17.05.2017: anton chizhov

Conductance-based refractory density model of a neuronal statistical ensemble

Rapid reaction of brain cortex to stimuli is mainly due to cooperative activity of neuronal populations. Population activity is governed by the equations derived from those for single neurons. For a population of adaptive and non-adaptive Hodgkin-Huxley (HH)-like neurons as an infinite set of similar neurons receiving a common input and individual white or color gaussian noise, a conductance-based refractory density (CBRD) approach has been developed [2,3], which extends the approach elaborated for one-parametric neurons [1]. Neurons of such population constitute a 1-d continuum in the phase space of the time elapsed since their last spikes (t*). The HH-like equations are parametrized in this phase space. Evolution of the neuronal density determines the population firing rate dynamics. The key element of the CBRD approach is a hazard function which evaluates neuronal probability of spiking for a given mean membrane potential distributed in t*. The hazard function is derived from solving a first-time passage problem with Kolmogorov-Fokker-Planck equation for linearized voltage, thus it is universal for a wide range of basic neuron models. The CBRD model is quite precise in comparison with Monte-Carlo simulations for HH-neurons, analytical steady-state solutions for leaky integrate-and-fire neurons and experimental multi-trial recordings in a single neuron. The CBRD model of a single population has been further extended to the case of lognormally distributed input current. Basing on CBRD, a complex model of interacted cortical neuronal populations has been constructed and compared with known experimental intracellular and optical recordings in the primary visual cortex [4], and with recordings of interictal activity in slices of rat's entorhinal cortex. The CBRD method is recommended for large-scale simulations.