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Mathematical model of tumour cord growth along the source of nutrient

S. Astanin, A. Tosin (2010)

Mathematical Modelling of Natural Phenomena

A mathematical model of the tumour growth along a blood vessel is proposed. The model employs the mixture theory approach to describe a tissue which consists of cells, extracellular matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is paid to consistent description of oxygen consumption and growth processes based on the energy balance. A finite difference numerical...

Mathematical models of tumor growth systems

Takashi Suzuki (2012)

Mathematica Bohemica

We study a class of parabolic-ODE systems modeling tumor growth, its mathematical modeling and the global in time existence of the solution obtained by the method of Lyapunov functions.

Mechanisms of Cell Motion in Confined Geometries

R. J. Hawkins, R. Voituriez (2010)

Mathematical Modelling of Natural Phenomena

We present a simple mechanism of cell motility in a confined geometry, inspired by recent motility assays in microfabricated channels. This mechanism relies mainly on the coupling of actin polymerisation at the cell membrane to geometric confinement. We first show analytically using a minimal model of polymerising viscoelastic gel confined in a narrow channel that spontaneous motion occurs due to polymerisation alone. Interestingly, this mechanism...

Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling

R. M. H. Merks, P. Koolwijk (2009)

Mathematical Modelling of Natural Phenomena

Cell-based, mathematical models help make sense of morphogenesis—i.e. cells organizing into shape and pattern—by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in...

Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models

A. R.A. Anderson, K. A. Rejniak, P. Gerlee, V. Quaranta (2010)

Mathematical Modelling of Natural Phenomena

Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid...

Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents

S. R. McDougall, M. A.J. Chaplain, A. Stéphanou, A. R.A. Anderson (2010)

Mathematical Modelling of Natural Phenomena

Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

A. Marrocco, H. Henry, I. B. Holland, M. Plapp, S. J. Séror, B. Perthame (2010)

Mathematical Modelling of Natural Phenomena

Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare...

Multiphase and Multiscale Trends in Cancer Modelling

L. Preziosi, A. Tosin (2009)

Mathematical Modelling of Natural Phenomena

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.

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