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On neural substrates of cognition: Theory, experiments and application in brain computer interfaces

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Recent experiments with high-resolution brain imaging techniques provide an amazing view on the complex spatio-temporal dynamics of cortical processes. There is ample of evidence pointing to frequent transitions between periods of large-scale synchronization and intermittent desynchronization at alpha-theta rates (period length of 0.1 s to 0.25s). These observations have been interpreted based on the cinematic model of cognitive processing. In the corresponding mathematical theories, brains are perceived as open thermodynamic systems converting noisy sensory data into meaningful knowledge. We employ a graph-theoretic model called neuropercolation, which extends the concept of phase transitions to large interactive populations of nerve cells. We show that normal brains operate at the edge of criticality, where phase transitions are manifested via intermittent phase synchronization. Cortical phase transitions are viewed as neural correlates of cognition and serve as basis for non-invasive cognitive monitoring using novel brain-computer interfaces.
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On Neural Substrates of Cognition
Theory, Experiments and Application in Brain Computer Interfaces
Robert Kozma
Department of Mathematical Sciences
University of Memphis
Memphis, TN 38152, USA
rkozma@memphis.edu
Walter J. Freeman
Division of Neuroscience
University of California at Berkeley
Berkeley, CA 94720, USA
dfreeman@berkeley.edu
Abstract Recent experiments with high-
resolution brain imaging techniques provide an
amazing view on the complex spatio-temporal
dynamics of cortical processes. There is ample of
evidence pointing to frequent transitions between
periods of large-scale synchronization and
intermittent desynchronization at alpha-theta rates
(period length of 0.1 s to 0.25s). These observations
have been interpreted based on the cinematic model
of cognitive processing. In the corresponding
mathematical theories, brains are perceived as open
thermodynamic systems converting noisy sensory
data into meaningful knowledge. We employ a
graph-theoretic model called neuropercolation,
which extends the concept of phase transitions to
large interactive populations of nerve cells. We show
that normal brains operate at the edge of criticality,
where phase transitions are manifested via
intermittent phase synchronization. Cortical phase
transitions are viewed as neural correlates of
cognition and serve as basis for non-invasive
cognitive monitoring using novel brain-computer
interfaces.
KeywordsEEG, Phase Transition, Brain Computer
Interface (BCI), High-density Array.
I. INTRODUCTION
Brain computer interfaces (BCIs) explore the
possibility to establish a communication channel
between brains and external devices such as computers.
The potential benefits are enormous. In clinical setting
BCIs can help to diagnose, predict, and treat cognitive
diseases at an early stage; they can also drastically
improve the quality of life of physically disabled
people. These clinical methods are often invasive, i.e.,
they involve the placement of implants on brains by
opening the scull (Yamakawa, 2012). In everyday life,
noninvasive BCIs are increasingly popular, for
example, the entertainment industry, and they have the
potential to serve as personal assistants in physical
training and exercises. BCIs are young and immature
technologies, and they are still at the very early stage of
their development. Clearly, a large number of
technological challenges must be solved before BCIs
widespread proliferation in broad segments of the
society.
Here we focus on noninvasive devices, when the BCI
electrodes are located on the scull far away from the
cortical neurons. Extracting meaningful information
from the signals of such electrodes may seem daunting.
Indeed, significant exponents of the neuroscience
community consider the obstacles impenetrable and the
related activities outright foolish. The impossibility of
the task has been compared to the burlesque assignment
of Keystone Cops who try to eavesdrop on a single
conservation from outside a giant football stadium
(Marcus and Koch, 2014).
Or one may compare the situation to the case of a
group of free men of fishing trade installing a dense
array of flotation-sensors on the surface of a lake. They
keep applying ever more sophisticated tools and models
to their multi-channel bobbing-record. Methods, which
can indeed catch some statistical signs of at least the
movements of some of the creatures beneath the surface
they are monitoring. These swirls and eddies, they
proclaim, are the real secret of the piece of nature that is
the lake. Keystone Cops and free fishermen illustrate
the prevalent view concerning the apparent
impossibility of brain monitoring using noninvasive
devices. However, increasing experimental evidence
indicates that, in spite of the difficulties, this task can be
solved (Kozma and Freeman, 2014).
