How Nucleus Mechanics and ECM Microstructure Influence the Invasion of Single Cells and Multicellular Aggregates

Giverso, Chiara; Arduino, Alessandro; Preziosi, Luigi

doi:10.1007/s11538-017-0262-9

Cited by 18 publications

(18 citation statements)

References 69 publications

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“… 2017 ) and a three-dimensional model describing nucleus mechanics during cell migration and deformation (Giverso et al. 2018 ), one of the major advantages of our modeling is its efficiency regarding CPU time, which enables to carry out Monte Carlo simulations for evaluation of parameter sensitivity. A further merit of the current model is its simplicity.…”

Section: Discussionmentioning

confidence: 99%

A phenomenological model for cell and nucleus deformation during cancer metastasis

Chen

Weihs

Dijk

et al. 2018

Biomech Model Mechanobiol

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Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.Electronic supplementary materialThe online version of this article (10.1007/s10237-018-1036-5) contains supplementary material, which is available to authorized users.

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Section: Discussionmentioning

confidence: 99%

A phenomenological model for cell and nucleus deformation during cancer metastasis

Chen

Weihs

Dijk

et al. 2018

Biomech Model Mechanobiol

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“…Using a modelling strategy similar to that proposed by Gallinato et al [35] and Giverso et al [37], we define the effective mobility coefficient µ 23 as whereμ 23 > 0 is the maximum mobility of ovarian cancer cells through the interface that models the peritoneal lining, the function A(t, x) > 0 represents the average cross-section of the pores of the membrane at position x ∈ Σ 23 and time t ≥ 0, and the parameter A 0 > 0 is the critical value of the average pores' cross-section below which, according to "the physical limit of cell migration" [83], the membrane is completely impermeable to cancer cells. The evolution of the function A(t, x) is governed by the following differential equation In Eq.…”

Section: S2 Formal Derivation Of the Continuity Condition (46) Forφmentioning

confidence: 99%

Derivation and Application of Effective Interface Conditions for Continuum Mechanical Models of Cell Invasion through Thin Membranes

Chaplain¹,

Giverso²,

Lorenzi³

et al. 2019

SIAM J. Appl. Math.

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We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.

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“…The next two papers investigate metastasis. Giverso et al (2017) address mechanical issues in tumor growth dynamics. The majority of experimental (and theoretical) research on cell motion is carried out in two spatial dimensions, but it is becoming increasingly clear that movement in vivo, which of course is in three dimensions, is different in important ways.…”

Section: Special Issue On Mathematical Oncologymentioning

confidence: 99%

Mathematical Oncology

Anderson

Maini²

2018

Bull Math Biol

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Despite a huge amount of research effort, cancer continues to be a major killer. One of the main reasons for this is the immense complexity of the disease. Cancer is a multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. Conversely, tissue level properties, such as blood flow, produce Darwinian selection forces that govern the local distribution of cellular phenotypes and genotypes. Changes in tissue lead to a disruption of organ form and function that can ultimately lead to failure and death (Fig. 1). This multiscale aspect of cancer has largely been neglected in the reductionist paradigm, which typically views cancer as "a disease of the genes". The reason for this is clear as the remarkable advances in molecular technology have greatly enhanced quantitative measurements at the genetic scale, while cellular-or tissue-scale properties remain the province of pathology and radiology, which generally lack such tools. The genomic revolution has led to the development of an extensive set of tools to measure and analyze gene expression and mutation. However, the mapping of these changes to in vivo structure and function of cancer cells and tissue remains limited. Furthermore, while tumor evolution is often viewed as a mutation-driven process, it is

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How Nucleus Mechanics and ECM Microstructure Influence the Invasion of Single Cells and Multicellular Aggregates

Cited by 18 publications

References 69 publications

A phenomenological model for cell and nucleus deformation during cancer metastasis

A phenomenological model for cell and nucleus deformation during cancer metastasis

Derivation and Application of Effective Interface Conditions for Continuum Mechanical Models of Cell Invasion through Thin Membranes

Mathematical Oncology

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