PhD Studentships in the Groups “Analysis and Partial Differential Equations” and “Numerical Analysis and Scientific Computing”
Type of award
Postgraduate Research
PhD project
This is a project in the broad area of applied and numerical analysis for nonlinear partial differential equations with applications to cell biology.
Force generation by biological cells underpins all cellular functions. However, accurate measurement of cellular forces is challenging due to the spatial scales which make direct experimental measurements infeasible. Traction force microscopy (TFM) attempts to sidestep this challenge by estimating forces indirectly from deformations of the medium upon which the cells exert force.
Crucial to this estimation is the formulation of an appropriate constitutive law relating force generation to medium deformation as well as the formulation, analysis & approximation of a well-posed inverse problem to recover forces from the observed deformation. TFM is used to estimate forces generated by cells in vitro on synthetic substrates where the mechanics is approximated by a linearly elastic law. However, nonlinear constitutive laws arise in most practical settings, e.g. force generation by cells in the fibrous extra cellular medium. In the in vitro setting, when the forces exerted are large, the linear regime is no longer appropriate, such as when cells cause wrinkling in their vicinity which can only be captured by nonlinear models. A further challenge arises in the numerical approximation of the inverse problem which mandates the solution of the forward model. This is well understood in the linear case but much less studied and more challenging for nonlinear models.
This project seeks to develop a framework for the formulation of well-posed inverse problems related to traction force microscopy (TFM). We will focus on energetic models for the mechanics of the medium which involve appropriate notions of convexity (e.g. polyconvexity, quasiconvexity) such that the forward problem is well-posed but nonetheless allow for enough generality to be applicable. We will also develop, analyse & implement numerical methods for the approximation of the inverse problem. The project would be suitable for a student interested in some, or all, of the following areas: analysis of PDEs, continuum modelling, finite element methods, numerical analysis and mathematical biology.
Amount
- Fully-paid tuition fees for three & a half years at the home fee status.
- A tax-free bursary for living costs for three and a half years (£18,622 pa in 2023/24).
- Additional financial support is provided to cover short-term & long-term travel.
- If you are not a UK national, nor an EU national with UK settled/pre-settled
status, you will need to apply for a student study visa before admission.
Eligibility
Applicants must hold, or expect to hold, at least a UK upper second class degree (or non-UK equivalent qualification) in Physics/Mathematics, or a closely-related area, or else a lower second class degree followed by a relevant Master's degree.
To apply, please click the 'Apply' button, above.
Select the PhD in Physics/Mathematics, with an entry date of September 2024.
In the Finance & Fees section, state that you wish to be considered for studentship no MPS/2024/KOU
We advise early application as the position will be filled as soon as a suitable applicant can be found.
Contact us
If you have practical questions about the progress of your on-line application or your eligibility, contact [email protected]
For academic questions about the project, contact Dr Koumatos at [email protected] or Dr Venkataraman at [email protected]