Noninvasive BCIs using EEG electrodes placed on
the scalp provide a feasible method for measuring the
brain electrical activity, for a review; see (Liao et al.,
2012). In recent years, EEG sensors and sensing circuit
designs have enabled the integration of sensors into
portable multimodal acquisition devices to measure a
wide variety of physiological signals. In this essay we
describe the experimentally documented intermittent
phase synchronization-desynchronization effects
carrying cognitive content. Then we introduce
neuropercolation as a mathematical approach to model
the synchronization transitions. We conclude with the
need for future developments of high-density scalp
EEG arrays for building efficient BCI devices.
II. CINEMATIC THEORY OF COGNITION
Various brain imaging technologies can be used to
monitor cognitive functions, including functional
magnetic resonance imaging (fMRI), positron emission
tomography (PET), electroencephalograms (EEGs),
near-infrared spectroscopy (NIRS), and others
(Mazaheri and Jensen, 2006).
Figure 1. Illustration of the cognitive cycle, according to the
cinematic theory of cognition. Top: 64 superimposed band-pass
filtered ECoG signals. The 64 analytic amplitudes show drastic
reduction during an intermittent singularity (blue bars). These are the
null spikes (within the vertical blue bars), which are spatially and
temporally localized. Bottom: During the singularity, phase cones
convey the transition from microscopic disorder to macroscopic
order. The amplitudes are high between the blue bars, and they
correspond to the metastable AM patterns carrying the cognitive
content.
During the past years, strong evidence has emerged
in the literature about the existence of sudden jumps in
measured cortical activities. Lehmann identifies
microstates in brain activity and jumps between them
(Lehman, 1998). Rapid switches in EEG activity have
been described by (Freeman et al., 2003, Stam, 2003).
A comprehensive overview of stability, metastability,
and transitions in brain activity is given in (Le Van
Quyen 2001; Werner 2007). Mathematical theory of
heteroclinic channels in winnerless competition is a
powerful approach of modeling sudden switches in
cognitive behavior (Rabinovich et al., 2012). Chaotic
itinerancy is a mathematical theory that describes the
trajectory of a dynamical system, which intermittently
visits “attractor ruins” as it traverses across the
landscape (Tsuda, 2001).
Here we summarize the cinematic theory of
cognition based on experimental studies of sudden
transitions in brain dynamics using electrocorticograms
(ECoGs). ECoGs indicate the presence of spatio-
temporal dynamics over the cortical surface in the form
of amplitude modulation (AM) patterns, which
intermittently collapse at the theta rates and give rise to
rapidly propagating phase modulated (PM) patterns.
The observed dynamics has been shown to be of
cognitive relevance carrying useful information on the
meaning of sensory information perceived by the
subject.
In the terminology of cinematic theory, the
metastable AM patters are the frames and the sudden
transitions through singularity represent the shutter, see
Fig. 1. This result is based on a 64-channel intracranial
experiment, where the analytic amplitudes (AA) and
analytic phases (AP) are obtained following Hilbert
transformation of the beta-gamma filtered ECoG
signals. Intensive work has been conducted to describe
dynamic transitions in cognitive processing as part of
the action-perception (Freeman and Quiroga, 2013).
Recent scalp EEG studies evidence that AM and PM
patterns are observable by non-intrusive experimental
techniques as well (Ruiz et al., 2010).
III. NEURPERCOLATION MODEL OF PHASE
TRANSITION
Neuropercolation is a family of probabilistic models
based on the mathematical theory of probabilistic
cellular automata on lattices and random graphs.
Neuropercolation is motivated by the structural and
dynamical properties of large-scale neural populations.
Neuropercolation extends the concept of phase
transitions to interactive neural populations exhibiting
frequent sudden transitions in their spatio-temporal
dynamics. Neuropercolation develops equations for the
probability distributions of macroscopic state variables
using percolation theory as an alternative to models
based on differential equations (Kozma et al., 2005;
Puljic and Kozma, 2008).
Neuropercolation is a natural domain for modeling
collective properties of brain networks, especially near
critical states, when the behavior of the system changes
abruptly with the variation of some parameter.
