ENGINEERING TRIPOS PART IIA - 2012/2013

Module 3G2 - Mathematical Physiology

Module Leader: Dr A. Kabla (ajk61@eng)

Additional Lecturer: Dr M Lengyeln(ml468@eng)

Timing: Lent term
Structure: 16L

AIMS

This course focuses on the quantitative modelling of biological systems. A wide variety of topics are touched upon, from biochemistry and cellular function to neural activity and respiration. In all cases, the emphasis is on finding the simplest mathematical model that describes the observations and allows us to identify the relevant physiological parameters. The models often take the form of a simple functional relationship between two variables, or a set of coupled differential equations. The course tries to show where the equations come from and lead to: what assumptions are needed and what simple and robust conclusions can be drawn.

Further details and online resources

SYLLABUS

Physical and chemical principles (4L A. Kabla)

• Molecular transport, diffusion, osmotic pressure
• Chemical reactions, law of mass action, kinetics
• Enzyme catalysis, Michaelis-Menten model, cooperativity.
• Gases, partial pressures and solubility

Electrophysiology (5L M. Lengyel)

• Biophysical bases of cellular electrogenesis and basic ingredients of the equivalent circuit model.
• Action potential generation in neurons: Hodgkin-Huxley model.
• Phase plane analysis;reduced models,extension to bursting and pacemaking activity
• Signal propagation along dendritic and axonal projections, and across chemical and electrical synapses. .

Blood Physiology (3L A. Kabla)

• Blood physiology, composition
• Gas storage in red blood cells
• Blood rheology, Cason equation, flow in capilleries

Physiological transport systems (4L A. Kabla)

• Circulatory system, heart, cardiac output, arterial pulse
• Vessel compliance, pulsatile flow profile
• flow in caplliery beds, filtration
• Respiratory system, gas exchange in the lungs, ventilation-perfusion

COURSEWORK

Physiology of speech production. Vocal tract acoustics & dynamics of the vocal folds.

OBJECTIVES

On finishing this module the student will:

• have a basic grasp of what functions are necessary for a living organism
• have an overview of the modelling techniques that are used to understand those functions

REFERENCES

Please see the Booklist for Part IIA Courses for module references.

Last updated: May 2012