Years ago, Steve Wirkus and I coauthored (with several undergraduate students) a paper that first introduced the idea of using limit-cycle oscillators to model bipolar patients. Our model was a toy model, but years later several of my colleagues at Oxford have been doing amazing things from a more data-centric perspective. Their latest paper is especially exciting for me. It does what we dreamed about and speculated about 12 years ago in our paper: taking the basic idea of a limit-cycle oscillator and combining it with clinical data in a realistic way. (The authors of this work understandably also incorporate noise into their model.)
Quoting the last few lines of our conclusions: "In this respect, we view our work as a first step in developing mathematical models of the mood swings of bipolar individuals. Our intent is to provide a mathematical framework that ultimately leads to the development of more detailed models of bipolar disorder that incorporate clinical data. With this work, we hope to motivate the collection of time-series data from clinical trials that will lead to refinements of our model that incorporate such data. In our view, dynamical systems theory and mathematical modeling in general can lead to important advancements in the understanding of bipolar disorder."
(Tip of the cap to Society for Industrial and Applied Mathematics, who shared a popular account of the work on Facebook.)
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