Activity dependent model for neuronal avalanches

Cortical networks exhibit diverse patters of spontaneous neural activity, including oscillations, synchrony and waves. The spontaneous activity often in addition exhibits slow alternations between high activity periods, or bursts, followed by essentially quiet periods. Bursts can last from a few to several hundreds of milliseconds and, if analysed at a finer temporal scale, show a complex structure in terms of neu-ronal avalanches. As discussed in previous chapters, neuronal avalanches exhibit dynamics similar to self-organized criticality Avalanches have been observed in organotypic cultures from coronal slices of rat cortex (Beggs and Plenz, 2003), where neuronal avalanches are stable for many hours (Beggs and Plenz, 2004). The size and duration of neuronal avalanches follow power law distributions with very stable exponents, typical features of a system in a critical state, where large fluctuations are present and system responses do not have a characteristic size. The same critical dynamics has been measured also in vivo in rat cortical layers during early post-natal development (Gireesh and Plenz, 2008), inthe cortex of awake adult rhesus monkeys (Petermann et al., 2009), as well as in dissociated neurons from rat hippocampus (Mazzoni et al., 2007; Pasquale et al., 2008) or leech ganglia (Mazzoni et al., 2007). The term SOC usually refers to a mechanism of slow energy accumulation and fast energy redistribution driving the system toward a critical state, where the distribution of avalanche sizes is a power law obtained without fine tuning of a particular system or model parameter. The simplicity of the mechanism at the basis of SOC suggests that many physical and biological phenomena characterized by power laws in the size distribution, might represent natural realizations of SOC. While the sizes and durations of avalanches have been intensively studied in neu-ronal systems, the quiet periods between neuronal avalanches are much less understood. In vitro preparations, such quiescent periods are often called down-states and can last up to several seconds, in contrast to periods of avalanche activity, which gen