PhD Studentship in Mathematical and Statistical Neuroscience

Ref: 1399

Mathematical modelling and uncertainty quantification as tools to enable personalised treatment for people with epilepsy

Location: Streatham Campus, University of Exeter, EX4 4QJ

Primary Supervisor:  Professor John R Terry

Secondary Supervisor: Dr D Williamson

A fully funded PhD studentship is available to work with Professor John Terry and Dr Daniel Williamson (University of Exeter). The studentship would suit someone with interests in differential equations, dynamical systems or statistics, with an interest to apply these techniques in the field of neuroscience. Interested candidates are strongly advised to contact Professor John Terry (details below) prior to submitting a full application.

The project has two main aims. The first aim is to understand the relationship between numerical continuation, a technique for mapping out paths of bifurcations in parameter space, and statistical methods in Uncertainty Quantification (UQ) such as emulation and history matching, that can be used to map these paths probabilistically. To achieve this we will start from normal forms of co-dimension one bifurcations and build up to nonlinear models with many parameters and complex bifurcation structures. Through studying and comparing both methods in low dimensional cases where numerical continuation is computationally expensive, we then aim to adapt the UQ methods in order to map paths of bifurcations probabilistically in high dimensional parameter spaces where UQ can efficiently operation but where continuation is infeasible. The second aim is to apply this understanding to make patient specific predictions regarding treatment options for people with epilepsy through fusing mathematical models with clinical datasets recorded using EEG. Here we will use physiologically inspired mathematical models that can replicate the complex waveforms observed in EEG and apply UQ methods such as calibration and history matching in order to characterise seizure evolution in terms of the path through parameter space of the model, whilst accounting for the structural uncertainties present when comparing measurements from real human brains with the outputs of our mathematical models. We will then seek to classify patients based on these identified paths and compare with known clinical outcomes, such as drug responsiveness and seizure remission.

The project will support research funded as part of a large-scale MRC grant entitled "Brain Networks in Epilepsy: Endophenotypes and Generative Models" which is held jointly between the University and Exeter and King's College London. The ideal candidate will have a strong background in mathematics or statistics or a closely aligned discipline (you should hold or be expected to achieve a minimum of  a 2.i undergraduate degree) with an interest in applying theoretical methods in neuroscience. Candidates should be prepared to take part in an interview either in person or via Skype.

Contact for informal enquiries: Professor John R.Terry (J.Terry@exeter.ac.uk)

Application criteria:  Applicants should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in mathematics, statistics or a closely aligned discipline. Masters level experience in mathematics, statistics or computational neuroscience is desirable.

Tuition fees and a stipend of £13,863 for three years are available for eligible UK/EU students

Contact: Postgraduate Research Office emps-pgr-ad@exeter.ac.uk