All Outputs (31)

Pushed and pulled fronts in a discrete reaction-diffusion equation (2015)
Journal Article
King, J. R., & O'Dea, R. D. (2015). Pushed and pulled fronts in a discrete reaction-diffusion equation. Journal of Engineering Mathematics, https://doi.org/10.1007/s10665-015-9829-3

We consider the propagation of wave fronts connecting unstable and stable uniform solutions to a discrete reaction-diffusion equation on a one-dimensional integer lattice. The dependence of the wavespeed on the coupling strength µ between lattice poi... Read More about Pushed and pulled fronts in a discrete reaction-diffusion equation.

A geometric network model of intrinsic grey-matter connectivity of the human brain (2015)
Journal Article
Lo, Y.-P., O'Dea, R. D., Crofts, J. J., Han, C. E., & Kaiser, M. (2015). A geometric network model of intrinsic grey-matter connectivity of the human brain. Scientific Reports, 5, Article e15397. https://doi.org/10.1038/srep15397

Network science provides a general framework for analysing the large-scale brain networks that naturally arise from modern neuroimaging studies, and a key goal in theoretical neuroscience is to understand the extent to which these neural architecture... Read More about A geometric network model of intrinsic grey-matter connectivity of the human brain.

A multiscale analysis of nutrient transport and biological tissue growth in vitro (2014)
Journal Article
O'Dea, R. D., Nelson, M. R., El Haj, A., Waters, S. L., & Byrne, H. M. (2014). A multiscale analysis of nutrient transport and biological tissue growth in vitro. Mathematical Medicine and Biology, https://doi.org/10.1093/imammb/dqu015

In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenisation method to accommodate explicitly the influence of the underlying microscale structur... Read More about A multiscale analysis of nutrient transport and biological tissue growth in vitro.

The interplay between tissue growth and scaffold degradation in engineered tissue constructs (2013)
Journal Article
O'Dea, R. D., Osborne, J., El Haj, A., Byrne, H., & Waters, S. (2013). The interplay between tissue growth and scaffold degradation in engineered tissue constructs. Journal of Mathematical Biology, 67(5), https://doi.org/10.1007/s00285-012-0587-9

In vitro tissue engineering is emerging as a potential tool to meet the high demand for replacement tissue, caused by the increased incidence of tissue degeneration and damage. A key challenge in this field is ensuring that the mechanical properties... Read More about The interplay between tissue growth and scaffold degradation in engineered tissue constructs.

Spreading dynamics on spatially constrained complex brain networks (2013)
Journal Article
O'Dea, R. D., Crofts, J. J., & Kaiser, M. (2013). Spreading dynamics on spatially constrained complex brain networks. Interface, 10(81), https://doi.org/10.1098/%E2%80%8Brsif.2013.0016

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics, and has been widely undertaken. Typically, however, networks employed in theoretical studies bear... Read More about Spreading dynamics on spatially constrained complex brain networks.

Continuum limits of pattern formation in hexagonal-cell monolayers (2012)
Journal Article
O'Dea, R. D., & King, J. R. (2012). Continuum limits of pattern formation in hexagonal-cell monolayers. Journal of Mathematical Biology, 64(3), https://doi.org/10.1007/s00285-011-0427-3

Intercellular signalling is key in determining cell fate. In closely packed tissues such as epithelia, juxtacrine signalling is thought to be a mechanism for the generation of fine-grained spatial patterns in cell differentiation commonly observed in... Read More about Continuum limits of pattern formation in hexagonal-cell monolayers.

The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling (2011)
Journal Article
O'Dea, R. D., & King, J. R. (2013). The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling. Mathematical Medicine and Biology, 30(2), https://doi.org/10.1093/imammb/dqr028

Juxtacrine signalling mechanisms are known to be crucial in tissue and organ development, leading to spatial patterns in gene expression. We investigate the patterning behaviour of a discrete model of juxtacrine cell signalling due to Owen \& Sherrat... Read More about The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling.

Multiscale analysis of pattern formation via intercellular signalling (2011)
Journal Article
O'Dea, R. D., & King, J. R. (2011). Multiscale analysis of pattern formation via intercellular signalling. Mathematical Biosciences, 231(2), https://doi.org/10.1016/j.mbs.2011.03.003

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adj... Read More about Multiscale analysis of pattern formation via intercellular signalling.

The influence of bioreactor geometry and the mechanical environment on engineered tissues (2010)
Journal Article
Osborne, J., O'Dea, R. D., Whiteley, J., Byrne, H., & Waters, S. (2010). The influence of bioreactor geometry and the mechanical environment on engineered tissues. Journal of Biomechanical Engineering, 132(5), Article 051006. https://doi.org/10.1115/1.4001160

A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium and porous scaffold are treated as distinct phases. The bioreactor system is... Read More about The influence of bioreactor geometry and the mechanical environment on engineered tissues.

A multiphase model for tissue construct growth in a perfusion bioreactor (2010)
Journal Article
O'Dea, R. D., Waters, S. L., & Byrne, H. M. (2010). A multiphase model for tissue construct growth in a perfusion bioreactor. Mathematical Medicine and Biology, 27(2), https://doi.org/10.1093/imammb/dqp003

The growth of a cell population within a rigid porous scaffold in a perfusion bioreactor is studied, using a three phase continuum model of the type presented by Lemon et al. (2006, Multiphase modelling of tissue growth using the theory of mixtures.... Read More about A multiphase model for tissue construct growth in a perfusion bioreactor.

A two-fluid model for tissue growth within a dynamic flow environment (2008)
Journal Article
O'Dea, R. D., Waters, S. L., & Byrne, H. M. (2008). A two-fluid model for tissue growth within a dynamic flow environment. European Journal of Applied Mathematics, 19, https://doi.org/10.1017/S0956792508007687

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture... Read More about A two-fluid model for tissue growth within a dynamic flow environment.