Dynamic Behavior Of Sources

EEG waveforms recorded on the scalp are due to a linear superposition of contributions from billions of microcurrent sources or, expressed another way, by thousands to millions of columnar sources P(r',t) located in cerebral cortex, as indicted by Eq. (3). However, the underlying physiological bases for the dynamic behavior of the sources are mostly unknown. The 10-Hz range oscillations of alpha rhythm, the 1Hz range oscillations of deep sleep, and other waveforms in the EEG zoo must be based on some sort of characteristic time delays produced at smaller scales. Such delays can evidently be developed in neural networks that cover a wide range of spatial scales.

Locally generated activity in small networks and more globally generated activity involving spatially extensive networks up to the global scale of the entire cerebral cortex may be reasonably assumed. The local network category includes so-called thalamic pacemakers that could possibly impose oscillations in specific frequency ranges on cortex (local resonances). Other possible mechanisms occur at intermediate scales between local and global. These involve feedback between cortex and thalamus or between specific cortical locations. Preferred frequencies generated at intermediate scales may be termed regional resonances. At the global scale, the generation of resonant frequencies (global resonances) due to standing waves of synaptic action has been proposed.

Delays in local networks are believed due mainly to rise and decay times of postsynaptic potentials. In contrast, global delays occur as a result of propagation of action potentials along axons connecting distant cortical regions (corticocortical fibers). Delays in regional networks may involve both local and global mechanisms. A working conjecture is that local, regional, and global resonant phenomena all potentially contribute to source dynamics. However, the relative contributions of networks with different sizes may be quite different in different brain states. The transition from awake to anesthesia states is an example of a local to global change. The ECoG changes from rhythms depending strongly on location to rhythms that look similar over widespread cortical locations. Another example is desynchronization (amplitude reduction) of alpha rhythms that occurs with eye opening and certain mental tasks.

Several mathematical theories have been developed since the early 1970s to explain the physiological bases for source dynamics—that is, the underlying reasons for specific time-dependent behaviors of the source function P(r',t). Distinct theories may compete, complement each other, or both. Some common EEG properties for which plausible quantitative explanations have emerged naturally from mathematical theories include the following observed relations: frequency ranges, amplitude versus frequency, spatial versus temporal frequency, maturation of alpha rhythm, alpha frequency-brain size correlation, frequency versus corticocortical propagation speed, frequency versus scalp propagation speed, frequency dependence on neurotransmitter action, and mechanisms for cross-scale interactions between hierarchical networks. Because the brain is so complex, such theories must involve many approximations to genuine physiology and anatomy. As a result, verification or falsification of specific theories for the physiological bases for EEG is difficult. However, such mathematical theories can profoundly influence our general conceptual framework of brain processes and suggest new studies to test these ideas.

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