Mathematical physiology

Aims and objectives

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 neurons.

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.

Lecture synopsis

  1. Review of enzyme reactions and Michaelis-Menten theory.
  2. Membrane transport.
  3. Hodgkin-Huxley model.
  4. Phase plane analysis: Fitzhugh-Nagumo model.
  5. Wave propagation.
  6. Calcium dynamics.
  7. Calcium waves.
  8. Spiral waves.
  9. The heart as a pump.
  10. A model of the circulation.
  11. Nervous control of heart rate.
  12. Respiratory control.
  13. The Mackey-Glass model.
  14. The Grodins model.
  15. Blood cell production.
  16. Stem cell control model.

Course materials

These can be downloaded as pdf files; currently available are