84 research outputs found
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
Inverse Reconstruction of Cell Proliferation Laws in Cancer Invasion Modelling
The process of local cancer cell invasion of the surrounding tissue is key for the overall tumour growth and spread within the human body, the past 3 decades witnessing intense mathematical modelling efforts in these regards. However, for a deep understanding of the cancer invasion process these modelling studies require robust data assimilation approaches. While being of crucial importance in assimilating potential clinical data, the inverse problems approaches in cancer modelling are still in their early stages, with questions regarding the retrieval of the characteristics of tumour cells motility, cells mutations, and cells population proliferation, remaining widely open. This study deals with the identification and reconstruction of the usually unknown cancer cell proliferation law in cancer modelling from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. Considering two basic tumour configurations, associated with the case of one cancer cells population and two cancer cells subpopulations that exercise their dynamics within the extracellular matrix, we combine Tikhonov regularisation and gaussian mollification approaches with finite element and finite differences approximations to reconstruct the proliferation laws for each of these sub-populations from both exact and noisy measurements. Our inverse problem formulation is accompanied by numerical examples for the reconstruction of several proliferation laws used in cancer growth modelling
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
Inverse problems for blood perfusion identification
In this thesis we investigate a sequence of important inverse problems associated with the bio-heat transient flow equation which models the heat transfer within the human body. Given the physical importance of the blood perfusion coefficient that appears in the bio-heat equation, attention is focused on the inverse problems concerning the accurate recovery of this information when exact and noisy measurements are considered in terms of the mass, flux, or temperature, which we sampled over the specific regions of the media under investigation. Five different cases are considered for the retrieval of the perfusion coefficient, namely when this parameter is assumed to be either constant, or dependent on time, space, temperature, or on both space and time. Theanalytica:l and numerical techniques that arc used to investigate the existence and uniqueness of the solution for this inverse coefficient identification are embedded in an extensiveú computational approach for the retrieval of the perfusion coefficient. Boundary integral methods, for the constant and the time-dependent cases, or Crank-Nicolson-type global schemes or local methods based on solutions of the first-kind integral equations, in the space, temperature, or space and time cases, are used in conjunction either with Gaussian mollification or with Tikhonov regularization methods, which arc coupled with optimization techniques. Analytically, a number of uniqueness and existence criteria and structural results are formulated and proved
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