Summer Project: Modelling Menstrual Hormones and Behaviour

Monday 15 October 2012

Over the summer, Chrissy Gavin (year 3->4, MMath) worked on the MILES funded project "Modelling menstrual hormones and behaviour". The first part of the project involved collecting data from 30 participants at 12 time points. The data collected was progesterone and oestrogen levels together with the results of some reaction time tests. The purpose of the project was to consider how the two hormone levels affected performance on the reaction time tests at different points in the menstrual cycle.

Once the data had been collected, Chrissy set to work to analyse it. First of all the data was fitted with the first few terms of a Fourier series on the assumption that the data was time periodic. The time variable was then shifted, to make the peak of progesterone occur at time zero, and scaled, so that the period of the cycle was one. The graphs from all the participants could then be averaged. The trajectory in a two-dimensional "phase plane" plot of progesterone against oestrogen was coloured according to the value of the percentage correct or average reaction time from the tests.

Before starting the study, it had been anticipated that the test results could be found as some function of the two hormone levels. The two hormone phase plot had a crossing point and it was found that the test results on the two branches at this crossing point were very different, which shows that the initial assumption was in fact incorrect. We then tested to see whether the test results could be found as a (linear) function of the two hormone levels and their (time) derivatives, and a very good fit to the data was found.

The supervisors for this project were Philip Aston (Mathematics) and Adam McNamara and Kay Moakes (Psychology).