Learn More
We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe(More)
A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes(More)
Aquaporins are membrane channels that facilitate water movement across cell membranes. In plants, aquaporins contribute to water relations. Here, we establish a new link between aquaporin-dependent tissue hydraulics and auxin-regulated root development in Arabidopsis thaliana. We report that most aquaporin genes are repressed during lateral root formation(More)
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. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue(More)
The nematode Caenorhabditis elegans is the first animal whose genome is completely sequenced, providing a rich source of gene information relevant to metazoan biology and human disease. This abundant sequence information permits a broad-based gene inactivation approach in C. elegans, in which chemically mutagenized nematode populations are screened by PCR(More)
Many solid tumour growth models are formulated as systems of parabolic and/or hyperbolic equations. Here an alternative, two-phase theory is developed to describe solid tumour growth. Versions of earlier models are recovered when suitable limits of the new model are taken. We contend that the multi-phase approach represents a more general, and natural,(More)
The growth of a tumour in a rigid walled cylindrical duct is examined in order to model the initial stages of tumour cell expansion in ductal carcinoma in situ (DCIS) of the breast. A nutrient-limited growth model is formulated, in which cell movement is described by a Stokes flow constitutive relation. The effects on the shape of the tumour boundary of the(More)
A novel real-time quantitative PCR (QPCR) assay is described for monitoring CMV DNA load in clinical specimens using the LightCycler. The assay is rapid (< 40 min), easy to carry out, robust, reliable and is capable of detecting from 10 to over 2 x 10(5) CMV DNA copies with a wide linear range. Amplification and detection occur simultaneously, avoiding the(More)
In this paper we adapt an avascular tumour growth model to compare the effects of drug application on multicell spheroids and on monolayer cultures. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generates volume changes described by a velocity field. The drug is modelled as an externally(More)
The stability of a planar tumour growing into neighbouring tissue is examined and, in particular, its dependence on the properties of the tumour and of the surrounding material studied. An abundant supply of nutrient is assumed, so the proliferation of cells is uninhibited (resulting in exponential growth). We consider two possible constitutive relations.(More)