Dynamics of activity fronts in a continuum mean field model of cortex
© Bojak et al; licensee BioMed Central Ltd. 2010
Published: 20 July 2010
The functional organization of cortex appears to be roughly columnar, with the laminar sub-structure of each column organizing its micro-circuitry. These columns tessellate the two-dimensional cortical sheet with high density, e.g., 2,000 cm2 of human cortex contain 105 to 106 macrocolumns, comprising about 105 neurons each. Continuum mean field models (cMFMs) describe the mean activity of such columns by approximating the cortical sheet as continuous excitable medium . cMFMs can generate rich patterns of emergent spatiotemporal activity . This has been used to understand phenomena from visual hallucinations to the generation of EEG signals. Pattern boundaries are here defined as the interface between low and high states of average neural activity.
Changes of brain activity are often of greater interest than the current state per se. On the cortical sheet, two-dimensional patterns can be defined by boundaries between high and low states of activity, and their dynamics can be specified by tracking the evolution of these interfaces. Using a simple cMFM, we show here that one can describe the motion of activity fronts with equations of reduced complexity, which nevertheless reproduce the observed dynamics faithfully. This improves our ability to study pattern formation and suggests more generally that modelling the interfaces of patterns, rather than the patterns themselves, may lead to novel, efficient descriptions of brain activity.
- Coombes S: Large-scale neural dynamics: Simple and complex. Neuroimage. 2010, doi:10.1016/j.neuroimage.2010.01.045Google Scholar
- Coombes S, Venkov NA, Shiau L, Bojak I, Liley DTJ, Laing CR: Modeling electrocortical activity through improved local approximations of integral neural field equations. Phys Rev E Stat Nonlin Soft Matter Phys. 2007, 76: 051901.View ArticlePubMedGoogle Scholar
- Bojak I, Liley DTJ: Axonal velocity distributions in neural field equations. PLoS Comput Biol. 6: e1000653-10.1371/journal.pcbi.1000653.Google Scholar
This article is published under license to BioMed Central Ltd.