The impact of cell crowding and active cell movement on vascular tumour growth

A multiscale model for vascular tumour growth is presented which includes systems of ordinary differential equations for the cell cycle and regulation of apoptosis in individual cells, coupled to partial differential equations for the spatio-temporal dynamics of nutrient and key signalling chemicals. Furthermore, these subcellular and tissue layers are incorporated into a cellular automaton framework for cancerous and normal tissue with an embedded vascular network. The model is the extension of previous work and includes novel features such as cell movement and contact inhibition. We presented a detailed simulation study of the effects of these additions on the invasive behaviour of tumour cells and the tumour's response to chemotherapy. In particular, we find that cell movement alone increases the rate of tumour growth and expansion, but that increasing the tumour cell carrying capacity leads to the formation of less invasive dense hypoxic tumours containing fewer tumour cells. However, when an increased carrying capacity is combined with significant tumour cell movement, the tumour grows and spreads more rapidly, accompanied by large spatio-temporal fluctuations in hypoxia, and hence in the number of quiescent cells. Since, in the model, hypoxic/quiescent cells produce VEGF which stimulates vascular adaptation, such fluctuations can dramatically affect drug delivery and the degree of success of chemotherapy

Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total

Mesoscopic and continuum modelling of angiogenesis

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.Comment: 48 pages, 13 figure

Object-Oriented Paradigms for Modelling Vascular\ud Tumour Growth: a Case Study

Motivated by a family of related hybrid multiscale models, we have built an object-oriented framework for developing and implementing multiscale models of vascular tumour growth. The models are implemented in our framework as a case study to highlight how object-oriented programming techniques and good object-oriented design may be used effectively to develop hybrid multiscale models of vascular tumour growth. The intention is that this paper will serve as a useful reference for researchers modelling complex biological systems and that these researchers will employ some of the techniques presented herein in their own projects

On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution

Exploring the interdependencies of research funders in the UK

Investment in medical research is vital to the continuing improvement of the UK's health and wealth. It is through research that we expand our understanding of disease and develop new treatments for patients. Medical research charities currently contribute over £1 billion annually to medical research in the UK, of which over £350 million is provided by Cancer Research UK. Many charities, including Cancer Research UK, receive no government funding for their research activity. Cancer Research UK is engaged in a programme of work in order to better understand the medical research funding environment and demonstrate the importance of sustained investment. A key part of that is the Office of Health Economics‟ (OHE) 2011 report “Exploring the interdependency between public and charitable medical research”. This study found that there are substantial benefits, both financial and qualitative, from the existence of a variety of funders and that reductions in the level of government financial support for medical research are likely to have broader negative effects. This contributed to other evidence which found that the activities and funding of the charity, public and private sectors respectively are complementary, i.e. mutually reinforcing, rather than duplicative or merely substituting for one another. “Exploring the interdependencies of research funders in the UK” by the Office of Health Economics (OHE) and SPRU: Science and Technology Policy Research at the University of Sussex, represents a continued effort to build the evidence base around the funding of medical research. This report uncovers the extent to which funders of cancer research are interdependent, nationally and internationally. Key figures show that two thirds of publications acknowledging external support have relied on multiple funders, while just under half benefited from overseas funding, and almost a fifth are also supported by industry. In addition the analysis shows that the general public would not want tax funding of cancer research to be reduced, but would not donate enough to charities to compensate for any such reduction

A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

Derivation of a Hele-Shaw type system from a cell model with active motion

We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is considered here as a standard diffusion process. The free boundary model is derived from a description at the cell level using the asymptotic of a stiff pressure limit. Compared to the case when active motion is neglected, the pressure satisfies the same complementarity Hele-Shaw type formula. However, the cell density is smoother (Lipschitz continuous), while there is a deep change in the free boundary velocity, which is no longer given by the gradient of the pressure, because some kind of 'mushy region' prepares the tumor invasion