941 research outputs found
Preface
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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
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
We present multiscale models of cancer tumor invasion with components at the
molecular, cellular, and tissue levels. We provide biological justifications
for the model components, present computational results from the model, and
discuss the scientific-computing methodology used to solve the model equations.
The models and methodology presented in this paper form the basis for
developing and treating increasingly complex, mechanistic models of tumor
invasion that will be more predictive and less phenomenological. Because many
of the features of the cancer models, such as taxis, aging and growth, are seen
in other biological systems, the models and methods discussed here also provide
a template for handling a broader range of biological problems
Two-scale Moving Boundary Dynamics of Cancer Invasion:Heterotypic Cell Populations Evolution in Heterogeneous ECM
This book contains a collection of original research articles and review articles that describe novel mathematical modeling techniques and the application of those techniques to models of cell motility in a variety of contexts. The aim is to highlight some of the recent mathematical work geared at understanding the coordination of intracellular processes involved in the movement of cells. This collection will benefit researchers interested in cell motility as well graduate students taking a topics course in this area.
A level-set approach for a multi-scale cancer invasion model
The quest for a deeper understanding of the cancer growth and spread process focuses on the naturally multiscale nature of cancer invasion, which requires an appropriate multiscale modeling and analysis approach. The cross-talk between the dynamics of the cancer cell population on the tissue scale (macroscale) and the proteolytic molecular processes along the tumor border on the cell scale (microscale) plays a particularly important role within the invasion processes, leading to dramatic changes in tumor morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new formulation of this process involving a novel derivation of the macro scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells
Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving Boundary Cancer Invasion
Cancer cell invasion is recognised as one of the hallmarks of cancer and
involves several inner-related multiscale processes that ultimately contribute
to its spread into the surrounding tissue. In order to gain a deeper
understanding of the tumour invasion process, we pay special attention to the
interacting dynamics between the cancer cell population and various
constituents of the surrounding tumour microenvironment. To that end, we
consider the key role that ECM plays within the human body tissue, providing
not only structure and support to surrounding cells, but also acting as a
platform for cells communication and spatial movement. There are several other
vital structures within the ECM, however we are going to focus primarily on
fibrous proteins, such as fibronectin. These fibres play a crucial role in
tumour progression, enabling the anchorage of tumour cells to the ECM. In this
work we consider the two-scale dynamic cross-talk between cancer cells and a
two component ECM (consisting of both a fibre and a non-fibre phase). To that
end, we incorporate the interlinked two-scale dynamics of cells-ECM
interactions within the tumour support that contributes simultaneously both to
cell-adhesion and to the dynamic rearrangement and restructuring of the ECM
fibres. Furthermore, this is embedded within a multiscale moving boundary
approach for the invading cancer cell population, in the presence of
cell-adhesion at the tissue scale and cell-scale fibre redistribution activity
and leading edge matrix degrading enzyme molecular proteolytic processes. The
overall modelling framework will be accompanied by computational results that
will explore the impact on cancer invasion patterns of different levels of cell
adhesion in conjunction with the continuous ECM fibres rearrangement.Comment: 44 pages, 17 figure
Cell-scale degradation of peritumoural extracellular matrix fibre network and its role within tissue-scale cancer invasion
Local cancer invasion of tissue is a complex, multiscale process which plays
an essential role in tumour progression. Occurring over many different temporal
and spatial scales, the first stage of invasion is the secretion of matrix
degrading enzymes (MDEs) by the cancer cells that consequently degrade the
surrounding extracellular matrix (ECM). This process is vital for creating
space in which the cancer cells can progress and it is driven by the activities
of specific matrix metalloproteinases (MMPs). In this paper, we consider the
key role of two MMPs by developing further the novel two-part multiscale model
introduced in [33] to better relate at micro-scale the two micro-scale
activities that were considered there, namely, the micro-dynamics concerning
the continuous rearrangement of the naturally oriented ECM fibres within the
bulk of the tumour and MDEs proteolytic micro-dynamics that take place in an
appropriate cell-scale neighbourhood of the tumour boundary. Focussing
primarily on the activities of the membrane-tethered MT1-MMP and the soluble
MMP-2 with the fibrous ECM phase, in this work we investigate the MT1-MMP/MMP-2
cascade and its overall effect on tumour progression. To that end, we will
propose a new multiscale modelling framework by considering the degradation of
the ECM fibres not only to take place at macro-scale in the bulk of the tumour
but also explicitly in the micro-scale neighbourhood of the tumour interface as
a consequence of the interactions with molecular fluxes of MDEs that exercise
their spatial dynamics at the invasive edge of the tumour
Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix
Local cancer cell invasion is a complex process involving many cellular and
tissue interactions and is an important prerequisite for metastatic spread, the
main cause of cancer related deaths. Occurring over many different temporal and
spatial scales, the first stage of local invasion is the secretion of
matrix-degrading enzymes (MDEs) and the resulting degradation of the
extra-cellular matrix (ECM). This process creates space in which the cells can
invade and thus enlarge the tumour. As a tumour increases in malignancy, the
cancer cells adopt the ability to mutate into secondary cell subpopulations
giving rise to a heterogeneous tumour. This new cell subpopulation often
carries higher invasive qualities and permits a quicker spread of the tumour.
Building upon the recent multiscale modelling framework for cancer invasion
within a fibrous ECM introduced in Shuttleworth and Trucu (2019), in this paper
we consider the process of local invasion by a heterotypic tumour consisting of
two cancer cell populations mixed with a two-phase ECM. To that end, we address
the double feedback link between the tissue-scale cancer dynamics and the
cell-scale molecular processes through the development of a two-part modelling
framework that crucially incorporates the multiscale dynamic redistribution of
oriented fibres occurring within a two-phase extra-cellular matrix and combines
this with the multiscale leading edge dynamics exploring key matrix-degrading
enzymes molecular processes along the tumour interface that drive the movement
of the cancer boundary. The modelling framework will be accompanied by
computational results that explore the effects of the underlying fibre network
on the overall pattern of cancer invasion
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