Cycle 5 System of Rhythms Simple to Complex Dynamics

May 01, 2012 04:43 PM see msg from Tom Dean to syz on April 30 2012 copied at the cbottom and taken

from the chapter summary of Cycle 5.

starts at page 111:

Chapter 5 = cycle 5.

central tenet of this Cycle is that brain dynamics constantly shifts from the complex to the predicatble.

Neuronal ensemble activities shuttel back and forth btwn the interference prone complex and the

robust predictable oscillatory snychrony.

112  delta is 0.5 to 4

theta is 4 to 8

alpha 8 to 12;

beta 12 to 30

gamma is higher.

112 page

drug-free rodent, HC theta should be designated  theta-alpha  cuz it varies btwn 5 and 10 hz.

The exact mechaims of most brain oscillations are not known.

page 113

began looking at  3 HC rhythms in rat

theta 4 to 10

gamma 30 to80

and a fast osc  140 to 200;

precise timing is necessary for successful prediction of change in physic enviro from coord of muscles to antic of enviro events.

sponges ... slow oscillators

page 115

thick axons conduct faster but occupy more space.

Informing multiple postsynap targets ocated btwn 0.5 and 5 millimeters of a single neuron takes

1 to 10 msc... prob becomes even larger when more complex events are repres in incr large ensembles.

must have the coooperative activ of hundred of neurons to discharge their postsyn target.

Must be coordinated in time

Recognizing someones face,  fecalling her first and last names, her profession, our last meeting,

our common friends... do not occur simultan.

these cognitvie events  require hierarchical procesing;

searate procesindsg requires the engagemont of neornal networks at mult spatial scales.

Each oscill cycle is a temporal proce window... signaling begins and ends the encoded or transferred msg.

The wavelength of the oscill cycle determines the tempr window and indirectly the size of the neuronal pool involved.

SLOW OSCILLat can involve many neurons involving large brain areas

page 116

whereas short time windows of fast oscillators facilitate local integration.

Computation in the brain always means that info is MOVED from one place to another.

The path length and connectivity is important...

the cycle lengths of the oscil limit how far info gets transferred in one step.

Fast oscillations favor local decisions,

invovlement of distant neuronal groups in distinct structures in obtaining a global consensus requires more time.

page 117

ULTRADIAN and CIRCADIAN RHYTHMS

hypothalamic suprachiasmatic nucleus is the circadian pacemaker in mammals

it has 20,000 neurons in the human suprachia nucleus.

individual cells ENTRAIN into coherent oscillations thru their connex.

GABA and gap junctions among inhib neuosn appear essential for synchronizing the neurons.

The circad clock is so SLOW  cuz it takes 4 to 6 hours to make a protein from a gene.

complex feedback loop with 4 freshly produced proteins.

Embedded within the circadian cycle at 2 well-documented  ULTRADIAN rythms

fasteris at 90 to 100 mins whereas the slower is 3 to 8 hours.

shorter is superimposed on the longer.

page 119

1/f  Statistical Behavior of EEG;

When a goal is scored in a football stadium,

the coordinated ROAR of the fans can be hear d for miles,

in contrast to uncoordinated local conversaitons.

Similarly, slow rhythms involve v large numbers of cells and can be HEARD over a long distance,

whereas localized fast oscillations involve only s small fraction of neurons.

See figure 5.2... in this log log plat we see a straight line... the hallmark of scale-free systems.

Amplitude A increases as the frequency decreases.

A critcal aspect of brain oscillators is that the freqs of neighboring families are not integers of each other.

The osc are not locked together... they maintein their independenced

they attaract and repel each other and never settle to a stable attractor.

page 121

there is transient coupling of osciallators at mult spatial scales... so a unified system with mult time scales emerges.

1/f even applies below a minute (of wavelength).

The scale-invariant feature of EEG is the math telltale sign of self-organizaiton.  the temporal memory effect.

page 123    flucturaitons of brain-generated and perceived sounds, like music and speech also exhibit 1/f power spectra.

music has temproal patterns tuned to the brains aiblity to detect them.

Weber's Psychophys Law and Large-Scale Brain Dynamics

see footnote:  monkeys can recognize melodies... happy birthday and yankeed doodle... 2 octaves apart.

page 124...

Rudolfo Llinas... octaves =>  icnrpower...  underlie qualia of music.

<a id="node_footnote_Temp_1" name="node_footnote_Temp_1"> </a><a href="#node_call_footnote_Temp_1">1</a> From Chapter (Cycle) 5 of Buzsáki’s “Rhythms of the Brain” [<a href="#node_bib_1">1</a>]:

<a id="node_sec_Temp_2" name="node_sec_Temp_2"> </a>this is from page 126 of the book.

