Mathematical physiology: preamble

This course develops the subject of mathematical biology into the realm of physiology. The basic topics covered in a book such as that of J.D. Murray revolve around the mathematical subjects of oscillations, travelling waves, spatial pattern, singular perturbation theory, and reaction-diffusion systems, as exemplified in the study of predator-prey systems, enzyme kinetics, the Fisher equation, the Belousov-Zhabotinskii reaction and diffusion-driven instability. This course assumes a familiarity with these topics, and also with some of the biological background, and extends it specifically to the study of physiological systems. In particular, there is an attempt to treat a sequence of topics at a range of scales, from the intra-cellular to the systemic. Most of the techniques should  be familiar and are assumed (phase plane analysis, stability theory, relaxation oscillations), but there will be some new material introduced, such as wave propagation in three dimensions and differential-delay equations. The specific topics of the course are trans-membrane ion transport, signal propagation in nerve cells, calcium oscillations, action of the heart, control of respiration and blood cell production.

Lecture delivery 

Lectures are face to face on Mondays and Tuesdays; apparently these will also be live-streamed and also recorded. They will follow the format of the online 2020 recorded lectures, that is, delivered at the lectern with handwritten lecture notes on the screen. There will thus be much less writing on the board. The written lecture notes define the course. There are also printed lecture notes, which by this stage have been elaborated almost to book form. Various other resources will be provided, as described below. The 2020 lectures as recorded were the following, with duration in minutes:

1. Trans-membrane ion transport			29
2. Ionic currents						43
3. Hodgkin-Huxley model				50
4. FitzHugh-Nagumo equation			43
5. Signal propagation					42
6. Calcium dynamics					39
7. Wave propagation					35
8. Electrochemical action of the heart		50
9. Waves in 2 or 3 dimensions			56
10. The heart as a pump				39
11. Heart and blood flow models			44
12. Nervous control of the heart			47
13. Respiratory control					38
14. Grodins model					54
15. Blood cell production				46
16. Maturation model of RBC production		52

The lecture material will be identical to this, but depending on circumstances, the division of the live lectures may be slightly altered. For example, it looks like lecture 2 might start in lecture 1. With luck, everything will get done, but if not, I may refer you to the 2020 recorded lectures for live gaps. In any case, these may be of independent usefulness.

Web resources

Announcements

The announcements section in moodle will be used to alert you to resource posting. For example, the printed lecture notes will likely be upgraded during the term, and when this is done, an announcement will be made.

Discussion

There is also a discussion forum. I will probably try and open this up. How it is used is unpredictable. It may be questions for lecturer or tutor, or it may just be for intra-student discussion.

Problem sheets

There are four problem sheets in the assignments section. These have already (1/10/21) been posted. They contain questions labelled A,B,C. Only B questions should be handed in for marking, and only these will be gone through in detail in the classes. The A questions should be relatively straightforward, while the C questions provide further opportunities for practice. With luck, there may be time for questions in class on the C questions (and after that, the A questions). My feeling is that you will want to have a go at some of the A or C questions as well as the B ones. Answers to everything will be posted after work is submitted.

Other resources

Also in the course material section, you will find
1. This file.
2. A folder: written_notes. This folder contains the written notes of the lectures as a pdf. These will be shown on screen during the live lectures.
3. A folder: printed_notes. This contains the printed lecture notes. As already mentioned, updates to these may be provided during term (and even after).
4. A folder: answers. The problem sheet answers will be posted here after work is submitted and presumably before the classes (though that depends on their timing).
5. A folder: fhs_answers. During online revision in TT2020 and TT2021, I wrote out answers to a lot of old fhs questions, and these will be posted here. They come with a health warning, as they are just my version of the answers to questions which I mostly (except the last three years) did not set. They will be of use next Trinity Term.

There should also be the Panopto lectures recorded in 2020, but these are being uploaded by the administrative staff, hopefully soon.

Andrew Fowler
1/10/2020