Search

We introduce a guided network growth model, which we call the degree product rule process, that uses solely local information when adding new edges. For small numbers of candidate edges our process gives rise to a second order phase transition, but becomes first order in the limit of global choice. We provide the set of critical exponents required to characterize the nature of this percolation transition. Such a process permits interventions which can delay the onset of percolation while tempering the explosiveness caused by cluster product rule processes., Comment: 6 pages, 5 figures, 1 table

Focal seizures are episodes of pathological brain activity that appear to arise from a localised area of the brain. The onset patterns of focal seizure activity have been studied intensively, and they have largely been distinguished into two types - low amplitude fast oscillations (LAF), or high amplitude spikes (HAS). Here we explore whether these two patterns arise from fundamentally different mechanisms. Here, we use a previously established computational model of neocortical tissue, and validate it as an adequate model using clinical recordings of focal seizures. We then reproduce the two onset patterns in their most defining properties and investigate the possible mechanisms underlying the different focal seizure onset patterns in the model. We show that the two patterns are associated with different mechanisms at the spatial scale of a single ECoG electrode. The LAF onset is initiated by independent patches of localised activity, which slowly invade the surrounding tissue and coalesce over time. In contrast, the HAS onset is a global, systemic transition to a coexisting seizure state triggered by a local event. We find that such a global transition is enabled by an increase in the excitability of the "healthy" surrounding tissue, which by itself does not generate seizures, but can support seizure activity when incited. In our simulations, the difference in surrounding tissue excitability also offers a simple explanation of the clinically reported difference in surgical outcomes. Finally, we demonstrate in the model how changes in tissue excitability could be elucidated, in principle, using active stimulation. Taken together, our modelling results suggest that the excitability of the tissue surrounding the seizure core may play a determining role in the seizure onset pattern, as well as in the surgical outcome.