The link between atherosclerosis and regions of disturbed flow and low wall shear stress is now firmly established, but the causal mechanisms underlying the link are not yet understood. It is now recognised that the endothelium is not simply a passive barrier between the blood and the vessel wall, but plays an active role in maintaining vascular homeostasis and participates in the onset of atherosclerosis. Calcium signalling is one of the principal intracellular signalling mechanisms by which endothelial cells (EC) respond to external stimuli, such as fluid shear stress and ligand binding. Previous studies have separately modelled mass transport of chemical species in the bloodstream and calcium dynamics in EC via the inositol triphosphate (IPa) signalling pathway. In this study, we integrate these two important components to provide an inclusive model for the calcium response of the endothelium in an arbitrary vessel geometry. This enables the combined effects of fluid flow and biochemical stimulation on EC to be investigated. Model results show that low endothelial calcium levels in the area of disturbed flow at an arterial widening may be one contributing factor to the onset of vascular disease.

The growth of human cancers is characterised by long and variable cell cycle times that are controlled by stochastic events prior to DNA replication and cell division. Treatment with radiotherapy or chemotherapy induces a complex chain of events involving reversible cell cycle arrest and cell death. In this paper we have developed a mathematical model that has the potential to describe the growth of human tumour cells and their responses to therapy. We have used the model to predict the response of cells to mitotic arrest, and have compared the results to experimental data using a human melanoma cell line exposed to the anticancer drug paclitaxel. Cells were analysed for DNA content at multiple time points by flow cytometry. An excellent correspondence was obtained between predicted and experimental data. We discuss possible extensions to the model to describe the behaviour of cell populations in vivo.

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Abstract. Using Bloch waves to represent the full solution of Maxwell's equations in periodic media, we study the limit where the material's period becomes much smaller than the wavelength. It is seen that for steady state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the nonvanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.

Most anti-cancer drugs in use today exert their effects by inducing a programmed cell death mechanism. This process, termed apoptosis, is accompanied by degradation of the DNA and produces cells with a range of DNA contents. We have previously developed a phase transition mathematical model to describe the mammalian cell division cycle in terms of cell cycle phases and the transition rates between these phases. We now extend this model here to incorporate a transition to a programmed cell death phase whereby cellular DNA is progressively degraded with time. We have utilised the technique of flow cytometry to analyse the behaviour of a melanoma cell line (NZM13) that was exposed to paclitaxel, a drug used frequently in the treatment of cancer. The flow cytometry profiles included a complex mixture of living cells whose DNA content was increasing with time and dying cells whose DNA content was decreasing with time. Application of the mathematical model enabled estimation of the rate constant for entry of mitotic cells into apoptosis (0.035 per hour) and the duration of the period of DNA degradation (51 hours). These results provide a dynamic model of the action of an anticancer drug that can be extended to improve the clinical outcome in individual cancer patients.

Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.

Objective The management of twin-twin transfusion syndrome (TTTS) in its early stages (Quintero Stages I and II) is controversial. We describe the prevalence, severity, incidence and rate of progression of recipienttwin cardiomyopathy in Stages I and II TTTS. Methods Among 451 cases of TTTS evaluated between 2004 and 2009, 123 (27.3%)

In this paper we firstly present three alternative formulations of a mathematical model for human tumour cell lines unperturbed by cancer therapy. The model counts the number density of cells in each phase of the cell cycle over time where cells are differentiated by their DNA content. Data are available from the Auckland Cancer Society Research Centre, Auckland, New Zealand, in the form of DNA histograms or profiles from 11 different human tumour cell lines (i.e. in vitro) unperturbed by cancer therapy. We then apply one (computationally fast) formulation of the model and discover that although in general different combinations of parameter values give rise to very different DNA profiles it is possible that different combinations of parameter values give rise to virtually identical profiles. Experimental estimates of the rate of transition from the G1-phase (growth) to the S-phase (DNA synthesis) enable us to uniquely determine other model parameters of interest that give the least square error between the model and data. We finally apply our model to each of the 11 different cell lines and compare cell cycle phase transit times. Although the DNA histograms of each of the cell lines have similar shapes these cell lines have different combinations of transit times to each other, which could explain why they often react very differently when exposed to anti-cancer therapies during laboratory experiments. An understanding of the in vitro situation may give an insight into why some human cancer patients do not respond to cancer therapy.