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LMS/EPSRC Short Course on Mathematical Biology
January 9-14, 2005
Organiser: Dr. Matthias Heil
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Introduction
Over the past decades, mathematics has increasingly (and successfully)
been applied to the modelling and analysis of many biological and
physiological problems. Mathematical Biology has thus developed
into an active, varied and inherently interdisciplinary field
of research. Major advances have been made (e.g.) in the modelling of
disease spreading and tumour growth, in the analysis of biological
pattern formation and in physiological fluid mechanics. The complexity of
biological and physiological systems makes them a rich source of
challenging problems whose analysis often stimulates the development
of novel mathematical techniques.
Many mathematics departments in the UK now offer courses in
Mathematical Biology but typically the syllabi of these courses only cover
a small subset of the entire field, reflecting the research interests
within each department. This problem persists at PhD level and especially
first year PhD students often fail to appreciate the breadth of
the field. The aim of this course is to provide first and
second year mathematics PhD students with an overview of four main
research areas in Mathematical Biology. The course will start with
an opening lecture on `Bioconvection'. This will be
followed by
three eight-hour courses on `Modelling
Biological Pattern Formation', `Biological Fluid
Mechanics' and `Tumour Modelling'.
The four invited lecturers are leading researchers in their respective
fields and are widely known as enthusiastic and stimulating teachers.
Programme
The course will open with a formal welcome on Sunday evening, followed
by
Prof. Nick Hill's opening lecture on Bioconvection.
Courses I-III will start on Monday morning. Each course
will consist of eight one-hour sessions which will comprise of
formal lectures and tutorials in the form of examples classes and
group work sessions. Five to six of the eight sessions will be given
as lectures and the lecturers will distribute their tutorials flexibly
within their programme. The lecturers will run the tutorials
themselves to ensure that they get direct
feedback from the students. Printed course notes and example sheets
will be provided for all courses.
Course Overview
This course considers the phenomenon of spatiotemporal pattern formation
in developing biological systems. Although genetics plays a key role
in development, a study of genetics alone cannot inform us of the
mechanisms that give rise to the spectacular variety of patterns we
see in nature. We will explore a number of models that have been
proposed to account for spatial patterning, ranging from simple
gradient models, through to more complex models in which patterning is
hypothesized to occur via the process of self-organisation. We will
focus on reaction-diffusion models, for example, Turing models and
cell-chemotactic models, and explore mathematically, the phenomena of
excitability and diffusion-driven instability. The applications of the
models and the insight they give to biological patterning will be
discussed.
The course will start with a general overview of biological fluid mechanics
and will give a short review of the relevant fluid and solid mechanics. Following
this, four problems in the area of physiological fluid mechanics will be
studied in greater detail: (i) pulse wave propagation and flow
patterns in the arteries; (ii) collapsible tube models for
blood flow in the veins; (iii) flow patterns in the lung; Taylor
dispersion; (iv) airway closure; surface-tension-driven instabilities of
the lung's liquid lining. We will develop simple mathematical models
of these physiological systems and use the models to analyse the
system's behaviour. Finally, an overview of current research problems
will be given.
The main aim of this course is to show how mathematical techniques can be
used to investigate and provide insight into the mechanisms that regulate
different aspects of solid tumour growth. The models we study will include:
systems of coupled differential equations that describe vascular tumour growth
(when the tumour is connected by the host's blood supply and has an
effectively limitless supply of nutrients); moving boundary problems that
describe avascular tumour growth (when the tumour lacks its own blood supply
and relies on nutrient diffusion to sustain its growth); and, probabilistic
models of angiogenesis (the process by which an avascular tumour becomes
vascularised by stimulating the formation of a new blood supply from
neighbouring vessels). Whilst the models and analytical techniques employed
will apply to tumours, the methods are sufficiently general in nature that
they will be applicable in other areas of mathematical biology and
applied mathematics.
Accommodation
Accommodation has been arranged in (rather posh!) single rooms at the
Chancellor's Conference Centre
In addition to accommodation, breakfast, lunch and evening meal will
be provided for course residents.
Registration
The registration fee is 100 pounds which, for UK-based research
students, includes the cost of course accommodation and meals.
Participants must pay their own travel costs.
EPSRC-supported students can expect that their registration fees and
travel costs will be met by their
departments from the EPSRC Research Training and Support Grant that is
paid to universities with each studentship award.
The number of participants will be limited and those
interested are encouraged to make an early application.
An online application form is available from the
London Mathematical Society.
The closing date for applications is 12 November 2004.
Further Information
Further information is available from:
Dr. Matthias Heil
Department of Mathematics
University of Manchester
Oxford Road
Manchester M13 9PL
Tel. +44 (0)161 275 5808
Fax. +44 (0)161 275
5819
M.Heil@maths.man.ac.uk.
Page last modified: September 24, 2004
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