Dynamics of coupled thalamocortical modules
The electroencephalogram (EEG) is a readily-obtained, noninvasive, and objective measure of brain activity. In contrast to functional brain imaging, the EEG can be recorded in almost anyone, including subjects who are moving, and patients whose medical condition requires close observation and/or support equipment, and it is possible to obtain prolonged recordings spanning many behavioral states. At present, the utility of the EEG as a scientific tool has been limited by the indirect nature of the relationship between surface recordings and the underlying brain activity.
To bridge this gap, Robinson and colleagues proposed a model of EEG dynamics at the level of neuronal populations. The Robinson model consists of a single thalamocortical module with four homogeneous populations (cortical excitatory, cortical inhibitory, thalamic relay nucleus, and reticular nucleus). Each population has two dynamical variables: an average firing rate and an average potential. Their evolution is governed by a system of delayed-differential equations (DDE's). The Robinson model accounts for the spectral features of the EEG across a range of normal behavioral states (eyes open, eyes closed, and the four stages of slow-wave sleep). These spectral features can be recovered from the linearized behavior of the model near its fixed points. However, because of its very simple spatial structure, the Robinson model cannot account for patterns of spatial interactions across cortical regions or changes in the EEG due to focal brain abnormalities. It also does not account for state transitions; different states are obtained by changing the effective connectivity strengths 'by hand.'
To begin to develop a population model that could account for these phenomena, we investigated the dynamics of a system consisting of two ''Robinson modules'', each with its own cortical and thalamic components. Corresponding to known anatomy, we coupled these modules by adding a third population of reticular neurons that are shared between the modules. The shared population is reciprocally connected with the relay nuclei of both modules, and receives input from the cortical components of both modules. We studied the global dynamics of this system across a two-parameter family of coupling scenarios: one parameter indicates the strength of the connections with the shared population, and one indicates the strength of the connections with the specific populations.
A complete bifurcation diagram was constructed for the coupling of ''Robinson modules'' in the eyes-open state. The bifurcation diagram delineates three regions of qualitatively different behavior. In the first region, a symmetric fixed point is asymptotically stable. This corresponds to synchronization of the modules. In the second region, a symmetric periodic solution, arising at a Hopf bifurcation, is asymptotically stable. This also corresponds to synchronization, but the periodic nature of the solution leads to a sharpened spectral peak. The third region arises via a pitchfork bifurcation, spawning two additional fixed points while destabilizing the symmetric solution. Qualitatively, this corresponds to winner-take-all behavior because one of the modules maintains an elevated activity level and the other is suppressed.
In sum, coupling two simple thalamocortical modules together can yield several different qualitative behavioral regimes.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). Dynamics of coupled thalamocortical modules.
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.001
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Received:
28 Jan 2009;
Published Online:
28 Jan 2009.