Project description: Mathematical models in biomedical engineering, for e.g. computational models of haemodynamics, often have a large number of unknown parameters. These parameters must be estimated through clinical measurements acquired individually in each patient. However, it is not clear which measurements are most informative about the parameters and which parameters are most relevant to answer a given clinical question. This project will develop a framework for this problem of ‘optimal design’ through recent developments in probabilistic analysis and information theory [1,2,3] with a particular focus on problems encountered in biomedical engineering. Furthermore, within the developed framework, this project will assess how, and if, virtual subjects (i.e. computational models) can be used to replace real subjects in a clinical trial.
Location: Zienkiewicz Centre for Computational Engineering, Bay Campus, Swansea University.
Primary supervisor: Dr. Sanjay Pant
 S. Pant. Information sensitivity functions to assess parameter information gain and identifiability of dynamical systems, Journal of The Royal Society Interface, 15:142, 20170871, 2018.  D. Lombardi and S. Pant. A non-parametric k-nearest neighbour entropy estimator. Physical Review-E, 93:013310, 2016.  S. Pant and D. Lombardi. An information-theoretic approach to assess practical identifiability of parametric dynamical systems. Mathematical Biosciences, 268:66–79, 2015.
Eligibility Candidates should hold a first or upper second class honours degree (or its equivalent) in engineering, mathematics, or physics, or a Master’s degree in a subject area related to the project.
A strong background in numerical methods and fluid mechanics is required. Knowledge/experience of programming in at least one compiled language (C, C++, or Fortran) and one interpreted language (MATLAB or Python) is essential. An interest in physiology and probabilistic modelling is desirable.
Studentships funded by EPSRC are subject to UK/EU residency eligibility.
This scholarship covers the full cost of UK/EU tuition fees and an annual stipend of £14,777.