Neuropercolation incorporates the following major
generalizations based on the features of the neuropil,
the filamentous neural tissue in the cortex.
Noisy interaction: The dynamics of the interacting
neural populations is inherently non-deterministic
due to dendritic noise and other random effects in
the nervous tissue and external noise acting on the
population. Neuropercolation includes a small
random component, which can act as a control
parameter.
Long axonal effects: In neural populations, most of
the connections are short, but there are a relatively
few long-range connections mediated by long
axons. The effect of long-range axons is similar to
small-world phenomena.
Inhibition: The cortex contains excitatory and
inhibitory connections. Inhibition contributes to the
emergence of sustained narrow-band oscillations in
the neural tissue. Inhibition is modeled by the
interaction of excitatory and inhibitory populations
in neuropercolation models.
Multi-layer neuropercolation models have been
built for implementing hierarchical models of cortical
populations (Freeman 2001; Kozma and Puljic, 2013).
The results indicate that multi-layer neuropercolation
reproduces intermittent phase transitions observed in
brains. Long axons communicating across mesoscopic
cortical distances control the rapid switching from one
pattern to another. The functional advantage of a
network structure with overlapping hubs, similar to the
observed “Rich Club” has been analyzed based on the
pioneer neurons concept.
IV. HIGH-DENSITY SCALP EEG ARRAY FOR
MEASURING SPACE-TIME DISCONTINUITIES
The human scalp EEG contains massive information
that is correlated with higher cognitive functions.
Samples taken from arrays of electrodes show that the
information is in the form of spatiotemporal patterns of
briefly stationary bursts of electric potential differences
(Freeman and Quiroga, 2013). The bursts are generated
by masses of cortical neurons located 10-30 mm below
the scalp surface. They are signals that are
contaminated by electrical noise from scalp muscles
located 2-5 mm beneath the scalp surface.
Theoretical considerations indicate the need for a
high-density array with spatial resolution in the range of
3-5 mm. In order to produce robust spatial power
spectral densities, it is required to have a linear array of
64 electrodes. The spacing requirement is based on
analyses of the spatial frequencies imposed on the scalp
EEG by the gyri and sulci of the cortex (Ramon et al.,
2009); the typical width and length of gyri are on the
order of 10 and 30 cm, giving a spatial Nyquist
frequency of 0.2 cycles/mm. The temporal Nyquist
frequency of 2000 Hz is based on the need for temporal
precision in measurements of the phase of signals in the
high gamma and epsilon ranges, respectively 30-80 Hz
and 80-200 Hz.
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Figure 2. Illustration of the high-density EEG array combined with
model studies using hierarchical neuropercolation model exhibiting
repeated phase transitions. The required massive simulations and
hypothesis generation is best performed using a dedicated FPGA chip
device. The experimental device is a headband of length about 25-30
cm, placed along the forehead. Both approaches lead to temporal-
spatial patterns (insets), which can be described as trajectories in a
phase space. This approach allows direct comparison between
experiment and model, generating and testing several hypotheses
about the relevance of phase transitions in complex neurodynamic
systems for explaining cognitive state changes. The approach is a
generalization based on ECoG experiments on learning and strategy
change in gerbils (Ohl et al., 2001).
Previous studies have shown that the PSDt of the
EEG is fA, where the exponent is 2<A<4, while on
average the EMG PSDt conforms to fB, where B = 0
(Freeman et al., 2003). Therefore the EMG imposes a
plateau onto the combined PSDt, with an inflection at a
high frequency, fH, on transit from fA to fB above fH.
Subjects can be trained by biofeedback, on seeing the
PSDt, to minimize EMG and reveal the signals in the
upper gamma ranges.
V. CONCLUSIONS
BCI technology is developed based on noninvasive
scalp electroencephalogram (EEG). Main conclusions
are as follows:
The proposed approach is based on the monitoring
of the experimentally documented intermittent
phase synchronization-desynchronization effects,
which carry the cognitive content.
We introduce an integrated experimental and
modeling approach using neuropercolation. The
neuropercolation model is used to interpret the
experimental data in real time using massive
parallel computing on a chip.
