Maths In Medicine And Biology
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 (www.maths.nottingham.ac.uk/research/cmmb/) 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.
Tissue Engineering
Tissue engineering is an exciting field which promises to revolutionise the science of regenerative medicine, for example, using a patient’s own cells to generate replacement bone
tissue. In the UK a number of tissue engineering groups collaborate with Mathematical Scientists to help improve their understanding of tissue growth, and how best to optimise
growth conditions, for example to grow stronger bones. An
extremely complex issue is how to
“grow” organs with complex structures– should we design systems that naturally develop into
appropriate structures (emergent pattern
formation), or try to direct growth with specific scaffold
geometries? Many of the
mathematical modelling tools are similar to those used in modelling cancer.
Employment
Opportunities
There is an ever-increasing demand for mathematicians trained in the application of mathematics to biological and medical systems. Employment opportunities include the
healthcare sector, government departments, environmental agencies, and the pharmaceutical,
medical-device and food industries, in addition to an ever expanding variety of opportunities in academia.
Leading UK universities
and the UK government
(via the research councils)
are investing heavily in
multidisciplinary research
at the interface between
mathematics and the
biomedical sciences.
The Society for Mathematical Biology (www.smb.org) lists many jobs in internationally leading universities around the world (mathematical medicine and biology offers an excellent opportunity to travel). The Association of the British Pharmaceutical Industry report "Sustaining the skills pipeline" notes that "There is a growing demand for mathematical scientists . with a variety of modelling techniques . shortages are a worldwide problem." Recently developed courses in Mathematical Medicine and Biology aim to correct this shortage in the UK.
Article provided by The University of Nottingham School of Mathematical Sciences
Related Links:
Biomedical Engineering
Mathematics
