cognition and clinical diagnoses. These results suggest these networks may be an intrinsic aspect of neural activity.

Indeed, the same set of structured patterns of neural activity have been found during "active" states, such as, while completing different tasks. For instance, there is a high degree of correspondence between networks extracted during rest and those extracted during tasks measuring sensorimotor and higher-level cognitive abilities (i.e., working memory).Even completing a task as complicated as following the plot of a movie elicits the same network architecture as observed in the resting brain. The correspondence between task and rest-based networks is so strong that task-based fMRI network activity can be predicted from the resting state, and rest-task network pairs can be identified at the individual level16. Together, these results suggest that rest and task-based patterns of brain activity likely share a similar underlying neural architecture, despite distinct experiences and cognitive processes.

There are, however, important differences between the patterns of brain activity elicited during rest and task-based paradigms, and the set of experiences and cognitive processes associated with each. For instance, the presence or absence of a task is accompanied by increases in variability across different scales including neuronal firing rates changes in field potentials, variation in fMRI blood oxygen level dependent (BOLD signal) and in EEG frequency bands Furthermore, through transcranial direct current stimulation (tDCS) it has been shown that frontal-lobe stimulation increases one’s proclivity to mind wander . Importantly, these differences are associated with changes in properties of neural activity but not in changes in the underlying neural architecture.

Is there a way to identify the shared neural architecture underlying the cognitive processes associated with rest and active states while also quantifying how these processes diverge from that shared architecture of neural activity? In this paper, we applied mathematical methods analogous to those of quantum mechanics, and the concept of phase space to EEG recorded during rest and movie-watching to extract spatial and transitional properties of dynamic neural activity. Quantum mechanics was developed to describe the dynamics of the subatomic world in terms of probability amplitudes and densities of states. Quantum systems (in the Schrodinger formulation of quantum mechanics) are described by wavefunctions which square to a probability distribution leading to the loss of local determinism and the Heisenberg uncertainty principle (for an overview/intro to the subject see. This uncertainty principle places a fundamental limit on the location and the momentum of a point particle . In essence, if the position of a particle is known there is an underlying uncertainty in its momentum (one cannot precisely say how fast it is going) and vice versa. In addition to the adaptation of the wavefunction approach to quantum mechanics in this paper, we also employed a phase space model. Phase space is a widely used tool in the study of dynamical systems, where the positional variables are paired with their conjugate momenta which establishes a multidimensional space that describes all possible configurations of the given system. This space spans the entire range of states that a system can exist in, each point (in this hyper-space) represents a single state of the system. Phase space and its assorted formalisms are a classical concept, and we simply use it as another tool for analysing the EEG data. Herein, the mathematical methods of quantum mechanics are applied to EEG data to extract a proxy to phase space. This quasi-quantum approach naturally generates the concepts of ‘average’ position, ‘average’ momentum and culminates in an analogous Heisenberg uncertainty principle.

In this paper, we posit that using mathematical tools drawn from quantum mechanics, an underlying pattern representative of task and resting brain activity can be realised, in which differences across conditions are apparent, but culminates in a task independent constant value. It is important to note that we are not claiming that the brain behaves as a quantum object as some believe . Rather, we have employed some of the analytical tools from the Schrodinger formulation of quantum mechanics to the brain with the aim of gaining new insight into resting and task-based brain dynamics. Not only does devising this model probe questions into the functions of the brain, but it also provides a novel approach to analysing the myriad of data available in neuroscience.