# MATHEMATICAL BIOLOGY AND PHYSIOLOGY - 2019/0

Module code: MATM040

## Module Overview

Mathematical biology is concerned with using mathematical techniques and models to shed light on the fundamental processes that underly biology. By abstracting biological detail into a formal mathematical setting we can identify what the mechanisms are that drive the observed phenomena, and can make predictions about system behaviour. Looking at a concrete example in cancer biology, it can be shown that tumour growth can be well-described using a simple system of linear partial differential equations. From this system we can then ascertain that tumour growth is initially limited by the availability of nutrients and can predict the result of different treatment methodologies.

To work in this field the mathematical biologist must develop a broad library of models, techniques and experience and be willing to engage with biological detail. They must learn to be conversant with e.g. systems of ordinary differential equations, partial differential equations and discrete models, and to analyse these systems using techniques ranging from stability analysis and phase plane diagrams, to looking for travelling wave solutions and applying asymptotic methods. A key aspect of the work is validating the derived models using experimental results.

### Module provider

Mathematics

DUNLOP Carina (Maths)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 117

Lecture Hours: 33

Semester 1

None.

## Module content

Indicative content includes:

• Introduction to mathematical modelling of biological and physiological problems. This will include basic modelling methodology, dimensional analysis and the need for data analysis and model validation.

• Models without spatial dependence including: discrete models for population genetics; signal-response dynamics and enzyme kinetics; oscillators and excitable systems with application to neurons (Fitzhugh-Nagumo models).

• Spatially dependent models. Diffusion and reaction-diffusion equations: derivation and interpretation. Application including some of morphogenesis, tumour modelling, cell motility and taxis.

• Selection of advanced techniques such as parameter estimation, asymptotic analysis and modelling case studies.

## Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION (2 HOURS) 70
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 10
Coursework ASSESSED COURSEWORK 20

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

• Understanding of the modelling process applied to biological problems.

• The ability to critically select and apply appropriate models and techniques.

• Subject knowledge through the discussion of standard models, their derivations and key parameters.

• Analytical ability through the solution of unseen problems.

Thus, the summative assessment for this module consists of:

• One two hour examination worth 70% of the module mark.

• One in-semester test and

• One piece of assessed coursework

Formative assessment and feedback

Students will receive written feedback via a number of marked coursework assignments over the 11 week period. Students will also receive verbal feedback during modelling classes, and during small group work activities that will take place as integral parts of the lecture.

## Module aims

• To show the power of applying mathematical techniques to biological and physiological problems, illustrating how such an approach can produce results that contribute significantly to biological understanding and thus enable the development of new therapies and technologies.
• To develop the necessary biological and physiological modelling skills for real-world situations.
• Introduce a range of biological models and techniques, and developing an understanding of their applicability in any given context.

## Learning outcomes

 Attributes Developed 001 Understand the process of modelling as applied to biological problems including model validation by comparison with experimental data; KCT 002 Critically select from a range of mathematical techniques as appropriate to the biological application; KCT 003 Apply techniques such as dimensional analysis, asymptotic analysis and stability analysis to problems in biology; KC 004 Analyse and solve a range of biological models including signal-response dynamics, discrete biologically inspired models, diffusion-based models, and models for tumour progression. KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Provide a detailed introduction to mathematical biological and physiological modelling.

• Develop the ability to critically select appropriate models and mathematical techniques for use in this field.

• Provide experience of applying advanced methods to analyse and solve biologically inspired models.

The learning and teaching methods include:

• 3 x 1 hour contact hours per week for 11 weeks split between lectures and modelling classes.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.