LMS/EPSRC Short Course on Mathematical Biology

January 9-14, 2005

Organiser: Dr. Matthias Heil

[Introduction]

[Further Information]

Here's the latest update of the programme incl. directions to Chancellors etc.

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

Modelling biological pattern formation (Prof. Philip Maini, University of Oxford)

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.

Biological fluid mechanics (Dr. Matthias Heil, University of Manchester)

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.

Modelling solid tumour growth (Prof. Helen Byrne, University of Nottingham)

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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