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Mathematical models of bipolar disorder

✍ Scribed by Darryl Daugherty; Tairi Roque-Urrea; John Urrea-Roque; Jessica Troyer; Stephen Wirkus; Mason A. Porter

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 495 KB
Volume: 14
Category: Article
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2008.10.027

No coin nor oath required. For personal study only.

✦ Synopsis

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

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