Figure 3.

Canonical microcircuit neural field model: “CMC”. This figure shows the evolution equations that specify a canonical microcircuit (CMC) neural mass model of a single source. This model contains four populations occupying different cortical layers: the pyramidal cell population of the Jansen and Rit model is effectively split into two subpopulations allowing a separation of the neuronal populations that elaborate forward and backward connections in cortical hierarchies. As with the ERP and LFP models, second-order differential equations (shown earlier in Figure 1 decomposed into two first order ODEs), mediate a linear convolution of presynaptic activity [a sigmoidal function of presynaptic membrane depolarization σ(v)] to produce postsynaptic depolarization (v), dependent on membrane time constants (1/κ_e/i) and average post-synaptic depolarizations (H_e/i) at excitatory (e) and inhibitory (i) synapses. This depolarization gives rise to firing rates within each sub-population that provide inputs to other populations. Replacing connectivity parameters d, with a connectivity matrix over space and time D(x,t) enables one to generalize the neural mass model to a neural field model. This effectively converts the ordinary differential equations in this figure into partial differential equations or neural field equations.