Mathematical abstraction

The third stage in the Blue Brain workflow is the choice or design of mathematical abstractions describing the structure and function of the brain at different levels of organization. Examples include the equations used to describe the functioning of individual ion channels (based on the Hodgkin-Huxley phenomenological model) and flows of electric current along neuronal fibers (based on discretized versions of classical cable equations).

Effective modeling requires appropriate mathematical abstractions for all relevant aspects of brain biophysics at all levels of brain organization. Particularly important in this respect is the role of geometry. Given that geometry influences brain structure and function at all levels of organization, from individual atoms to the whole brain, a key goal of the Blue Brain project has been to create abstractions describing the basic principles underlying the structure and construction of neural circuitry. Another crucially important element, to be included in future digital reconstructions, is plasticity, which affects models and parameters at all scales.