Joint Research Conference

June 24-26, 2014

Designing Experiments for Differential Equations Models

Abstract:

In general, choosing an experimental design for an ordinary differential equation (ODE) in order to maximise information about unknown parameters is not a well studied problem in statistics. Although we can often gather a large amount of data for each run, the number of runs we have may be limited due to logistical factors. We may have a lot of data, but it is highly correlated according to some parameters, which may be unknown.
 We are motivated by an application in biological sciences to explore the mechanism for amino acid placental transport. It is believed that this process can be modelled by an ordinary differential equation (ODE) which describes how the concentration of the amino acid on the outside and the inside of a cell membrane varies with time. The ODE is simple to simulate, but it is not possible to write down an analytic solution; it depends on unknown biological parameters which we wish to estimate with minimum variance. 
 Experiments can be performed on placental tissue where the initial concentrations on the inside and outside of the cell membrane are measured, and subsequent concentrations measured at various time points. Placentas are hard to obtain, and the experiment time-consuming to perform, with the result that the number of measurements possible is limited. It is therefore important that we accurately determine which experiments to perform, in terms of initial concentrations and measurement times. In this talk, we set out some of the problems in generalising this approach and how we have attempted to solve it for particular examples. Although the application here is biological, this work can generalise to many chemical or biological processes that are governed by ODEs.