APPLICATIONS OF MATHEMATICS IN MEDICINE
S. Sivaloganathan, J. Drake, M. Lewis, S. McKee, J. D.Murray
James M. Drake (Neurosurgeon, HSC, University of Toronto)
Peter Sleight (Cardiologist, Oxford University)
July 21 - July 26, 2003
Summer School Program - Introduction to Mathematical Medicine, to be
held at the University of Waterloo
The five mini-courses which comprise the summer program are introductory
but intensive courses given by enthusiastic and stimulating instructors,
who are leading researchers in these fields. The recommended prerequisites
for the courses are a strong 4th year level undergraduate background
in Applied Mathematics; the courses will also be accessible to medical
researchers with engineering/mathematical research interests. A schedule
of the courses is available here.
Summer School Program Overview
Mathematical Modelling and Design of Medical Diagnostic Tools
Prof. S. McKee, University of Strathclyde, Scotland
This course will start with enzyme kinetics, introducing the ideas
of the Law of Mass Action, nondimensionalisation, and perturbation
analysis. It will also briefly introduce autocatalysis, and cooperative
reactions. A pregnancy testing kit will be mathematically modelled
and analysed: this will introduce the use of Laplace transforms
in partial differential equations and asymptotic results. The vascular
system will be discussed and solutions for pusatile blood flow will
be derived. This in turn will be applied in the analysis of a catheter
in the pulmonary artery which is heated one degree above blood temperature.
Knowing the power input we deduce the cardiac output. Finally Infectious
diseases are discussed. In particular the SIR model is dealt with;
this is followed by an analysis of a sexually transmitted disease
and then the spread of rabies is considered.
Medical Image Processing
Dr. Hongmei Zhu, Depts. of Radiology and Clinical Neurosciences,
MR Research Centre, Calgary
The prinicipal objectives of this course are to provide an introduction
to basic concepts and techniques for medical image processing and
to promote students' interests for further study and research in
medical imaging processing. To achieve these goals, we will illustrate
the applications of the fundamental principles and various techniques
with a focus on one particular neurological disease.
The whole course consists of five sub-sessions, covering from fundamental
to advanced topics:
i) brief overviews of the disease pathology and related imaging
ii) image fundamentals and transforms,
iii) image enhancement and co-registration,
iv) image segmentation, multi-spectral analysis, and effective visulalization,
v) other exciting research topics in medical imaging. For each session,
a number of techniques will be introduced and a list of references
will be provided.
Physiological Fluid Dynamics
Prof. O. Jensen, University of Nottingham, U.K.
The lectures will cover the following topics. The course will start
with a general overview of biological fluid mechanics and briefly
review the relevant fluid and solid mechanics. It will then focus
on the following four topics.
i) Internal physiological flows: oscillatory tube flow; secondary
flow due to vessel curvature; flow through bifurcations.
ii) Flow in collapsible tubes: wave propagation, choking, elastic
jumps and self-excited oscillations.
iii) Blood flow in the microcirculation: squeezing of red blood
cells through narrow capillaries; neutrophil rolling.
iv) Surface tension effects in the lung: airway closure, airway
reopening; spreading of surfactants.
Modelling Solid Tumour Growth
Dr. Helen Byrne, University of Nottingham, U. K.
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.
Introduction to Mathematical Neurophysiology
Dr. G. deVries, University of Alberta
This short course will introduce students to the physics and biology
of neurons and neural systems, as well as the mathematical tools
that are helpful in understanding their behaviour. We will begin
with a review of the structure of the neuron, experimental techniques
to study the electrical potential across cell membranes, the nerve
impulse, and the Hodgkin-Huxley model of the nerve impulse. This
review will lead to a discussion of concepts such as excitability,
bistability, oscillations, threshold, etc. We finish with a look
at how neurons communicate, how to model interactions between neurons,
and how such interactions affect population behaviour.
July 28-30, 2003
Applications of Mathematics in Medicine Workshop at the Fields Institute
The workshop "Applications of Mathematics in Medicine" will
be run at the Fields Institute 28-30 July 2003 and will be very broad
in scope with talks covering topics from Neurophysiology, oncology,
physiological fluid dynamics, biomechanics, neurosurgery to sleep apnia
and psychiatry. The invited speakers are all leading authorities in
their fields and workshop participants will have the opportunity to
interact with the speakers and each other and to initiate collaborations
where interests overlap. The aim of the workshop is to bring applied
mathematicians and physicians/medical researchers together to discuss
problems of current interest to the medical community. As such, the
talks will be accessible to the medical and applied mathematical communities
- with some talks focused on purely medical aspects of certain problems
and others on modeling and applied mathematical aspects of medical problems.
The workshop will also provide graduate students and researchers starting
in this field a good overview of this vibrant and exciting interdisciplinary
field of research. A schedule for the workshop is available here.
Jacques Belair, University of Montreal, Mathematics
Helen Byrne, University of Nottingham
Sue Ann Campbell, University of Waterloo
James M. Drake, Department of Neurosurgery, Hospital for
C. Ross Ethier, Toronto Western Research Institute
John Flanagan, Toronto Western Research Institute
Jon Hunter, Mt. Sinai Hospital
Bill Langford, University of Guelph
Oliver Jensen, University of Nottingham
Miles Johnston, Sunnybrook Hospital, University of Toronto
James P. Keener, University of Utah, Mathematics
Mohammed Kohandel, University of Waterloo
William Langford, University of Guelph
Andre Longtin, Physics, University of Ottawa
Michael C. Mackey, Department of Physiology, McGill University
John Milton, The University of Chicago Hospitals
Robert Miura, New Jersey Institute of Technology, Neuroscience
Amit Oza, Oncology, Princess Margaret Hospital
Andrew Seely, University of Ottawa
Frances K. Skinner, Toronto Western Research Institute
Colin Studholme, Radiology, University of California San
Hugh R.Wilson and Fran Wilkinson, Centre for Vision Research,
Hongmei Zhu, Depts. of Radiology and Clinical Neurosciences,
MR Research Centre, Calgary
The registration fee for the Summer School and Workshop are $100 each.
Onsite registration will be available at the events.
Blocks of rooms for the conference have been booked at two Toronto
hotels for the evenings of July 27-30. The hotels are the Days
Inn Toronto Downtown and the Delta
Chelsea Hotel. All conference participants should make their own
hotel reservations, before June 27, 2003 to have the rooms guaranteed
- participants should identify themselves as members of the Fields Institute
in order to obtain the conference rate. Information about the hotels
are available through the Fields Institute
Housing page. Information for participants seeking budget accomodation
at campus residences may be found through our Summer
For more information please contact: gensci(PUT_AT_SIGN_HERE)fields.utoronto.ca
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