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- Helen M. Byrne, Luigi Preziosi
- Mathematical medicine and biology : a journal ofâ€¦
- 2003

In this paper the theory of mixtures is used to develop a two-phase model of an avascular tumour, which comprises a solid, cellular, phase and a liquid phase. Mass and momentum balances which areâ€¦ (More)

- TomÃ¡s AlarcÃ³n, Helen M. Byrne, Philip K. Maini
- Multiscale Modeling & Simulation
- 2005

We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction betweenâ€¦ (More)

- Helen M. Byrne, Dirk Drasdo
- Journal of mathematical biology
- 2009

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by aâ€¦ (More)

- Markus R. Owen, Helen M. Byrne, Claire E. Lewis
- Journal of theoretical biology
- 2004

Poor drug delivery and low rates of cell proliferation are two factors associated with hypoxia that diminish the efficacy of many chemotherapeutic drugs. Since macrophages are known to migrateâ€¦ (More)

- Christopher J. W. Breward, Helen M. Byrne, Claire E. Lewis
- Bulletin of mathematical biology
- 2003

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass andâ€¦ (More)

- Helen M. Byrne, John R. King, D. L. Sean McElwain, Luigi Preziosi
- Appl. Math. Lett.
- 2003

- Helen M. Byrne
- Nature Reviews Cancer
- 2010

This Timeline article charts progress in mathematical modelling of cancer over the past 50 years, highlighting the different theoretical approaches that have been used to dissect the disease and theâ€¦ (More)

- Joe M Pitt-Francis, Pras Pathmanathan, +16 authors David J Gavaghan
- Computer Physics Communications
- 2009

Article history: Received 31 March 2009 Received in revised form 29 June 2009 Accepted 1 July 2009 Available online 26 August 2009 PACS: 87 87.19.Hh 87.19.xj

- Trachette L. Jackson, Helen M. Byrne
- Mathematical biosciences
- 2002

In this paper, a mathematical modeling framework is presented which describes the growth, encapsulation, and transcapsular spread of solid tumors. The model is based on the physical forces andâ€¦ (More)

- Greg Lemon, John R. King, Helen M. Byrne, Oliver E. Jensen, Kevin M. Shakesheff
- Journal of mathematical biology
- 2006

This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering.â€¦ (More)