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Maths can be usefully applied to a wide range of topics in medicine and biology, from the firing of a single brain cell to the spread of diseases (such as HIV, influenza and foot and mouth) through a population. Examples even include modelling the use of maggots in wound healing!

 

Mathematical models can help us to understand diseases and make predictions about biological processes. This may lead to new or improved treatments for problems such as cancer and heart disease, and contribute to new advances in biotechnology. Postgraduate courses in Mathematical Medicine and Biology enable students to develop their knowledge and understanding of research at the interface, without assuming any prior biological knowledge. Students develop core skills in applied mathematical modelling, and specific techniques and skills suitable for academic and industrial biomaths research. In addition to traditional taught courses, interdisciplinary projects and study groups are ideal ways to gain relevant training and experience of the type of problems encountered by academic and industrial researchers. The Centre for Mathematical Medicine and Biology at the University of Nottingham is a prime example of a group at the forefront of academic research and training the next generation of biological modellers. Many other UK universities have similar research groups focused on biomaths (e.g. Cambridge, Dundee, Glasgow, Oxford). The range of biomedical topics being considered from a mathematical perspective is vast, but here we give a flavour of some of them:

Cancer Modelling

 

This exciting area of research aims to increase our understanding of the complex dynamic interactions that underlie cancer, from the defective signalling pathways within cells that allow for uncontrolled cell growth, to the macroscopic tissue interactions that can lead to a build up of fluid pressure that can impede drug delivery. Relevant mathematical tools range from ordinary and stochastic differential equation models for cell signalling to partial differential equations describing the continuum mechanics of growing and deforming tumours. Ideally, such mathematical models help us to understand how cancers grow and spread, and how best to treat them. For example, relatively simple models can show how best to use combination therapies whilst minimising drug resistance.

Physiological Fluid Mechanics

 

This has for many years been at the centre of UK research at the interface between mathematics and biology. It aims to address the physical mechanisms controlling biological fluid flows, which often include significant interactions between fluid and solid. For example, blood flow is crucially linked with the dynamics of the blood vessel wall, and modelling has played a critical role in understanding bloodflow-related risk factors in cardiovascular disease. Similarly, the behaviour of the airway walls is a major determinant of air flow in the lung (and the details of this interaction have serious implications in the case of diseases such as asthma). External flows, such as those involved in animal flight and swimming, have also been the subject of extensive biomaths research. All these examples require the mathematical analysis of systems that couple fluid mechanical equations with those for the interface.

Theoretical Neuroscience

Theoretical Neuroscience helps us understand the function of the nervous system. Hodgkin & Huxley won the Nobel prize in 1952 for their research which combined experiments on squid neurons with the first mathematical model of neuronal firing (a set of ordinary differential equations). Others have focused on the interactions between groups of neurons within the brain. These models capture the essential features of the biological system, from currents through a tiny patch of cell membrane, to learning and memory in many millions of cells. Currently, theoretical neuroscience is undergoing a rapid expansion, often in close collaboration with experimentalists. The mathematics of nonlinear dynamical systems plays a crucial role in theoretical neuroscience.