The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields

Abstract

The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space–time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

Numerical modelling of plasticity induced by transcranial magnetic stimulation

“…We base this work upon the well-documented mean-field theory of Robinson and co-workers [40,39,7,37]. Rather than modeling individual neurons, we consider averaging properties over local groups of neurons.…”

“…The transfer functions L ab (ω) and Γ ab (ω) can be written in Fourier space as follows. The synaptic and soma response is typically described by a bi-exponential function [39,40,21,7]. For the case of excitatory synapses (i.e.…”

“…The axonal transfer function can be modelled with a damped wave equation [19,40,26,7]; we use the form of Robinson et al [40], leading to:…”

“…The transfer function Q T e (f ) can be broadly related to the electroencephalogram (EEG) [7]. Experimentally, for example, Massimini et al have shown that low frequency (0.8 Hz) rTMS can trigger slow wave oscillations during stage 2-4 sleep [28].…”

“…Neural behaviour is modelled in terms of average firing rates and axonal flux rates of populations of neurons, rather than in terms of the behaviours of individual neurons [51,30,9,19,40,4,46,7,37,52]. This approach is particularly suited to the modelling of large-scale measures of brain activity, such as the electroencephalogram (EEG), which involve the sampling of many neurons.…”