Next-generation neural mass and field modeling

Abstract

The Wilson–Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson–Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson–Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

Mean-field models for EEG/MEG: from oscillations to waves

“…Jansen and Rit [23] demonstrated that transitions between seizures and healthy brain activity could be viewed as transitions between coexisting oscillatory solutions. A similar approach for this model (without gap junctions) can be found in [9]. With gap junctions switched on in both populations (…”

“…with theoretical work by Laing on how to treat gap-junctions [30] and by Coombes and Byrne [10] on the inclusion of realistic synaptic currents (governed by reversal potentials and dynamic conductance changes). Recent work in [9] has also considered the inclusion of finite action potential speeds. In this paper we consider a synthesis of modelling work to date on developing a new class of mean-field models fit for use in complementing neuroimaging studies, and present some new results emphasising the important role of local gap-junction coupling in shaping brain rhythms and waves.…”

“…Beta decrease and rebound are special cases of event related synchrony/de-synchrony (ERS/ERD), as measured by changes in power at given frequencies in EEG/MEG recordings [47], and as such this class of model clearly has wider applicability than standard neural mass models that cannot describe ERD/ERS because their level of coarse-graining does not allow one to interrogate the degree of within-population synchrony. By merging this new dynamical model of neural tissue with anatomical connectome data it has also been possible to gain a perspective on whole brain dynamics, and preliminary work in [9] has given insight into how patterns of resting state functional-connectivity can emerge and how they might be disrupted by transcranial magnetic stimulation. Despite the success of the next generation models that include synaptic processing it is well to recognise the importance of direct electrical communication between neurons that can arise via gap-junctions.…”

Graph neural fields: a framework for spatiotemporal dynamical models on the human connectome

“…Discrete surface-based models are defined on a (highly-sampled) cortex and are therefore finite-dimensional. In several studies, region-based and discrete surface-based models are collectively referred to as networks of neural masses [17,31,32]. Continuous surface-based models are better known as neural field models and are defined on the entire cortex and are thus infinite-dimensional [23,26,33].…”

“…Region-based models are constructed by parcellating the cortex into a number of regionsof-interest (ROIs), placing a local model in each ROI, and connecting them according to a given connectome (see [2,17,32] for reviews). The ROIs are usually obtained from structural or functional cortical atlases and the number of ROIs is in the order of a hundred or less.…”