Since September 2020, I have been studying for a PhD in the School of Mathematical Sciences at the University of Nottingham, which I hope to finish in May 2024.

My project title is currently ‘Finite Element Methods for Fluid-Structure Interaction Problems‘ and is supervised by Paul Houston, Matthew Hubbard, and Reuben O’Dea. The focus of the project is to accurately characterise maternal blood flow and the corresponding nutrient transport in the human placenta, which we numerically simulate using discontinuous Galerkin finite element methods with an in-house package called AptoFEM. We work closely with collaborators in MRI Physics and Life Sciences, for which we can gather useful parameter and validation data; in particular, we have developed numerical simulations for MRI of placental flow.

Please take a look below at the reports and talks for more info. Through the PhD, I have also taught the first-year Mathematics for Natural Sciences Python course (MTHS1001), and provided help in workshops on the fourth-year mathematics C++ course (MATH4064).

Reports

PhD Third Year Report

  • Detailed overview of placenta literature
  • Numerical methods of DGFEMs introduced
  • Blood flow modelling as porous medium using Navier-Stokes-Darcy
  • Simple blood flow simulations in representative 2D geometries, with comparison between a selection of possible flow models
  • Corresponding nutrient transport simulations
  • Variation of structural parameters and how this affects nutrient uptake
  • Numerical MRI: generating MRI signals from a simulated flow field

PhD Second Year Report

  • Broad overview of FEM and placenta literature
  • Blood flow modelling as porous medium
  • Simple blood flow simulations in representative 2D geometries
  • Synthetic MRI generation, toward model validation
  • Model development: septal veins, nutrient transport, and variable permeabilit

PhD First Year Report

  • Broad overview of FEM and placenta literature
  • Introduction to hp-FEM
  • DGFEM discretisations of Poisson’s equation and Stokes flow
  • 1D residual error indicators
  • Design of an OOP FEM code

Talks

Placental Haemodynamics (November 2022, February 2023, April 2023, May 2023)

  • Modified version of September 2022 talk
  • Introduction to FEMs, placentas, and porous medium modelling
  • Placentone and 2D placenta slice flow results
  • Flow comparison with septal veins
  • Oxygen transport
  • Immediate next steps

Placental Haemodynamics (September 2022)

  • Modified version of May 2022 talk
  • Introduction to FEMs, placentas, and porous medium modelling
  • Placentone and 2D placenta slice flow results
  • Flow comparison with septal veins
  • Oxygen transport
  • Immediate next steps

Placental Haemodynamics (May 2022)

  • Modified version of December 2021 talk
  • Introduction to FEMs and placentas
  • Modelling of porous media
  • “box-circle” Darcy-Brinkman flow results
  • “inverted-circle-slice-6” Darcy-Brinkman flow results
  • Outlook

Placental Haemodynamics (December 2021)

  • Introduction to FEMs and placentas
  • Modelling of porous media
  • “box-circle” Darcy-Brinkman flow results
  • Outlook

A Recipe for Adaptive hp-FEMs (April 2021)

  • Overview of FEMs
  • Interactive example
  • C++ implementation & numerical experiments
  • hp-adaptive FEMs in action
  • Possible extensions

Outreach Talks

Maths “Careers” Talk (February 2021)

  • Background
  • Experiences
  • Work experiences
  • Day-to-day on the PhD
  • PhD top tips

Teaching

Core and MTHS1001 Python (2020–2022)

  • First year programming
  • Introduction to variables and data structures
  • Basic plotting

MATH4063 Scientific Computation and C++ (2022)

  • Fourth year programming
  • Basic control and data structures
  • Memory management
  • Object-oriented programming