Lorentz Center - Brain Equations: Challenges and Next Generation Mathematical Models from 13 Apr 2015 through 17 Apr 2015
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    Brain Equations: Challenges and Next Generation Mathematical Models
    from 13 Apr 2015 through 17 Apr 2015


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)

These discussion papers sparked of a lot of discussion. For instance about models and how to evaluate them. It is inevitable that models in neuroscience cover many scales: from the microscale at the single neuron activity, as measured by micro-electrodes, to mesoscale collective synaptic currents as measured by EEG. Neural fields provide the framework to describe neural activity at the mesoscale. Structural information from dMRI can directly be used to infer results on connectivity, one of the ingredients for the neural fields. Mathematically challenging inverse problems arise when coupling EEG data to neural field equations. The same can be said for other modalities, like MRI, fMRI or SPECT. While the latter modalities give information about function, and the neural fields are based on structure, the inverse problem couples structure to function.

A 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 a breakthrough.
                At present the math departments of the technical universities are preparing a large proposal to further develop
mathematical methods to image the brain. The discussion at the Lorentz center on the relation between structure and function is part of this proposal.


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.