Undergraduate Teaching 2019-20

Engineering Tripos Part IIA, 3G2: Mathematical Physiology, 2017-18

Engineering Tripos Part IIA, 3G2: Mathematical Physiology, 2017-18

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Module Leader

Dr A Kabla

Lecturers

Dr A Kabla and Prof M Lengyel

Lab Leader

Dr A Kabla

Timing and Structure

Lent term. 16 lectures.

Aims

The aims of the course are to:

  • Provide a basic understanding of what functions are necessary for a living organism, and how they are achieved.
  • Provide an overview of the modelling techniques that are used to understand those functions.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Express physical, mechanical and chemical principles in the context of physiological processes
  • Understand underlying assumptions and check their validity
  • Use mathematical and computational tools to identify and discuss solutions

Content

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.

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 T OLeary)

  • 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. 

Learning objectives: 

  • Learn about how vocal folds generate sound
  • Understand the process of modeling a complex physiological process, from hypothesis to numerical solutions.
  • Learn how to solve numerically non-linear differential equations.
  • Develop Python/Matlab skills

Practical information:

  • Sessions will take place in the EIETL, around week 3.
  • This activity involves preliminary work (about 1h).

Full Technical Report:

Students will have the option to produce a Full Technical Report (FTR).

Booklists

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

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

 
Last modified: 07/08/2017 08:34