Mathematical Physiology
### 3G2 Mathematical Physiology

### Lecture and coursework materials

### Supervisions

### Topics

### Coursework

### Reading list

**timing:** Lent term, 16 lectures

**assessment:** written exam (1.5 hours) at the start of Easter term

**module leader:** Alexandre Kabla (ajk61)

see official syllabus at the Teaching Office website

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.

lecturer | topic | handouts | example sheet |
---|---|---|---|

Dr. Alexandre Kabla | Physical and chemical principles | Handouts | examples paper 0 (IB revisions) examples paper 1 solutions |

Dr. Máté Lengyel | Electrophysiology
| introduction: slides
channel currents: slides notes resting membrane potential: slides action potential: slides propagation: slides | example questions |

Dr. Alexandre Kabla | Physiological systems
| Handouts 2
Handouts 3 |
examples paper 2
solutions (1->7) solutions (8->11) |

Dr. Alexandre Kabla | Coursework: Speech Production sign-up sheet | lab description VTDemo.exe Matlab file default_params.m Matlab file run_oscil.m | Supporting material: Matlab ode45 Help file Anonymous functions References: Titze (1988) Laje et al. (2001) |

Please use the link below (click on the dates) to sign up to exactly one of the supervision time slots. Each time slot can fit up to 4 students on a first-come, first-served basis. Make sure you use your CRSid for signing up. Note: if you so wish, it is possible to prevent others editing your choice of supervision slot by signing into a (free) Doodle account before entering your CRSid & time choice.

Electrophysiology: March 7, 10, 11, 12, 13, 14: example paper

**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

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

*(Only selected chapters of these books are covered during the course.)*

**Main text book**

Keener J, Sneyd J. Mathematical Physiology. Springer, 2004.

**Additional reading**

Berg et al. Biochemistry (6th edition). W. H. Freeman and Co., 2007.

Kandel ER, Scwartz JH, Jessel TM. Principles of Neural Science (4th edition). McGraw-Hill, 2000.

see also Booklist for IIA courses