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Mathematical models for cancer invasion

School of Mathematics and Physics | PHD
Applications are now CLOSED
Funding
Funded
Reference Number
MAP/2020/29
Application Deadline
14 February 2020
Start Date
1 October 2020

Overview

Cancer cell migration is an essential stage in the development and expansion of tumours and their metastases. Once a malignant tumour arises in some part of the body, it can grow and make its way through the surrounding tissue matrix in order to reach the blood vessels. After transportation across the bloodstream and subsequent extravasation, tumour cells colonise distant sites where further neoplasms emerge. This process is known as metastasis.

Cancer is a very complicated illness. Construction of mathematical models describing
growth and dispersion of cancer cells and their analytical and numerical study can contribute
to a better understanding of the involved biological phenomena, enable predictions about the
development and the extent of a tumour, and even suggest approaches to therapy improvements.
Evolution equations are among the most convenient and versatile modelling tools in this
context. They allow to include different effects as ’building blocks’ and can be treated analytically as well as numerically.
A reasonable minimal model for tumour invasion is obtained by coupling a reaction-diffusiontransport PDE for the density of the tumour with an ODE for the density of the surrounding
tissue. Further components and various nonlinear effects could be introduced, such as: nonlinear diffusion, transport due to taxis (directed movement along the gradient of an attracting/repelling substance), nonlocality (in form of integral terms), modelling on different scales,
etc. The resulting mixed systems of equations of different types (e.g., PDEs and ODEs) are
highly nontrivial and not as yet well-studied. Often, new ideas are required in order to attack
them analytically.
The goal of this project is thus to develop and investigate some systems for tumour invasion
analytically. Performing numerical simulations, in order to illustrate the possible behaviour
of solutions, would be welcome as an addition, but this is not mandatory.
Prerequisites
For this project solid knowledge of and inclination for mathematical analysis is indispensable.
General acquaintance with PDEs is necessary. Even more important is to be familiar with
basic tools from analysis in infinite dimensional spaces (compactness, weak convergence, linear and compact operators, etc.), as well as with integration theory (Lebesgue measure and
integral).

Funding Information

Project Summary
Supervisor

Dr Anna Zhigun


Mode of Study

Full-time: 3 years


Apply now Register your interest

Mathematics overview

The Mathematical Research Centre conducts world-class research in the following areas: Algebra, Analysis, Operator Algebras, Algebraic Topology, Topological Data Analysis, PDEs, Survival Analysis, Bayesian Networks, Data Analytics and Operational Research. It maintains vibrant international links with a large number of researchers around the globe and regularly hosts international conferences and research visitors.

List of researchers, their interests and upcoming PhD projects can be found at:
https://web.am.qub.ac.uk/wp/msrc/.


Mode of study / duration
Registration is on a full-time or part-time basis, under the direction of a supervisory team appointed by the University. You will be expected to submit your thesis at the end of three years of full-time registration for PhD, or two years for MPhil (or part-time equivalent).

Mathematics Highlights
Industry Links
  • The School has many industry links, some of which are with Seagate Technology R&D, Andor Technology and AVX Ltd. Many of our graduates take up positions with these companies in posts such as Statistical Analysis Programmer, Trainee Accountant, Financial Engineer and Business Analyst.
Career Development
  • Graduates from the School take up employment through a number of companies such as Allstate, AquaQ Analytics, Citigroup, Deloitte, PwC, Randox, Seagate and UCAS.
World Class Facilities
  • Since 2014, the School has invested over £12 million in new world-class student and staff facilities. Maths and Physics students now have their own teaching centre that opened in 2016 housing experimental physics laboratories, two large computer rooms for mathematical simulations and student study plus a student interaction area.
Key Facts

  • Students will have access to our facilities, resources and our dedicated staff. The School of Maths & Physics is one of the largest Schools in the University. Staff are involved in cutting-edge research that spans a multitude of fields.
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Course content

Research Information

Research Themes
Information on the research interests and activities of academics in the Mathematical Science Research Centre can be found at https://web.am.qub.ac.uk/wp/msrc/. These interests fit into the themes: Algebra, Analysis, Data Science, Optimization and Operational Research, Partial Differential Equations, Statistics, Topology and Geometry.

