Stents, blood flow and pregnancy: mathematical modelling in the raw

McKee, S. and Mcginty, S. (2015) Stents, blood flow and pregnancy: mathematical modelling in the raw. In: Bissell, J. J., Caiado, C. C. S., Curtis, S., Goldstein, M. and Straughan, B. (eds.) Tipping Points: Modelling Social Problems and Health Tipping Points: Modelling Social Problems and Health. Series: Wiley series in computational and quantitative social science. John Wiley & Sons Ltd., pp. 95-112. ISBN 9781118752753 (doi: 10.1002/9781118992005.ch6)

Abstract

This chapter provides a brief overview of the philosophy of mathematical modelling before providing three examples in the area of medical science. The first concerns drug-eluting stents; the second deals with blood flow in arteries; and the third concerns a capillary-fill device whose best known application is as part of a pregnancy testing kit. In each case the models are simplifications of the underlying physical and biological problems, yet they still provide useful insights. Mathematical modelling of drug release from drug-eluting stents, and the resulting arterial drug distributions is of real importance in the design and optimisation of such devices since the alternative (experimentation) is often prohibitively expensive and may raise ethical issues. Modelling flow in pipes has a long history dating back to the early 20th century; as our second illustration of modelling techniques we demonstrate how the mathematics behind this early research can be developed and applied to model blood flow in arteries. In our third example, we present a nonlinear mathematical model which, using transform theory and other techniques, facilitated the design of one of the most useful medical diagnostic tools in contemporary society-the pregnancy testing kit.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: Mcginty, Dr Sean
• Authors: McKee, S., and Mcginty, S.
• College/School: College of Science and Engineering > School of Engineering
• Publisher: John Wiley & Sons Ltd.
• ISBN: 9781118752753