Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition

Guerra, Ângela R.; Rodríguez, Damyr; Montero, S.; Betancourt-Mar, J.A.; Martin, R. R.; Silva, E.; Bizzarri, Mariano; Cocho, G.; Mansilla, Ricardo; Nieto-Villar, J.M.

doi:10.1016/j.physa.2018.01.040

Cited by 21 publications

(25 citation statements)

References 44 publications

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“…A rather standard approach is to answer specific questions at each scale of interest by formulating dedicated models. These can be based on Statistical Mechanics [4], Kinetic Theories [5,6,7,8,9], and Continuum Mechanics [10,11] (and references therein), depending on whether the given problem involves the molecular, cellular, or the tissue scale. One of the main challenges, however, is to understand the complexes of phenomena that contribute to initiate the sprouting of a tumour, and to bridge across the physical scales at which they occur.…”

Section: Introductionmentioning

confidence: 99%

Self-influenced growth through evolving material inhomogeneities

Stefano¹,

Ramírez-Torres²,

Penta

et al. 2018

International Journal of Non-Linear Mechanics

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We reformulate a model of avascular tumour growth in which the tumour tissue is studied as a biphasic medium featuring an interstitial fluid and a solid phase. The description of growth relies on two fundamental features: One of those is given by the mass transfer among the constituents of the phases, which is taken into account through source and sink terms; the other one is the multiplicative decomposition of the deformation gradient tensor of the solid phase, with the introduction of a growth tensor, which represents the growth-induced structural changes of the tumour. In general, such tensor is non-integrable, and it may allow to define a Levi-Civita connection with non-trivial curvature. Moreover, its evolution is related to the source and sink of mass of the solid phase through an evolution equation. Our goal is to study how growth can be influenced by the inhomogeneity of the growth tensor. To this end, we study the evolution of the latter, as predicted by two different models. In the first one, the dependence of the growth tensor on the tumour's material points is not explicitly considered in the evolution equation. In the second model, instead, the inhomogeneity of the growth tensor is resolved explicitly by introducing the curvature associated with it into the evolution equation. Through numerical simulations, we compare the results produced by these two models, and we evaluate a possible role of the material inhomogeneities on growth.

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Section: Introductionmentioning

confidence: 99%

Self-influenced growth through evolving material inhomogeneities

Stefano¹,

Ramírez-Torres²,

Penta

et al. 2018

International Journal of Non-Linear Mechanics

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“…Most tumors release millions of cells into the bloodstream, but only a small number of metastatic lesions develop, indicating the inefficiency of the metastasis process [37] , this means weakness of metastasis, despite the fact that, as has been shown in previous work [16] , metastasis is a highly robust process. In the extravasation process, tumor cells undergo changes to improve adhesion; this process is closely related to the populations of the immune system and to the action of the new microenvironment [37] .…”

mentioning

confidence: 73%

“…In previous works we have shown that the growth of cancer studied through cell population models and interactions with immune cells, is a complex process. Control in such process could be precisely in that interaction with the immune system; this could be the source of its complexity and its adaptability [15,16] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of metastasis, a feasible way to detect the weakness

Guerra

Silva

Mansilla³

et al. 2020

Preprint

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Cancer is one of the main causes of death worldwide. 90% of deaths caused by this disease occur 12 due to metastasis. Two models are proposed that rescue fundamental aspects of metastasis, such as EMT (epithelial mesenchymal transition), extravasation and colonization. The results suggest that strengthening the immune system during EMT as well as its 19 specialization in the detection of DTCs (disseminated tumor cells) can be effective strategies in the 20 treatment of metastasis.

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“…In a previous work [31] we have shown that the rate of entropy production is a Lyapunov function, in fact we extended this formalism to the development of cancer [32,33,34,35,36,37]. Thus, we have the entropy production per unit time meets the necessary and sufficient conditions for Lyapunov function [30], such that , that allows us to affirm that the rate of entropy production is a Lyapunov function.…”

Section: Thermodynamics Frameworkmentioning

confidence: 86%

Deciphering the longevity of the mole-rats

Triana¹,

Cocho²,

Mansilla³

et al. 2018

IJOAR

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A theoretical model of a nonlinear network that outlines the general aspects of mole-rat resistance to age-related diseases, such as cancer and the action of ROS was elaborated. According to our conjecture, it was shown that the protection is established because hyaluronic acid of high molecular mass forms a non-linear network of interactions. That network leads to self-organization away from the thermodynamical equilibrium, which appears through a "first order" phase transition as a supercritical bifurcation of Andronov-Hopf type. Finally, it is shown how the rate of entropy production is a Lyapunov function of the dynamics of the process. Keywords:mole-rat

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Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition

Abstract: Highlights• Cancer as an open, complex, self-organizing nonlinear dynamic system.• The epithelial-mesenchymal transition appears as ""first order"" phase transition.• EMT exhibit a Shilnikov"s chaos.

Cited by 21 publications

References 44 publications

Self-influenced growth through evolving material inhomogeneities

Self-influenced growth through evolving material inhomogeneities

Mathematical modeling of metastasis, a feasible way to detect the weakness

Deciphering the longevity of the mole-rats

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