A schematic of mean field model for the S1 and ACC circuits. (A) In a reduced model, each brain area is described by an excitatory (E) and an inhibitory (I) population of neurons, with inter- and intra-population coupling. The S1→ACC coupling is assumed to be excitatory and unidirectional. (B) A detailed mean-field model that account for biological constraints and details. The pain-responsive ACC neuronal population, E2-1, is assumed to receive a direct excitatory input from the S1 population E1. wEE represents the basic coupling strength between the same type of neuronal populations (E-E or I-I), wEI represents the basic coupling strength between different types of neuronal populations (E-I or I-E). ρ is a negative number that scales the strength of inhibitory input from I-neurons. L < 1 is a positive number that scales the effect of long-range S1→ACC projection, κ represents the size ratio of S1 population to ACC population.