The information extracted from high-density EEG
array manifests neural correlates of higher
cognitive behaviors.
ACKNOWLEDGMENT
This work has been supported in part by DARPA
Physical Intelligence Program, Dr. Srinivasa Narayan,
and NSF CRCNS Program.
REFERENCES
[1] T. Yamakawa, T. Inoue, S. Aou, S. Ishizuka, M. Fujii, and M.
Suzuki, Minimally invasive ecog recording using the novel
subdural electrodes manipulated by a shape memory alloy
guidewire, Epilepsia, 52, p. 201 (2011).
[2] G. Marcus, C. Koch, The future of brain implants, The Wall
Street Journal, March 14, (2014).
[3] R. Kozma, W. J. Freeman, Unpublished (2014).
[4] L. D. Liao, C. T. Lin, et al. Biosensor Technologies for
Augmented BrainComputer Interfaces in the Next Decades,
Proc IEEE, 100 (13) , (2012) 1553-1566.
[5] A. Mazaheri, O. Jensen , Posterior alpha activity is not
phase-reset by visual stimuli, Proc. Natl. Acad. Sci. USA , 103
(2006) 2948-2952.
[6] D. Lehmann, W. K. Strik, B. Henggeler, T. Koenig, M.
Koukkou Brain electric microstates and momentary conscious
mind states as building blocks of spontaneous thinking: I. Visual
imagery and abstract thoughts, International Journal of
Psychophysiology , 29 , (1998) 1-11.
[7] W. J. Freeman, B. C. Burke, M. D. Holmes Aperiodic phase
re-setting in scalp EEG of beta-gamma oscillations by state
transitions at alpha-theta rates, {\it Human Brain Mapping , 19
(2003) 248-272.
[8] C. J. Stam, Nonlinear dynamic analysis of EEG, Clin.
Neurophysiology 116(10) , (2005) 2266-2301.
[9] M. Le Van Quyen, J. Foucher, J. P. Lachaux, et al. Comparison
of Hilbert transform and wavelet methods for the analysis of
neuronal synchrony, Journal of Neuroscience Methods , 111(2)
, (2001) 8398.
[10] G. Werner, Metastability, criticality, and phase transitions in
brains and its models, BioSystems, 90 , (2007) 496-508.
[11] M. I. Rabinovich, K. Friston and P. Varona, Principles of brain
dynamics: global state interactions , MIT Press, (2012).
[12] I. Tsuda Toward an interpretation of dynamic neural activity in
terms of chaotic dynamical systems, Behav. Brain Sciences, 24,
(2001) pp.793-847.
[13] W. J. Freeman, R. Quian Quiroga, R. Imaging Brain Function
with EEG: Advanced Temporal and Spatial Analysis of
Electroencephalographic and Electrocorticographic Signals.
Springer, New York (2013).
[14] Y. Ruiz, S. Pockett, W. J. Freeman, et al. A method to study
global spatial patterns related to sensory perception in scalp
EEG, J Neuroscience Methods, 191, (2010) 110-118.
[15] R. Kozma, M. Puljic, P. Balister, B. Bollobas, W. J. Freeman
Phase transitions in the neuropercolation model of neural
populations with mixed local and non-local interactions, Biol
Cybern, 92 (2005) 367-379.
[16] M. Puljic, R. Kozma Narrow-band oscillations in probabilistic
cellular automata, Phys. Rev. E. 78026214 (2008).
[17] W. J. Freeman WJ How Brains Make Up Their Minds. New
York: Columbia UP (2001).
[18] R. Kozma, M. Puljic Hierarchical random cellular neural
Networks for System-Level Brain-Like Signal Processing,
Neural Networks, 45, (2013) 101-110.
[19] C. Ramon, W. J. Freeman, M. Holmes Similarities Between
Simulated Spatial Spectra of Scalp EEG, MEG and Structural
MRI, Brain Topogr., (2009) 1573-6792.
[20] F. W. Ohl, H. Scheich, W.J. Freeman WJ Change in pattern of
ongoing cortical activity with auditory category learning, Nature
412 (2001) 733-736.
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