April 14, 2024

Scientific Committee:
S. Sivaloganathan, J. Drake, M. Lewis, S. McKee, J. D.Murray

Medical Advisors:
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 modalities,
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.

Summer School Course Schedule

Summer School Course notes index

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.

Invited Speakers

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 Sick Children
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 Francisco
Hugh R.Wilson and Fran Wilkinson, Centre for Vision Research, York University
Hongmei Zhu, Depts. of Radiology and Clinical Neurosciences, MR Research Centre, Calgary

Workshop Schedule


The registration fee for the Summer School and Workshop are $100 each. Onsite registration will be available at the events.

Workshop Housing

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 Accomodation page.

For more information please contact: gensci(PUT_AT_SIGN_HERE)

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