# C5.12 Mathematical Physiology - Material for the year 2019-2020

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B5.5 Further Mathematical Biology is highly recommended.

16 lectures

### Assessment type:

- Written Examination

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 B5.5 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.

Students will have developed an understanding of mathematical modelling of physiological systems and will have demonstrable knowledge of the mathematical theory necessary to analyse such models.

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.

Discrete delays in physiological systems. The Glass-Mackey model of respiration. Regulation of stem cell and blood cell production.

The principal text is:

- J. Keener and J. Sneyd,
*Mathematical Physiology*(Springer-Verlag, 1998). First edition or Second edition Vol I: Chs. 2, 7. Vol II: Chs. 11, 13, 14. (Springer-Verlag, 2009)]

Subsidiary mathematical texts are:

- J. D. Murray,
*Mathematical Biology*(Springer-Verlag, 2nd ed., 1993). [Third edition, Vols I and II, (Springer-Verlag, 2003).] - L. Glass and M. C. Mackey,
*From Clocks to Chaos*(Princeton University Press, 1988). - P. Grindrod,
*Patterns and Waves*(OUP, 1991).

General physiology texts are:

- R. M. Berne and M. N. Levy,
*Principles of Physiology*(2nd ed., Mosby, St. Louis, 1996). - J. R. Levick,
*An Introduction to Cardiovascular Physiology*(3rd ed. Butterworth-Heinemann, Oxford, 2000). - A. C. Guyton and J. E. Hall,
*Textbook of Medical Physiology*(10th ed., W. B. Saunders Co., Philadelphia, 2000).