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Brain Equations: Challenges and Next Generation Mathematical Models
Aim of the workshop
Neural mass models are most suitable in scale to relate to a variety of both clinical and experimental imaging modalities, such as EEG, MEG and fMRI. But since these models have a weak connection to known biology (for they do not include all relevant biological details), it is debatable how useful the results are that are obtained from these procedures. Although the performance of imaging techniques has vastly increased in the last two decades both in terms of spatial resolution and analysis techniques, neural mass models 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 was to identify the relevant challenges of neural mass models and define corresponding objectives for the community.
To prepare the discussion, three notes have been written:
_ The theory of elliptic condition: do we know what we need to know? (Stiliyan Kalitzin)
_ Inverse problems and data assimilation for brain equations - state and current challenges (Roland
_ Towards mean-field analysis of spiking neural networks (Hil Meijer and Sid Visser)
relevant discussion on the modelling was devoted to electro-neutrality. As it
turned out, many of the models used for spreading depression, also relevant for
epilepsy, have the aw that they don't respect this basic principle. New models
will have to be made that deal with this issue. This has not been settled
during the workshop, but the mere fact that this is yet agreed upon is already
To have the three notes available even before the start of the meeting was really helpful. It centered the discussion and showed the commitment of the authors to the workshop. There were relatively few talks and lots of time for discussion. This gave for instance ample time to discuss the electro-neutrality issue with some of the specialists present. As always, the staff of the Lorentz Center did a marvellous job to make everything very smooth.