19,059 research outputs found
Power-Law Scaling in the Brain Surface Electric Potential
Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form from 80 to 500 Hz. This scaling index, , is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, , increases. We observe a “knee” in the spectra at , implying the existence of a characteristic time scale . Below , we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory “asynchronous,” scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent “synchronous” rhythm-based paradigm
Macroscopic models of local field potentials and the apparent 1/f noise in brain activity
The power spectrum of local field potentials (LFPs) has been reported to
scale as the inverse of the frequency, but the origin of this "1/f noise" is at
present unclear. Macroscopic measurements in cortical tissue demonstrated that
electric conductivity (as well as permittivity) is frequency dependent, while
other measurements failed to evidence any dependence on frequency. In the
present paper, we propose a model of the genesis of LFPs which accounts for the
above data and contradictions. Starting from first principles (Maxwell
equations), we introduce a macroscopic formalism in which macroscopic
measurements are naturally incorporated, and also examine different physical
causes for the frequency dependence. We suggest that ionic diffusion primes
over electric field effects, and is responsible for the frequency dependence.
This explains the contradictory observations, and also reproduces the 1/f power
spectral structure of LFPs, as well as more complex frequency scaling. Finally,
we suggest a measurement method to reveal the frequency dependence of current
propagation in biological tissue, and which could be used to directly test the
predictions of the present formalism
Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media
The resistive or non-resistive nature of the extracellular space in the brain
is still debated, and is an important issue for correctly modeling
extracellular potentials. Here, we first show theoretically that if the medium
is resistive, the frequency scaling should be the same for electroencephalogram
(EEG) and magnetoencephalogram (MEG) signals at low frequencies (<10 Hz). To
test this prediction, we analyzed the spectrum of simultaneous EEG and MEG
measurements in four human subjects. The frequency scaling of EEG displays
coherent variations across the brain, in general between 1/f and 1/f^2, and
tends to be smaller in parietal/temporal regions. In a given region, although
the variability of the frequency scaling exponent was higher for MEG compared
to EEG, both signals consistently scale with a different exponent. In some
cases, the scaling was similar, but only when the signal-to-noise ratio of the
MEG was low. Several methods of noise correction for environmental and
instrumental noise were tested, and they all increased the difference between
EEG and MEG scaling. In conclusion, there is a significant difference in
frequency scaling between EEG and MEG, which can be explained if the
extracellular medium (including other layers such as dura matter and skull) is
globally non-resistive.Comment: Submitted to Journal of Computational Neuroscienc
A framework to reconcile frequency scaling measurements, from intracellular recordings, local-field potentials, up to EEG and MEG signals
In this viewpoint article, we discuss the electric properties of the medium
around neurons, which are important to correctly interpret extracellular
potentials or electric field effects in neural tissue. We focus on how these
electric properties shape the frequency scaling of brain signals at different
scales, such as intracellular recordings, the local field potential (LFP), the
electroencephalogram (EEG) or the magnetoencephalogram (MEG). These signals
display frequency-scaling properties which are not consistent with resistive
media. The medium appears to exert a frequency filtering scaling as
, which is the typical frequency scaling of ionic diffusion. Such a
scaling was also found recently by impedance measurements in physiological
conditions. Ionic diffusion appears to be the only possible explanation to
reconcile these measurements and the frequency-scaling properties found in
different brain signals. However, other measurements suggest that the
extracellular medium is essentially resistive. To resolve this discrepancy, we
show new evidence that metal-electrode measurements can be perturbed by shunt
currents going through the surface of the brain. Such a shunt may explain the
contradictory measurements, and together with ionic diffusion, provides a
framework where all observations can be reconciled. Finally, we propose a
method to perform measurements avoiding shunting effects, thus enabling to test
the predictions of this framework.Comment: (in press
Brain Dynamics across levels of Organization
After presenting evidence that the electrical activity recorded from the brain surface can reflect metastable state transitions of neuronal configurations at the mesoscopic level, I will suggest that their patterns may correspond to the distinctive spatio-temporal activity in the Dynamic Core (DC) and the Global Neuronal Workspace (GNW), respectively, in the models of the Edelman group on the one hand, and of Dehaene-Changeux, on the other. In both cases, the recursively reentrant activity flow in intra-cortical and cortical-subcortical neuron loops plays an essential and distinct role. Reasons will be given for viewing the temporal characteristics of this activity flow as signature of Self-Organized Criticality (SOC), notably in reference to the dynamics of neuronal avalanches. This point of view enables the use of statistical Physics approaches for exploring phase transitions, scaling and universality properties of DC and GNW, with relevance to the macroscopic electrical activity in EEG and EMG
Toward bio-inspired information processing with networks of nano-scale switching elements
Unconventional computing explores multi-scale platforms connecting
molecular-scale devices into networks for the development of scalable
neuromorphic architectures, often based on new materials and components with
new functionalities. We review some work investigating the functionalities of
locally connected networks of different types of switching elements as
computational substrates. In particular, we discuss reservoir computing with
networks of nonlinear nanoscale components. In usual neuromorphic paradigms,
the network synaptic weights are adjusted as a result of a training/learning
process. In reservoir computing, the non-linear network acts as a dynamical
system mixing and spreading the input signals over a large state space, and
only a readout layer is trained. We illustrate the most important concepts with
a few examples, featuring memristor networks with time-dependent and history
dependent resistances
A modified cable formalism for modeling neuronal membranes at high frequencies
Intracellular recordings of cortical neurons in vivo display intense
subthreshold membrane potential (Vm) activity. The power spectral density (PSD)
of the Vm displays a power-law structure at high frequencies (>50 Hz) with a
slope of about -2.5. This type of frequency scaling cannot be accounted for by
traditional models, as either single-compartment models or models based on
reconstructed cell morphologies display a frequency scaling with a slope close
to -4. This slope is due to the fact that the membrane resistance is
"short-circuited" by the capacitance for high frequencies, a situation which
may not be realistic. Here, we integrate non-ideal capacitors in cable
equations to reflect the fact that the capacitance cannot be charged
instantaneously. We show that the resulting "non-ideal" cable model can be
solved analytically using Fourier transforms. Numerical simulations using a
ball-and-stick model yield membrane potential activity with similar frequency
scaling as in the experiments. We also discuss the consequences of using
non-ideal capacitors on other cellular properties such as the transmission of
high frequencies, which is boosted in non-ideal cables, or voltage attenuation
in dendrites. These results suggest that cable equations based on non-ideal
capacitors should be used to capture the behavior of neuronal membranes at high
frequencies.Comment: To appear in Biophysical Journal; Submitted on May 25, 2007; accepted
on Sept 11th, 200
Power-law statistics and universal scaling in the absence of criticality
Critical states are sometimes identified experimentally through power-law
statistics or universal scaling functions. We show here that such features
naturally emerge from networks in self-sustained irregular regimes away from
criticality. In these regimes, statistical physics theory of large interacting
systems predict a regime where the nodes have independent and identically
distributed dynamics. We thus investigated the statistics of a system in which
units are replaced by independent stochastic surrogates, and found the same
power-law statistics, indicating that these are not sufficient to establish
criticality. We rather suggest that these are universal features of large-scale
networks when considered macroscopically. These results put caution on the
interpretation of scaling laws found in nature.Comment: in press in Phys. Rev.
- …