Modeling Neural Activity

Abstract

This paper provides an overview of different types of models for studying activity of nerve cells and their networks with a special emphasis on neural oscillations. One part describes the neuronal models based on the Hodgkin and Huxley formalism first described in the 1950s. It is discussed how further simplifications of this formalism enable mathematical analysis of the process of neural excitability. The focus of the paper’s second component is on network activity. Understanding network function is one of the important frontiers remaining in neuroscience. At present, experimental techniques can only provide global recordings or samples of the activity of the huge networks that form the nervous system. Models in neuroscience can therefore play a critical role by providing a framework for integration of necessarily incomplete datasets, thereby providing insight into the mechanisms of neural function. Network models can either explicitly contain individual network nodes that model the neurons, or they can be based on representations of compound population activity. The latter approach was pioneered by Wilson and Cowan in the 1970s. Finally I provide an overview and discuss how network models are employed in the study of neuronal network pathology such as epilepsy.

Mechanisms of Neurofeedback: A Computation-theoretic Approach

“…There are many computational models in the literature that address how brain rhythms are generated (see for a review, Van Drongelen, 2013). For the purposes of demonstrating a proof of concept, the details are not too important, other than that the model should be able to produce a useful proxy for the EEG signal.…”

Mathematical Modeling of Subthreshold Resonant Properties in Pyloric Dilator Neurons

“…These series circuits of negative inductance and resistance can be replaced by parallel circuit with a positive resistance and a series circuit of positive resistance and capacitance. This replacement for negative resistance and inductance elements helps us to model the equivalent electrical RLC circuit of PD neurons using hardware components [ 23 ] and to uncover the capacitor-like behavior of these channels. This result indicates that they act as a low-pass filter unlike the resonator currents that play a high-pass filter role in the resonant properties of neurons [ 24 ].…”

Parallel Computing for Brain Simulation

“…Wim van Drongelen [110] presented an overview of the different computer models of neurons and networks, focusing first on the Hodgkin-Huxley model, and subsequently on the activity of neural networks. Finally, the author analyzed how these models were used in the study of diseases such as epilepsy.…”