Postgraduate taught 

Mathematics / Applied Mathematics MSc

5M: Biological and Physiological Fluid Dynamics MATHS5044

  • Academic Session: 2019-20
  • School: School of Mathematics and Statistics
  • Credits: 20
  • Level: Level 5 (SCQF level 11)
  • Typically Offered: Either Semester 1 or Semester 2
  • Available to Visiting Students: No
  • Available to Erasmus Students: No

Short Description

A knowledge of fluid mechanics is essential in understanding how living creatures work and what happens in cardiovascular diseases. This module will introduce some to the main research areas in this exciting and rapidly-growing subject,including topics from blood flow in large and small vessels, respiration, and the swimming of micro-organisms.

Timetable

2 hours of lectures a week, over 11 weeks.

1 hour tutorial a week over 10 weeks (or equivalent)

Requirements of Entry

Mandatory Entry Requirements

either MATHS 4102 - 4H: Fluid Mechanics

or MATHS5068 - 5E: Fluid Mechanics

 

Recommended Entry Requirements

Assessment

Assessment

 

100% Final Exam

 

 

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? No

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

Course Aims

The course aims to introduce students to modern applications of fluid mechanics in biology and physiology.

A range of problems in biological and physiological fluid dynamics will be covered together with general principles used in constructing mathematical models. Specific topics include:

1. Blood flow in large arteries and veins.

2. Respiration.

3. Flow in small blood vessels.

4. Swimming of micro-organisms.

5. Bioconvection.

Intended Learning Outcomes of Course

By the end of this course, students will be able to:

 

1. Derive the equations of motion for pulse propagation in the large arteries.

 

2. Apply linear wave theory to pulse propagation in the large arteries.

 

3.  Use Riemann invariants and the method of characteristics to predict shock formation in the large arteries.

 

4. Derive and explain Womersley's theory for the velocity pulse profile

 

5. Relate the flow of blood to atherosclerosis.

 

6. Analyse the theories of pressure drop in inhalation and exhalation.

 

7. Explain wheezing.

 

8. Apply low Reynolds number theory to the motion of blood cells through capillaries.

 

9. Calculate the swimming velocity of a sheet and relate this to swimming by ciliates.

 

10. Use and resistive-force theory to analyse the swimming of bacteria and spermatozoa.

 

11. Derive equations for bioconvection and predict the onset of pattern formation using linear stability theory.

 

12. Criticise the above theories and identify their strengths and weaknesses.

Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.