- Australian Research Council Discovery Project (2020-2022) Mathematical models of 4D spheroids: mathematical model development and parameterisation. Matthew Simpson, Nikolas Haass and Michael Plank.
- MATRIX Mathematical Workshops (2020). Spatial structure in population models: bridging theory and data. Matthew Simpson, Michael Plank, Rachelle Binny and Maria Bruna.
- USA Aerospace Research and Development Research Program (2017-2018). Cellular hedging. Kevin Burrage and Matthew Simpson.
- Royal Society International Exchanges Scheme (2017-2019) Single-file diffusion in networks. Francis Woodhouse and Matthew Simpson.
- Banff International Research Station (2018) Mathematical and statistical challenges in bridging model development, parameter identification and model selection in the biological sciences. Ruth Baker, Daniel Coombs and Matthew Simpson.
- Australian Research Council Discovery Project (2017-2019) Mathematical models of cell migration in three-dimensional living tissues. Matthew Simpson, Ruth Baker and Michael Plank.
- Australian Research Council Future Fellowship (2014-2018) New data-driven mathematical models of collective cell motion. Matthew Simpson.
- Australian Research Council Discovery Project (2014-2016) A new hierarchy of mathematical models to quantify the role of ghrelin during cell invasion. Matthew Simpson, Scott McCue, Adrian Herington, Lisa Chopin and Philip Maini.
- CRC for Wound Management Innovation Project Grant (2013-2015) Cell clustering in wound healing. Matthew Simpson and Sean McElwain.
- Australian Research Council Discovery Project (2012-2014) Modelling cell invasion incorporating the epithelial to mesenchymal transition: Exploring therapies to control wound healing and cancer progression. Matthew Simpson, Sean McElwain, David Leavesley and Ruth Baker.
- Marsden Fund New Zealand (2012-2014) Cell invasion: Interactions across scales. Michael Plank, Matthew Simpson and Richard Law.
- Royal Society International Exchanges Scheme (2012-2014) Multiscale models of cell motility for populations with variable cell shape. Ruth Baker and Matthew Simpson.
- Australian Research Council Discovery (2006-2009) Multiscale modelling of cell migration in developmental biology. Kerry Landman, Barry Hughes and Matthew Simpson. Australian Postdoctoral fellowship to Matthew Simpson.
- Australian Research Council Small Grant (2001-2001) Experimental and numerical investigation of unconfined flow systems with seepage face boundaries. Prabhakar Clement and Matthew Simpson.
Potential Student Projects
I have a range of projects available for summer vacation, Honours and PhD students. Some of these include:
- Lattice-free models of collective cell migration, proliferation and differentiation processes.
- Developing continuum-limit descriptions for patchy experimental data using discrete models of collective cell behaviour and moment dynamics descriptions.
- Applying mean particle lifetime and mean action time concepts to provide new insight into mathematical models of heat and mass transfer with applications from civil and chemical engineering.
- Multiscale modelling of collective cell migration in complex microenvironments.
- New interpretations of observations of moving cell fronts using partial differential equations related to position-jump and velocity-jump discrete models.
Current projects that my group are working on include:
- Multiscale modelling of collective cell spreading in two-dimensional barrier assays. Key publications: Simpson et al (Royal Society Interface 2013), Treloar and Simpson (PLOS ONE 2013).
- Lattice-free models of collective cell migration and proliferation. Key publications: Plank and Simpson (Royal Society Interface 2012).
- Moment dynamics models of collective cell behaviour. Key publications: Baker and Simpson (Physical Review E 2010), Simpson et al. (Bulletin of Mathematical Biology, 2013).
- Mean particle lifetime and mean action time for general diffusive processes. Key publications: Ellery, Simpson, McCue and Baker (Physical Review E 2012), Ellery, Simpson, McCue and Baker (Physical Review E 2012).
- Quantifying the role of cell-to-cell adhesion in collective cell behaviour. Key publications: Simpson, Towne, McElwain and Upton (Physical Review E 2010).
- Velocity-jump processes of cell migration and cell proliferation with crowding effects. Key publications: Treloar, Simpson and McCue (Physical Review E, 2011), Treloar, Simpson and McCue (Journal of Physics A: Mathematical and Theoretical 2013), Simpson, Foy and McCue (Mathematical Biosciences, 2013).