Research Repository

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A multiphase multiscale model for nutrient limited tissue growth (2018)
Journal Article
Holden, E., Collis, J., Brook, B. S., & O'Dea, R. D. (2018). A multiphase multiscale model for nutrient limited tissue growth. ANZIAM Journal, 59(4), doi:10.1017/S1446181118000044. ISSN 1446-1811

In this work, an effective macroscale description is derived for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effect... Read More

Effective equations governing an active poroelastic medium (2017)
Journal Article
Collis, J., Brown, D., Hubbard, M. E., & O'Dea, R. D. (2017). Effective equations governing an active poroelastic medium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), doi:10.1098/rspa.2016.0755. ISSN 1364-5021

In this work we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation, and transport in an active poroelastic... Read More

Microstructural influences on growth and transport in biological tissue—a multiscale description (2017)
Book
Irons, L., Collis, J., & O'Dea, R. D. (2017). Microstructural influences on growth and transport in biological tissue—a multiscale description. In S. M. Becker (Ed.), Modeling of microscale transport in biological processesAcademic Press. doi:10.1016/B978-0-12-804595-4.00012-2

The detailed understanding of growth and transport dynamics within biological tissue is made particularly challenging by the complex and multiscale nature of this medium. For this reason so-called effective descriptions are frequently sought. These o... Read More

A multiscale analysis of drug transport and response for a multiphase tumor model (2016)
Journal Article
Collis, J., Hubbard, M. E., & O'Dea, R. D. (in press). A multiscale analysis of drug transport and response for a multiphase tumor model. European Journal of Applied Mathematics, doi:10.1017/S0956792516000413. ISSN 0956-7925

In this article we consider the spatial homogenization of a multi- phase model for avascular tumour growth and response to chemother- apeutic treatment. The key contribution of this work is the derivation of a system of homogenized partial differenti... Read More

Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth (2016)
Journal Article
Collis, J., Hubbard, M. E., & O'Dea, R. D. (2016). Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. Computer Methods in Applied Mechanics and Engineering, 309, doi:10.1016/j.cma.2016.06.015. ISSN 0045-7825

In this work we consider the discretization of a recently formulated (Collis et al., [22]) multiscale model for drug- and nutrient-limited tumour growth. The key contribution of this work is the proposal of a discontinuous Galerkin finite element sch... Read More

Goal-oriented a posteriori error estimation for the travel time functional in porous media flows (2015)
Journal Article
Cliffe, A., Collis, J., & Houston, P. (2015). Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. SIAM Journal on Scientific Computing, 37(2), doi:10.1137/140960499. ISSN 1064-8275

In this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows. The key application of this work is in the safety assessment of ra... Read More