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The Network Perspective

Siegfried Othmer, Ph.D.

Copyright, The Brian Othmer Foundation, 2002
(Not to be reproduced without permission)

In our clinical work over the last few years, there has been increasing focus on the training of homologous sites with bipolar (or two-channel) placement. This has extended our clinical efficiency and our clinical reach, so that we are now doing better with a number of conditions that we have traditionally lumped under the general rubric of brain instabilities. It has also made some things more difficult. The training is much more frequency-specific than any of the hemisphere-specific trainings that preceded it. Optimization of this kind of training may mean careful fine-tuning of the reward frequency, even down to the level of 0.5 Hz.

The question then arises as to why this training should be so particularly effective, and what brain mechanisms we are appealing to. We have increasingly thought in terms of brain timing and its disregulations as underlying much of psychopathology. One aspect of this is the "thalamocortical dysrythmias" model of Rodolfo Llinas. But there can be more subtle disregulations as well. The considerable frequency sensitivity of EEG training with the inter-hemispheric protocols suggests that the relevant variable being trained is the relative phase of the activity in the two hemispheres. That is to say, we are challenging the mechanisms by which phase is regulated.

What are these mechanisms? To date we have been explaining neurofeedback efficacy in terms of the rhythmic activity of thalamocortical networks. Life is lived between the extremes of the rhythmic, burst/silent mode of firing of such networks, and the more activated, tonic firing mode. By these means, the networks manage their activation-relaxation dynamics to subserve specific brain activities. However, there is a distinct dearth of internal linkages between the two thalami by which inter-hemispheric timing could be mediated directly.

There are cortical connections between the hemispheres, of course, including the corpus callosum and the anterior commissure. However, these involve significant transport delays, and it is problematic how they could mediate simultaneity of firing across the hemispheric fissure. There is another problem. When the corpus callosum is cut in an individual, perhaps to inhibit seizure susceptibility, we do not hazard an increase in psychopathology in that individual. In fact, discerning the absence of a corpus callosum may require some subtle tests. So neurofeedback is not remedying something that can be attributed to malfunctioning of the corpus callosum.

At this point, it may be helpful to view matters from the network perspective. As Paul Nunez points out ("Neocortical Dynamics"), any cortical region is linked to any other cortical region by no more than nominally three synaptic connections. Our cortex is therefore a case in point of a "small-world" problem, in which there are only a few "degrees of separation" between any two cortical sites. Each such linkage can be seen as playing a role in the communication of timing between different brain regions. With typically three links, such coupling is apparently very efficient. One can imagine the grosser features of brain timing as emerging from a kind of democracy at the microscopic level, in which each successful generation of an action potential contributes its bit to the mass action of ensembles, ultimately determining their collective frequency and phase characteristics.

An analogy would be water molecules interacting with their neighbors in the ocean and thereby contributing to wave phenomena observed at a larger scale. The appeal of this model is that one would no longer look for specific localization of timing control in cortex, but rather see brain rhythms as emergent properties of large-scale, distributed brain networks. Whereas the corpus callosum cannot account specifically for the observed phase and amplitude properties, it clearly does play a role in allowing cortex to satisfy the "small-world" model, which in turn permits the emergence of large-scale cortical resonance phenomena.

It is random networks that would give rise to the "democratic" model of brain rhythms. However, on any scale where we care to look, our brain networks are certainly not random. On the small scale of millimeters, we see intensive interconnectivity, or clustering. And on the larger scale, the distinctly non-random architecture is obvious. In the project of exploring the further implications of the network model, we are helped by a new book, "Linked, The New Science of Networks" by Albert-Laszlo Barabasi, a physicist. He observes that whereas random networks are a mathematician's delight, they are almost nowhere to be found in nature. On the other hand, certain unifying principles do appear to be observed quite generally in actual networks: It is the power-law distribution of connectivity, as opposed to the normal (Gaussian) distribution for random networks. There is no characteristic or typical value for connectivity in such a power-law dependence, and therefore these types of networks are referred to as "scale-free." From this follows the second defining characteristic of such networks. The power-law distribution falls off more slowly at large values than the exponential cutoff of the normal curve. Significantly, there are always nodes that have many more interconnections than the others. It is these highly inter-connected nodes that swing most of the weight. So much for democracy.

In our cerebrum, the average neuronal interconnectivity is in the range of 10exp3 to 10exp4. It is among the brainstem nuclei where we find neurons that project to perhaps as many as 500,000 cortical sites, two orders of magnitude greater. By the scale-free network model of the brain, it is such neurons that exert an extraordinary influence on network function, i.e. on brain timing. Moreover, they are in a unique position to mediate bi-hemispheric simultaneity. These are also the neurons that source our neuromodulators. They are the targets for psychopharmacology. Since there is a strong overlap between the conditions we deal with pharmacologically and those we address with neurofeedback, it should come as no surprise that we finally arrive at the hypothesis that neurofeedback impinges in some fashion upon the functioning of these brainstem nuclei.

The current working hypothesis, then, is that we should continue to look for distributed mechanisms for the subtle regulation of brain timing. However, we should allow for the likelihood that certain networks, such as the thalamocortical networks, the highly-connected projections from brainstem nuclei, and the networks involving other subcortical nuclei, play a predominant role. An intriguing notion that bears investigating is whether the thalamus itself constitutes a "small-world" network by virtue of intra-thalamic connections. Given the universality of Barabasi's observations with regard to realistic networks, could it be otherwise?

Finally, then, how does the brain organize phase? It was shown back in 1968 by Anderson and Anderssen that the alpha rhythm did not just come about by virtue of some fortuitous coalescence of neuronal events, but rather by explicit mechanisms of spindle generation and subsequent deconstruction. Presumably this is true in general for the organization of spindle-burst activity at any frequency. The ebb and flow of the amplitudes we observe in our reward bands are the result not of random brain noise but of explicit brain activity. These spindles arise out of distributed network relations.

David Kaiser has argued that the brain organizes internal communication via dynamic shifting between "functional conformity" and "functional differentiation." The relative phase of activity between two relevant sites indexes where we are on the continuum between these extrema. This organizing principle provides for no exception for inter-hemispheric relationships. The latter are not somehow left to chance. Since these inter-hemispheric phase relationships are as explictly managed as any other in the brain, we have in inter-hemispheric training perhaps the largest, most global scale at which the brain may be challenged to reorganize. And perhaps the most efficient.

 

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