- Poster presentation
- Open Access
Realistic activity propagation for mean field models of human cortex
- Ingo Bojak1Email author and
- David TJ Liley2
https://doi.org/10.1186/1471-2202-10-S1-P290
© Bojak and Liley; licensee BioMed Central Ltd. 2009
- Published: 13 July 2009
Keywords
- Partial Differential Equation
- Velocity Distribution
- Hopf Bifurcation
- Conduction Velocity
- Human Cortex
where Φ is the activity being propagated, S is a local source (e.g., a firing rate function), N α the total number of connections, c is the conduction velocity and σ the decay parameter, and n > 0 will usually be chosen as an integer.
This new PDE has the following advantages:
For n > 1 the connectivity implied by the PDE remains finite for small distances.
The PDE has a smooth velocity distribution, the shape of which depends only on n and c.
Number of fibres faster than a velocity threshold. Aboitiz et al. data [2] compared to a fit with the new PDE (blue), and with the damped wave equation matching the new PDE's median speed (green) or fit to the first three data points (cyan, a fit to all points is here not feasible due to severe functional mismatch).
There is no switch between finite wave number Hopf-Turing and Hopf bifurcations as is the case for the damped wave equation. Self-sustained oscillations can emerge as spatial patterns with arbitrarily small wavenumber.
We have investigated the bifurcations of this propagator both analytically and numerically on large grids. We have also compared to more detailed data from the rat [3], but find that they do not scale to human in a simple manner. Our new propagation PDE provides now for CMFMs the best match to activity conduction in humans, and can be easily adjusted as more human data become available later.
Authors’ Affiliations
References
- Jirsa VK, Haken H: Field theory of electromagnetic brain activity. Phys Rev Lett. 1996, 77: 960-963. 10.1103/PhysRevLett.77.960.PubMedView ArticleGoogle Scholar
- Aboitiz F, et al: Fiber composition of the human corpus callosum. Brain Res. 1992, 598: 143-153. 10.1016/0006-8993(92)90178-C.PubMedView ArticleGoogle Scholar
- Partadiredja G, et al: The number, size, and type of axons in rat subcortical white matter on left and right sides: A stereological, ultrastructural study. J Neurocytol. 2003, 32: 1165-1179. 10.1023/B:NEUR.0000021910.65920.41.PubMedView ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd.