A Multiscale Moving Boundary Model Arising in Cancer Invasion

Trucu, Dumitru; Lin, Ping; Chaplain, M. A. J.; Wang, Yangfan

doi:10.1137/110839011

Cited by 54 publications

(250 citation statements)

References 59 publications

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“…It is this breakdown of peritumoural ECM that enables the tumour opportunities to expand and proceed with its local invasion. Continuing with the terminology of the framework introduced in Trucu et al (2013), during a time interval [t 0 , t 0 + ∆t], the MDEs micro-dynamics is explored on the invasive leading edge of the tumour ∂Ω(t) enclosed by a complete cover of -size half-way shifted overlapping micro-domains { Y } Y ∈P (t) . Furthermore, the specific topological requirements detailed in full in Trucu et al (2013) that enable the construction of the covering bundle of microdomains { Y } Y ∈P (t) , allow us to capture the cell-scale MDEs activity in a neighbourhood of ∂Ω(t), exploring this molecular dynamics in both the overlapping inner regions Y ∩ Ω(t) and the peritumoural outside regions Y ∩ \Ω(t) where the MDEs get transported and degrade the ECM.…”

Section: The Multiscale Moving Boundary Approachmentioning

confidence: 99%

“…To complete the tumour macro-dynamics we use a novel predictor-corrector scheme developed in Shuttleworth and Trucu (2019) that accounts for the complexity of the cancer dynamics. Further, to obtain the microscopic boundary relocation, we explore the top-down and bottom-up links as well as solve the micro-dynamics via finite element approximation as detailed in Trucu et al (2013). The simulations of the model equations were all performed on MATLAB.…”

Section: Numerical Approaches and Initial Conditions For Computationsmentioning

confidence: 99%

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Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Shuttleworth

Trucu

2020

Journal of Theoretical Biology

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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 matrixdegrading 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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Section: The Multiscale Moving Boundary Approachmentioning

confidence: 99%

Section: Numerical Approaches and Initial Conditions For Computationsmentioning

confidence: 99%

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Shuttleworth

Trucu

2020

Journal of Theoretical Biology

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“…Multiscale approaches are appropriate to model and efficiently simulate such complex cellular systems [51][52][53]. In recent years, CA have often been applied to study cellular processes that are strongly influenced by cell heterogeneity depending on a local environment, which consists of molecules that, for instance, mediate signal transductions [45,54].…”

Section: Discussionmentioning

confidence: 99%

An explicit numerical scheme to efficiently simulate molecular diffusion in environments with dynamically changing barriers

Kossow

Rybacki

Millat

et al. 2015

Mathematical and Computer Modelling of Dynamical Systems

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Despite temporal changes in the quantities of molecules, the functioning of cells also depends on their distribution within cells and in their extracellular environment. The dynamics of molecules are often governed by diffusion in heterogeneous environments consisting of dynamically changing impenetrable barriers (excluded volumes). This provides a challenge for efficient simulations of cellular processes with large numbers of molecules. To model the diffusion of molecular mass in consideration of excluded volumes, we here present an explicit numerical scheme that approximates the diffusion equation by using cellular automata. Because this approach represents molecular diffusion at the macroscopic scale, it is more amenable for efficient simulations than comparable microscopic approaches that treat diffusing molecules individually. In contrast to implicit numerical schemes (macroscopic approach), our approach is capable of accounting for excluded volumes, even if those exhibit a dynamic of their own, without increasing computational costs. The presented approach can easily be integrated into certain types of spatio-temporal multiscale models, as demonstrated by an existing model investigating cancer progression. Thereby, it allows to take the spatial effects of a heterogeneous environment on diffusing molecules into account.

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“…In order to gain the full benefit of such modeling efforts (at the cell and receptor scale), we will also require to adapt the current model to take into account novel multi-scale modeling approaches, some of which have already been formulated specifically to investigate cancer invasion [cf. Trucu et al (2013)].…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modeling of Cancer Invasion: The Role of Membrane-Bound Matrix Metalloproteinases

Deakin¹,

Chaplain²

2013

Front. Oncol.

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One of the hallmarks of cancer growth and metastatic spread is the process of local invasion of the surrounding tissue. Cancer cells achieve protease-dependent invasion by the secretion of enzymes involved in proteolysis. These overly expressed proteolytic enzymes then proceed to degrade the host tissue allowing the cancer cells to disseminate throughout the microenvironment by active migration and interaction with components of the extracellular matrix (ECM) such as collagen. In this paper we develop a mathematical model of cancer invasion which consider the role of matrix metalloproteinases (MMPs). Specifically our model will focus on two distinct types of MMP, i.e., soluble, diffusible MMPs (e.g., MMP-2) and membrane-bound MMPs (e.g., MT1-MMP), and the roles each of these plays in cancer invasion. The implications of MMP-2 activation by MMP-14 and the tissue inhibitor of metalloproteinases-2 are considered alongside the effect the architecture of the matrix may have when applied to a model of cancer invasion. Elements of the ECM architecture investigated include pore size of the matrix, since in some highly dense collagen structures such as breast tissue, the cancer cells are unable to physically fit through a porous region, and the crosslinking of collagen fibers. In this scenario, cancer cells rely on membrane-bound MMPs to forge a path through which degradation by other MMPs and movement of cancer cells becomes possible.

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A Multiscale Moving Boundary Model Arising in Cancer Invasion

Cited by 54 publications

References 59 publications

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

An explicit numerical scheme to efficiently simulate molecular diffusion in environments with dynamically changing barriers

Mathematical Modeling of Cancer Invasion: The Role of Membrane-Bound Matrix Metalloproteinases

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