The use of many-body physics and thermodynamics to describe the dynamics of rhythmic generators in sensory cortices engaged in memory and learning
Introduction
A crucial issue in the study of brain functioning is the origin of different time scales occurring from the bio-molecular and cellular level to the one of amplitude modulated (AM) assemblies of coherently oscillating neurons [1, 2, 3, 4••, 5, 6]. I review such an issue in the frame of the dissipative quantum model of brain [5, 6, 7]. I will refer to the body of results emerging from observations of the densely packed neuropil, obtained by W.J. Freeman and his collaborators by means of high density electrode arrays fixed on the scalp or the epidural surface of cortical areas [1, 2, 3, 4••, 8, 9]. The set of the squared amplitudes of EEG signals from an array of n electrodes (typically 64) defines a feature vector of the spatial pattern of power at time t, specifying a point on a dynamic trajectory in the space of all possible brain states [10, 11, 12, 13]. The point is unique for a spatial AM pattern of an aperiodic carrier wave [14]. Similar AM patterns form a cluster in n-space. The trajectory of a sequence of points entering into a cluster signifies increased order from the perspective of an intentional state of the brain in relation with a conditioned stimulus: a cluster with a verified behavioral correlate denotes an ordered AM pattern with carrier frequencies in the beta and gamma ranges (12–80 Hz). They form during the active state and dissolve as the cortex returns to its receiving state after transmission. The cortex appears thus jumping abruptly from a receiving state to an active transmitting state, and then returning to the receiving, expectant state. These state transitions in cortex form frames of AM patterns in few ms, hold them for 80–120 ms, and repeat them at rates in alpha and theta ranges (3–12 Hz) of EEG [7, 15]. The patterns cover much of the hemisphere in rabbits and cats [14, 15, 16], and extend over the linear length of 19 cm [8] in human cortex with near zero phase dispersion [14, 15, 16, 17]. They have been detected in the resting state and in motor task related states of the human brain by MEG [18] and constitute a sort of rhythmic, although aperiodic, temporal functional activity of brain. Chemical diffusion [1, 2, 3, 19, 20, 21], electrochemical or other classical mediation vectors appear to be not compatible with the observed high rates of field modulation. The collective neuronal oscillations are then modeled as the macroscopic manifestations of the coherent quantum dynamics of basic components constituting the neuropil. EEGs [7, 22, 23, 24•, 25•] indeed allow observation of classical phenomena generated in the neuropil which cannot be explained without recurs to the underlying quantum dynamics. The quantum variables are the vibrational modes of the electric dipoles of water molecules and other macromolecules and ionic solutes which constitute the medium in which neurons and glia cells are embedded. Their reciprocal interaction leads to collective, unifying oscillations of membrane potential by ephapsis [25•] and accounts for the high rate of energy dissipation through ionic fluxes across membranes. I stress that neurons, glia cells and other microscopic organelles are considered to be classical elements in the dissipative quantum model. In sections ‘Filling the gap between microscopic dynamics and macroscopic observations’ and ‘Formation and life-time of coherent domains’, two points are shortly reviewed: first, how the transition occurs from the quantum level to the cellular level and all the way up to the level of macroscopic brain functioning and second, the appearance of different time scales and different sizes of neural coherent assemblies.
Section snippets
Filling the gap between microscopic dynamics and macroscopic observations
In brain studies, one interesting question to ask concerns how to fill the gap between the level of the molecular and cellular behavior, ruled by chemical random kinematics, and the level of the observable high effectiveness and reliability of brain macroscopic functioning. The dissipative quantum model may help answering to such a question.
The brain is an open dissipative system in continual reciprocal interaction with its environment. Inputs from the environment act as triggers of internal
Formation and life-time of coherent domains
The dynamic orderly activity of the brain, far from being described by the randomness characteristic of biochemical activity and individual properties of the cells, finds thus a description in the dynamical formation of coherent domains of different sizes and life-times [1, 2, 3, 4••, 5, 6, 7, 46, 47, 48, 49, 50]. In such a process the brain goes from disordered, gas-like state of high entropy, namely the low-density sparse, random firing of neurons in the background activity prior to a
Conclusions
The dissipative model describes the quantum dynamics out of which AM assemblies of oscillating neurons emerge. One finds that more are the links that brain establishes with its surrounds, more neuronal functional connections are formed. These play a more relevant role than the activity of the single neuron and are highly dynamic, with modulation time scales in the range of tenths/hundreds of milliseconds, as opposed to the structural or anatomical (quasi-stationary) connections. The functional
Conflict of interest
Nothing declared.
References and recommended reading
Papers of particular interest, published within the period of review, have been highlighted as:
• of special interest
•• of outstanding interest
Acknowledgements
INFN and Miur are acknowledged for partial financial support.
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