Bifurcations and multiscale cascades in cortical dynamics Michael Breakspear, Stuart Knock, UNSW, Australia Kevin Aquino, Peter Robinson, James Roberts, University of Sydney John Terry, Serafim Rodriguez, University of Bristol, UK

Bifurcations and multiscale cascades in cortical dynamics 1: Mean Field Brain Modelling Robinson et al. (2002) Phys Rev. E 65: Corticothalamic connectivity where describes dendritic filtering of synaptic currents model time (sec) ΦeΦe EEG time (sec) Pz V a membrane potentials Φ a field potentials Q a firing rates Cortico-cortical connectivty where describes propagating cortical field potentials Jirsa & Haken (1996) PRL a=e,i cortical populations a=s specific thalamic n. a=r reticular thalamic n. time (sec) ΦeΦe strongly damped

μ se Φ e (s -1 ) 3 Hz instability μ se Φ e (s -1 ) 10 Hz instability μ se Φ e (s -1 ) Bifurcations and multiscale cascades in cortical dynamics 2: Unifying explanation of seizures Breakspear et al. (2006) Cerebral Cortex doi: /cercor/bhj072 Global mode instabilities 1. Ignore spatial derivatives ( ) & 2. explore nonlinear bifurcations by changing μ se model Cortex-reticular–specific loop data model Cortex-specific loop data

1. Nonlinear frequency coupling Data 2. Amplitude modulation Data Bifurcations and multiscale cascades in cortical dynamics 3: Impact of global coupling on local mean fields Global corticocortical coupling Reintroduce spatial dependency in Absence seizure (3Hz spike and wave) regimen Model

Hindmarsh Rose: Between scales Hindmarsh Rose: Between systems Bifurcations and multiscale cascades in cortical dynamics 4: Multiscale temporal effects in neural systems Fast timescales, x 1,2 Slow timescales, x 3 Coupled nodes: Single node: Burst (slow) synchrony: c~0.35 Spike (slow+fast) synchrony: c>0.45 Dhamala et al. (2004) PRL c scale coarse fine scale fine coarse …and their anti-symmetric component, t aMS Calculate inter-scale effects as, Nakao et al. (2001) IJCB t MS

Healthy cortical Activity Seizures Bifurcations and multiscale cascades in cortical dynamics 5: Coupling of spatiotemporal scales in cortical activity μ se Φ e (s -1 ) 10 Hz instability Symmetric Antisymmetric Model Data scale coarse fine