Sean is currently a third year student at the Queensland University of Technology, studying a Bachelor of Mathematics, majoring in Applied and Computational Mathematics. He is interested in many area of mathematics, in particular, the biomedical applications of differential equations, calculus and linear algebra.
How To Cool Burns Using Maths
A recent collaboration between applied mathematicians and medical researchers at Queensland University of Technology has successfully applied an ordinary differential equation-based model of heat conduction to a series of animal experiments where heat conduction in living porcine tissue is investigated (Andrews et al. 2016). This initial study provides reliable estimates of the thermal conductivity of living porcine skin. This vacation scholar project will build on these preliminary results by analysing an existing, but as yet unpublished data set that explores the question of how to optimally cool a burn injury. This new data set describes temperature data from an in vivo porcine (pig) model of heat conduction where several burn injuries are subjected to different kinds of treatments such as applying cool water of varying temperatures over varying durations. The outcome of this project will be to identify the best strategy for cooling a burn injury. For example, we will explore how cool should the water be, and how long should it be applied for.
This project will train the vacation scholar in several key areas of applied mathematics. Skills developed will include:
• Mathematical modelling – how to idealise a physical heat conduction problem into a suitable model based on ordinary and partial differential equations;
• Mathematical analysis – exact solutions of the differential equations will be obtained using a variety of techniques (direct integration, integral transforms); and
• Model calibration – gradient-based methods for calibrating the mathematical model to experimental data will be used.
This project is sufficiently open-ended that the vacation research student could continue to study an extension of this topic for their Honours project in 2017.