A challenge in computational neuroscience is to develop neuronal models with minimal complexity to enable the development of large networks of brain regions to understand the functions they might implement. Biologically realistic neuronal models aim to replicate the electrical functioning of the cell at the level of ionic channels, and sometimes even include complex dendritic trees and intracellular molecular cascades. Such models are computationally intensive and not suitable for implementation in networks. Reduced order models, such as the one proposed by Izhikevich (2007), aim to preserve the key neurocomputational properties and so form an attractive alternative for implementation in large network models.
A systematic methodology is proposed to convert a biologically realistic neuronal model to an equivalent reduced order Izhikevich model, given the key morphological features that impact network structure. For instance, multiple compartments may be required, afferents may be distributed differently between basal and apical dendrites, and the synaptic plasticity mechanisms may be different at different dendritic sites. This will require careful design of the morphology of the reduced order model. By current mapping and phase portrait analysis, we suggest how such a biologically realistic model can be converted to a reduced order Izhikevich model that preserves the key neurocomputational and morphological features.