The course aims to provide an introduction which can bring students
within reach of current research topics in physiology,
by synthesising a coherent
description of the physiological background with realistic
mathematical models and their analysis. The concepts and treatment of
oscillations, waves and stability are central to the course, which
develops ideas introduced in the more elementary B8a course. In
addition, the lecture sequence aims to build understanding of the
workings of the human body by treating in sequence problems at the
intracellular, intercellular, whole organ and systemic levels.
B8a Mathematical ecology and biology is highly recommended.
Review of enzyme reactions and Michaelis-Menten theory. Trans-membrane ion
transport: Hodgkin-Huxley and Fitzhugh-Nagumo models.
Excitable media; wave propagation in
Calcium dynamics: calcium-induced calcium release.
Intracellular oscillations and wave propagation.
The electrochemical action of the heart. Spiral waves, tachycardia and
fibrillation. The heart as a pump. Regulation of blood flow.
Respiration and CO_2 control. Mackey and Grodins models.
Regulation of stem cell and blood cell production. Dynamical diseases.
Review of enzyme reactions and Michaelis-Menten theory.
Phase plane analysis: Fitzhugh-Nagumo model.
The heart as a pump.
A model of the circulation.
Nervous control of heart rate.
The Mackey-Glass model.
The Grodins model.
Blood cell production.
Stem cell control model.
These can be downloaded as pdf files; currently available are
Problem sheets. These are
now ready (16/1/06). I may add in some other questions later which
can be used in revision.
The classes are now up in Minerva.
Lecture notes These are now
available. They are still incomplete in parts but will be
updated as time permits.
The principal text is
Keener, J. and J. Sneyd 1998 Mathematical
physiology. Chs. 1,4,5,9-12,14-17. Springer-Verlag.