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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...
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.
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...
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...
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...
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...
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...
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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