Career Prospects

Introduction
Mathematical and statistical skills are in great demand in the economy, particularly the advanced skills developed at the PhD level.

Employment after the Course
As well as continuing in research careers, our PhD graduates have also gone on to work in finance, computing, data analysis, management and teaching. Our advisors will be happy to provide further information on the career prospects arising from your chosen research area. Further information on careers can be obtained from the School and the Faculty.

People teaching you

Dr David Barnes
Postgraduate Advisor - Mathematical Sciences Research Centre

Email: d.barnes@qub.ac.uk

Professor Ivan Todorov
Director of Research - Mathematical Sciences Research Centre

Email: i.todorov@qub.ac.uk

Learning Outcomes

Course structure

0

Facilities
Students will enjoy the benefits of modern practical laboratories, extensive computer facilities and interactive spaces.

Entrance requirements

Graduate
The minimum academic requirement for admission to a research degree programme is normally an Upper Second Class Honours degree from a UK or ROI HE provider, or an equivalent qualification acceptable to the University. Further information can be obtained by contacting the School.

International Students

For information on international qualification equivalents, please check the specific information for your country.

English Language Requirements

Evidence of an IELTS* score of 6.0, with not less than 5.5 in any component, or an equivalent qualification acceptable to the University is required. *Taken within the last 2 years.

International students wishing to apply to Queen's University Belfast (and for whom English is not their first language), must be able to demonstrate their proficiency in English in order to benefit fully from their course of study or research. Non-EEA nationals must also satisfy UK Visas and Immigration (UKVI) immigration requirements for English language for visa purposes.

For more information on English Language requirements for EEA and non-EEA nationals see: www.qub.ac.uk/EnglishLanguageReqs.

If you need to improve your English language skills before you enter this degree programme, INTO Queen's University Belfast offers a range of English language courses. These intensive and flexible courses are designed to improve your English ability for admission to this degree.

  • Academic English: an intensive English language and study skills course for successful university study at degree level
  • Pre-sessional English: a short intensive academic English course for students starting a degree programme at Queen's University Belfast and who need to improve their English.

Tuition Fees

Northern Ireland (NI) £4,407
England, Scotland or Wales (GB) £4,407
Other (non-UK) EU £4,407
International £16,950

More information on postgraduate tuition fees.

Mathematics costs

There are no specific additional course costs associated with this programme.

Additional course costs

All Students

Depending on the programme of study, there may also be other extra costs which are not covered by tuition fees, which students will need to consider when planning their studies . Students can borrow books and access online learning resources from any Queen's library. If students wish to purchase recommended texts, rather than borrow them from the University Library, prices per text can range from £30 to £100. Students should also budget between £30 to £100 per year for photocopying, memory sticks and printing charges. Students may wish to consider purchasing an electronic device; costs will vary depending on the specification of the model chosen. There are also additional charges for graduation ceremonies, and library fines. In undertaking a research project students may incur costs associated with transport and/or materials, and there will also be additional costs for printing and binding the thesis. There may also be individually tailored research project expenses and students should consult directly with the School for further information.

How do I fund my study?
1.PhD Opportunities

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2.Doctoral Training Centres at Queen's

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3.PhD loans

The Government offers doctoral loans of up to £26,445 for PhDs and equivalent postgraduate research programmes for English- or Welsh-resident UK and EU students, £10,000 for students in Scotland and up to £5,500 for Northern Ireland students.

4.International Scholarships

Information on Postgraduate Research scholarships for international students.

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How to Apply

Apply using our online Postgraduate Applications Portal go.qub.ac.uk/pgapply and follow the step-by-step instructions on how to apply.

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