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Unit information: Mathematical Modelling in Physiology and Medicine in 2021/22

Unit name Mathematical Modelling in Physiology and Medicine
Unit code EMATM0007
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Marucci
Open unit status Not open

Basic knowledge of non-linear systems, stability analysis and bifurcation theory e.g. EMAT33100 or equivalent



School/department Department of Engineering Mathematics
Faculty Faculty of Engineering

Description including Unit Aims

This unit aims to introduce mathematicians and engineers to some of the latest thinking in cell biology, neuroscience, systems and synthetic biology. It also aims to introduce modern mathematical techniques based on differential equations for understanding the dynamics of biological systems via numerical continuation, using the software XPP-aut. It will be shown how to derive mathematical equations from the basic laws of mass action that describe biochemical reactions, and therefore how certain chemical motifs carry out certain dynamical functions. A range of topics including ion channels and synthetic gene regulatory networks will be introduced using a combination of simple and advanced techniques.


  • To give students an appreciation of how mathematical models can be useful to understand complex biological processes.
  • To provide a point of entry into the modern research literature in cell biology, in systems and synthetic biology.
  • To explore modern mathematical techniques based on differential equations for understanding the dynamics of biological systems.

Intended Learning Outcomes

By the end of this unit students will have:

  1. an understanding of cell biology in terms of DNA, RNA, enzymes and proteins and the complex interactions among them, including the dynamics of larger, but basic, functional components such as ion channels.
  2. an appreciation of different forms of solution to biochemical differential equations, and the ability to simulate them.
  3. the ability to derive differential equations from biochemical reactions using the law of mass action, and Michaelis-Menten kinetics.
  4. an appreciation for the range of approaches to modelling a biological system, their comparative features, and how to choose among them.
  5. a grasp of the concept of synthetic biological networks and their functions.
  6. an understanding of excitability and how this can describe neuron behaviour.
  7. knowledge of the software XPP-aut for numerical continuation.

Teaching Information

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, practical activities supported by drop-in sessions, problem sheets and self-directed exercises.

Assessment Information

1 Summative Assessment, 100% - Coursework. This will assess all ILOs.


If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. EMATM0007).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.