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In vitro transmesothelial migration assays of ovarian cancer cells, isolated or
aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts
Models (CPM). We show that the simulations are in good agreement with the experimental
evidence and that the overall process is regulated by the activity of matrix
metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells
with the extracellular matrix and...
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...
When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from
neighbouring cells, degrade the basement membrane, and migrate through the extracellular
matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix
adhesion. In this paper we present a mathematical model of an intracellular pathway for
the interactions between a cancer cell and the extracellular matrix. Cancer cells use
similar...
Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous
cell proliferation and motility rates. The interplay of proliferation and migration
dynamics plays an important role in the invasion of these malignant tumors. We analyze the
regulation of proliferation and migration processes with a lattice-gas cellular automaton
(LGCA). We study and characterize the influence of the migration/proliferation dichotomy
(also known...
The cancer stem cell hypothesis has evolved to one of the most important paradigms in
biomedical research. During recent years evidence has been accumulating for the existence
of stem cell-like populations in different cancers, especially in leukemias. In the
current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We
apply the model to compare cellular properties of leukemic stem cells to those of their
benign counterparts....
Recent discovery of cancer stem cells in tumorigenic tissues has raised many questions
about their nature, origin, function and their behavior in cell culture. Most of current
experiments reporting a dynamics of cancer stem cell populations in culture show the
eventual stability of the percentages of these cell populations in the whole population of
cancer cells, independently of the starting conditions. In this paper we propose a
mathematical model...
In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations....
Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental
tool which can be used in conjunction with mathematical modeling to quantify the dynamic
behavior of a population of lymphocytes. In this survey we begin by providing an overview
of the mathematically relevant aspects of the data collection procedure. We then present
an overview of the large body of mathematical models, along with their assumptions and
uses,...
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...
Solid tumors and hematological cancers contain small population of tumor cells that are
believed to play a critical role in the development and progression of the disease. These
cells, named Cancer Stem Cells (CSCs), have been found in leukemia, myeloma, breast,
prostate, pancreas, colon, brain and lung cancers. It is also thought that CSCs drive the
metastatic spread of cancer. The CSC compartment features a specific and phenotypically
defined cell...
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...
This review aims at presenting a
synoptic, if not exhaustive, point of view on some of the problems
encountered by biologists and physicians who deal with natural
cell proliferation and disruptions of its physiological control in
cancer disease. It also aims at suggesting how mathematicians are
naturally challenged by these questions and how they might help,
not only biologists to deal theoretically with biological
complexity, but also physicians to optimise therapeutics, on which
last point the...
Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation
models governed by distributed fractional order differential equations
(DODEs) and multi-term fractional order differential equations are constructed.
The construction is based on the discretization leading to a generalized
difference scheme (containing a finite number of terms in the time
step and infinite number of terms in the space step) of the Cauchy problem
for...
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