November 19, 2003
Mathematical Models of BiPolar Disorder
Mathematical Models of BiPolar Disorder is the title of a paper on the ArXiV, by Mason Porter, VIGRE Postdoc, and several other undergraduates. This is a project that Mason carried to Georgia Tech from Cornell University. One of the undergraduates is Jessica Synder, participant in last summer's VIGRE REU program. For more information about the figure, see the paper.
Abstract of the paper: Bipolar disorder (manic depression) afflicts about one percent of the United States adult population. In this paper, we use limit cycle oscillators to model Bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes. We consider three nonlinear oscillator models of a single bipolar patient. In each case, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also study the dynamics of two individuals with bipolar II disorder who live together. We model such interactions between bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We conclude with a discussion of possible generalizations of our model, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.