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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...
We consider the early carcinogenesis model originally proposed as a deterministic
reaction-diffusion system. The model has been conceived to explore the spatial effects
stemming from growth regulation of pre-cancerous cells by diffusing growth factor
molecules. The model exhibited Turing instability producing transient spatial spikes in
cell density, which might be considered a model counterpart of emerging foci of malignant
cells. However, the process...
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...
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