Modeling neural oscillations

Abstract

A brief review of oscillatory activity in neurons and networks is given. Conditions required for neural oscillations are provided. Three mathematical methods for studying the coupling between neural oscillators are described: (i) weak coupling, (ii) firing time maps, and (iii) leaky integrate-and-fire methods. Several applications from macroscopic motor behavior to slice phenomena are provided. D

Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

“…Second, we assume that the input received in the closed network is similar to that used to generate the PRC. We do not require the weak coupling assumption that is often used in network analysis (Ermentrout and Chow 2002;Mancilla et al 2007; Netoff et al 2005b) and that assumes the phase response is linear. Instead, we make a third assumption-that the effects of one input die out before the next one is received.…”

“…Here we test the applicability of PRC-based firing time maps (Ermentrout and Chow 2002) to excitatory coupling of significant strength and duration, using a wide range of synaptic strengths (from 1 to 10,000 nS) and input durations (from 0.3 to 1.5 s). The membrane voltage recorded in the AB/PD complex was used to calculate synaptic current (I syn ) received by the model cell.…”

Amplitude Modulation Patterns of Local Field Potentials Reveal Asynchronous Neuronal Populations

“…The rationale for this identification is the assumption that narrowband oscillations must necessarily reflect the constructive summation of synchronous oscillators. Thus, a great amount of theoretical effort was directed to elucidate the coupling mechanism(s) producing synchronous firing (White et al, 1998;Ermentrout and Chow, 2002;Jones, 2002;Averbeck and Lee, 2004); however, this search can be expanded by taking into account aspects such as a statistical analysis of the degree of synchrony of the underlying oscillator population or an estimation of the number of oscillators involved. For example, very different phenomena can arise in LFP recordings, which involve only a mesoscopic quantity of oscillators (few tens of oscillators) when compared with macroscopic techniques (EEG), where millions of oscillators are involved.…”

Sensory Feedback Mechanism Underlying Entrainment of Central Pattern Generator to Mechanical Resonance

“…The neuronal circuits of CPGs have been extensively studied for a wide variety of animals, and their mathematical models have been developed and validated through comparisons of model predictions with experimental observations (Orlovsky et al, 1999;Cohen et al, 1992;Ermentrout and Chow, 2002). The simplest and perhaps most fundamental CPG consists of two (groups of) neurons with mutually inhibitory synaptic connections (Brown, 1911), and is called the half-center model or the reciprocal inhibition oscillator (RIO).…”