Mathematical Physiology

3G2 Mathematical Physiology

timing: Lent term, 16 lectures
assessment: written exam (1.5 hours) at the start of Easter term
module leader: Alexandre Kabla (ajk61)

Mathematical Physiology
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.

Lecture and coursework materials

lecturertopichandoutsexample sheet
Kabla
external link: Dr. Alexandre Kabla
Physical and chemical principlesexternal link: Handouts external link: examples paper 0 (IB revisions)
external link: examples paper 1
external link: solutions
Lengyel
external link: Dr. Máté Lengyel
Electrophysiology introduction: external link: slides
channel currents: external link: slides external link: notes
resting membrane potential: external link: slides
action potential: external link: slides
propagation: external link: slides
external link: example questions
external link: Dr. Alexandre Kabla Physiological systems external link: Handouts 2
external link: Handouts 3
external link: examples paper 2
external link: solutions (1->7)
external link: solutions (8->11)

external link: Dr. Alexandre KablaCoursework:
Speech Production
external link: sign-up sheet
external link: lab description

external link: VTDemo.exe
external link: Matlab file default_params.m
external link: Matlab file run_oscil.m

Supporting material:
external link: Matlab ode45 Help file
external link: Anonymous functions

References:
external link: Titze (1988)
external link: Laje et al. (2001)


Supervisions

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: external link: March 7, 10, 11, 12, 13, 14: external link: example paper


Topics

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.

Reading list

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

Main text book
Keener
external link: Keener J, Sneyd J. Mathematical Physiology. Springer, 2004.

Additional reading
Berg
external link: Berg et al. Biochemistry (6th edition). W. H. Freeman and Co., 2007.

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


see also external link: Booklist for IIA courses