<h3 class="section" >Noise and Spontaneous Brain Activity</h3>

The largest computer network of the neocortex yet built was constructed by Eugene Izhikevich and Gerald Edelman. Their three-dimensional model consisted of 100,000 neurons exhibiting some known cortical firing patterns. Each excitatory neuron was randomly connected to 75 local and 25 distant targets. Twenty percent of the neurons were GABAergic and wired locally, mimicking the proportions in the mammalian cortex. Despite such dense anatomical wiring, involving more than 7 million excitatory connections, neurons in the model remained dead silent unless external noise was provided to each neuron. At low levels of input noise, the system sustained oscillatory patterns with spatially uniform activity. High levels of input noise gave rise to asynchronous Poisson patterns of spiking activity that led to organized, sustained patterns. Other computer networks do not fare better. In contrast to the brain, most current models of the brain or pieces of the brain do not give rise to true spontaneous patterns without some externally supplied noise. They either are dead silent or generate avalanches of activity involving nearly the whole population. The usual explanation is that the network is not large and complex enough and therefore cannot generate enough noise. However, computer networks, including the supersized systems, fail to generate enough internal noise necessary for observing some desired patterns.

How large should a system be to generate continuous spontaneous patterns? My answer is that size is not the (only) issue. Even a very small real brain or neuronal networks with just a few dozen neurons can solve complex problems that would make man-made computer-controlled robots jealous. All real brains, small and large, possess spontaneous activity because they are complex enough. However, complexity does not simply emerge from increasing the number of constituents. Neuronal systems that consist of glutamatergic excitatory and GABAergic inhibitory neurons do not do much else than generate large epileptiform population discharges interrupted by silence. Indeed, this is exactly what an isolated piece of the mammalian cortex does. Fetal cortical tissue transplanted into the anterior chamber of the eye or into a blood-supplying cavity in the cortex generates synchronous discharges of various sizes followed by pauses of various lengths, a behavior not much different from that of sand piles. Isolated cortical slabs and cortical neurons grown as two-dimensional tissue culture generate similar burst/pause patterns. When isolated from their subcortical inputs, the nearly two million neurons in the rat hippocampus just sit and wait to be part of a giant collective scream. These intermittent patterns are a far cry from the 1/f dynamics of the intact mammalian cortex.

Applying external noise to a network is convenient, but it has some inconvenient consequences. In Izhikevich’s large model, noise intensity had to be increased fiovefold to shift the system from avalanches to irregular patterns. At this high level of noise, synchrony occurred only in response to strong external inputs, and the average firing rate of neurons doubled. Most important, 10 percent of all action potentials occurred in response to the externally applied noise rather than to internally generated synaptic activity. This seems like an inefficient system because such a large percentage of spikes are devoted to noise production. In models, this may not be such a big problem. However, energy calculations indicate that the brain cannot afford to waste so many spikes. Doubling the firing rate of neocortical neurons would exhaust their energy resources within minutes. Furthermore, spikes generated by noise will propagate activity and interfere with signal-related computation. So, is noise just a waste or is there something good about it? Find out in Cycle 6.

<h3 class="section" >Briefly ...</h3>

The collective behavior of neurons, summed up crudely as the mean field (EEG and MEG) is a blend of rhythms. Neuronal networks in the mammalian cortex generate several distinct oscillatory bands, covering frequencies from < 0.05 hertz to > 500 hertz. These neuronal oscillators are linked to the much slower metabolic oscillators. The mean frequencies of the experimentally observed oscillator categories form a linear progression on a natural logarithmic scale with a constant ratio between neighboring frequencies, leading to the separation of frequency bands. Because the ratios of the mean frequencies of the neighboring cortical oscillators are not integers, adjacent bands cannot linearly phase-lock with each other. Instead, oscillators of different bands couple with shifting phases and give rise to a state of perpetual fluctuation between unstable and transient stable phase synchrony. This metastability is due to the presence of multiple coupled oscillators that perpetually engage and disengage each other. The resulting interference dynamics are a fundamental feature of the global temporal organization of the cerebral cortex. The power density of the EEG or local field potential is inversely proportional to frequency (f) in the mammalian cortex.

This 1/fα power relationship implies that perturbations occurring at slow frequencies can cause a cascade of energy dissipation at higher frequencies, with the consequence that widespread slow oscillations modulate faster local events. The scale freedom, represented by the 1/fα statistics, is a signature of dynamic complexity, and its temporal correlations constrain the brain’s perceptual and cognitive abilities. The 1/fα (pink) neuronal “noise” is a result of oscillatory interactions at several temporal and spatial scales. These properties of neuronal oscillators are the result of the physical architecture of neuronal networks and the limited speed of neuronal communication due to axon conduction and synaptic delays.

Brain evolution opted for a complex wiring pattern in the mammalian cortex. The resulting 1/fα temporal statistics of mean field are the hallmark of the most complex dynamics and imply an inherently labile, self-organized state. Although brain states are highly labile, neuronal avalanches are prevented by oscillatory dynamics. Most oscillations are transient but last long enough to provide stability for holding and comparing information at linear time scales. Scale-free dynamics generate complexity, whereas oscillations allow for temporal predictions. Order in the brain does not emerge from disorder. Instead, transient order emerges from halfway between order and disorder from the territory of complexity. The dynamics in the cerebral cortex constantly alternate between the most complex metastable state and the highly predictable oscillatory state: the dynamic state transitions of the brain are of the complexity-order types. When needed, neuronal networks can shift quickly from a highly complex state to act as predictive coherent units due to the deterministic nature of oscillatory order.

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