Brain Equations: Challenges and Next Generation Mathematical Models

In the field of neuroscience, a variety of mathematical concepts have been successful in suggesting modern day ideas about brain function. Indeed, results from dynamical systems theory such as oscillation, synchrony, attractor and bifurcation are now widely accepted in this field of life sciences.  These are proven essential in understanding single cell and small network behaviour, for which biophysically realistic models can be developed.  Since these techniques are not applicable anymore at larger network, it is common practice to study collective dynamics – neural mass modelling.

Neural mass models are most suitable to relate to a variety of both clinical and experimental imaging modalities, such as EEG, MEG, fMRI and optogenetics. But since these models have a weak connection to known biology (for their premises are contrived), it is debatable how reliable the results are obtained from these procedures.

Although the standards of imaging techniques have vastly increased in the last two decades, neural mass models, on the other hand, have barely advanced. In order to ensure that the mathematical neuroscience community will be able to keep providing theoretical support to the life sciences, it is critical to push the field forward.

The primary aim of the workshop, therefore, is to identify the relevant challenges of neural mass models and define corresponding objectives for the community. On that account, we have selected several key subjects, which, we believe, have a high priority: neuro-glial-vascular interaction, integration across scales, dynamical analysis and epilepsy.