Dynamical Analysis of Hippocampal Circuitry under Opioid Addiction Suggests the Mechanism of the Relapse

Drug Addiction affects the limbic system by forming a memory in the hippocampus. Recently, we studied the effect of opioid addiction using a mean-field tripartite model for two pairs of pre and post-synaptic neurons and an astrocyte in the hippocampus. The results indicated an increase in the synchrony of neurons during opioid addiction, which represents memory formation. We added a network modeled by a correlation coefficient that shows the amount of convergence of the network. The neurons' output frequencies have feedback on input frequencies through this network. A first-order ODE models the network feedback on the inputs. The bifurcation diagram of average output frequency versus cues frequency during the withdrawal state indicates bistability. The dynamical analysis indicates that the high-frequency equilibrium points representing opioid addiction can cause relapse at withdrawal state.