Kinetic Models of Brain Activity

Brain imaging sciences, like neurosciences in general, have predominantly been an empirical endeavour. This paper argues that the maturation of kinetic models of large-scale neuronal activity will provide a unifying theory to underpin brain imaging sciences. In particular, this framework will provide a means of unifying data from different imaging modalities, afford a direct link with cognitive theories of brain function, equip researchers with novel data analysis methodologies and underpin a dialogue in which theoretical formalisms are iteratively refined or refuted through empirical studies. Three steps are crucial to this endeavour: (1) The extension of models of spiking neural ensembles (where the states of all neurons are specified) to statistical models of neural masses (where only a few moments of the distribution of states are specified); (2) The refinement of forward models, such as neurovascular coupling, which map neuronal states to observables; and (3) A theory which links the distribution of neuronal states to cognitive operations, hence informing cognitive neuroscience experiments. We provide illustrative examples of kinetic models of neuronal dynamics at the mesoscopic scale, focusing on the manner by which sensory inputs modify the expression of ongoing background activity. The paper concludes with an overview of some of the cutting edge developments in kinetic models of brain activity.