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Neural Oscillations
Continued
Saee Paliwal
TNU
What is an oscillation?
Simple Harmonic
Oscillation
phase
amplitud frequenc
e
y
power ∝ amplitude
Neuronal oscillations: Van der Pol
oscillators
Limit Cycle of a neuron
Mathematical foundation
Population oscillation
Coupled Oscillators
Local field potential of neuronal
oscillations
This is the
EEG
signal
Coupled oscillations
An example of oscillations in vivo
Analyzing the EEG signal
Fourier transform:
-
decomposition of a signal
from the time domain into
the frequency domain
Four kinds of
waves:
§beta (>13 Hz)
§alpha (8-13 Hz)
§theta (4-8 Hz)
Frequen
cy
Time
§delta (0.5-4 Hz)
Neural Mass Model:
Jansen and Rit, David and Friston
Characteristics
-
Excitatory and Inhibitory
connections
a few cubic mm of volume
(~10^4-~10^7 neurons)
describe large populations of
neurons with a handful of
parameters (mean-field
approximation)
Jansen and Rit model
Post-synaptic potential (PSP)
model: convolution of impulse
response and pre-synaptic
input
Impulse response. H is the
synaptic gain, t is the time
constant
Membrane potential to rate for
kth subpopulation.
c, r and e are population
parametrs (e.g. volatge
sensitivity)
Jansen and Rit, 1995
M/EEG
signal
Circuit Diagram
3 populations of neurons
comprise a cortical area:
- excitatory pyramidal cells
- excitatory stellate cells
- inhibitory interneurons
v is the membrane potential, m
is the mean firing rate,
output signal
Pulse
David and Friston, 2003
Simulation of Oscillations
Jansen and Rit model with David and
Friston extension
The power of synchrony
Long range synchrony: contributes to the “binding problem,” ie their
integration represents a “gestalt” or patter/representation of a object
-
-
Visual Cortex: neural populations respond to color/shape/motion, and synchrony allows
for the integration of these features into a percept (Eckhorn et al, 1988, Kreiter and
Singer, 1996, Fries et al, 1997)
Feature bindng extends to oflactory system (Freeman et al, 1978) and the auditory
system (Aersen et al, 1991)
It is also thought that synchronixation across several motor regions (ie motor cortex and
spinal chord) lead to coordinated motor activity (van Wijk et al, 2012
Task-related Synchrony
-
binding across regions has been related to task-specific features