  The neuronal circuit that controls obsessive and compulsive behaviors
involves a complex network of brain regions (some with known involvement in
reward processing). Among these are cortical regions, the striatum and the
thalamus (which compose the CSTC pathway), limbic areas such as the amygdala
and the hippocampus, and well as dopamine pathways. Abnormal dynamic behavior
in this brain network is a hallmark feature of patients with increased anxiety
and motor activity, like the ones affected by OCD. There is currently no clear
understanding of precisely what mechanisms generates these behaviors.
  We attempt to investigate a collection of connectivity hypotheses of OCD by
means of a computational model of the brain circuitry that governs reward and
motion execution. Mathematically, we use methods from ordinary differential
equations and continuous time dynamical systems. We use classical analytical
methods as well as computational approaches to study phenomena in the phase
plane (e.g., behavior of the system's solutions when given certain initial
conditions) and in the parameter space (e.g., sensitive dependence of initial
conditions).
  We find that different obsessive-compulsive subtypes may correspond to
different abnormalities in the network connectivity profiles. We suggest that
it is combinations of parameters (connectivity strengths between regions),
rather the than the value of any one parameter taken independently, that
provides the best basis for predicting behavior, and for understanding the
heterogeneity of the illness.
