Volume 10 Supplement 1
Realistic activity propagation for mean field models of human cortex
© Bojak and Liley; licensee BioMed Central Ltd. 2009
Published: 13 July 2009
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.
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 , 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.
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