Global generalized solutions to a chemotaxis model of capillary-sprout growth during tumor angiogenesis

We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is known to allow viscous shocks (so-called traveling waves). We introduce a relative entropy of the system, which can capture how close a solution at a given time is to a given shock wave in almost [Formula: see text]-sense. When the shock strength is small enough, we show the functional is non-increasing in time for any large initial perturbation. The contraction property holds independently of the strength of the diffusion.

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Analysis of a chemotaxis-convection model of capillary-sprout growth during tumor angiogenesis

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2019.123474 ◽

2020 ◽

Vol 481 (2) ◽

pp. 123474 ◽

Cited By ~ 4

Author(s):

Genglin Li ◽

Youshan Tao

Keyword(s):

Tumor Angiogenesis ◽

Convection Model ◽

Sprout Growth

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Explicit solutions of a simplified model of capillary sprout growth during tumor angiogenesis

Applied Mathematics Letters ◽

10.1016/0893-9659(95)00105-0 ◽

1996 ◽

Vol 9 (1) ◽

pp. 69-74 ◽

Cited By ~ 14

Author(s):

H.M. Byrne ◽

M.A.J. Chaplain

Keyword(s):

Tumor Angiogenesis ◽

Simplified Model ◽

Explicit Solutions ◽

Sprout Growth

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Extracellular matrix: the gatekeeper of tumor angiogenesis

Biochemical Society Transactions ◽

10.1042/bst20190653 ◽

2019 ◽

Vol 47 (5) ◽

pp. 1543-1555 ◽

Cited By ~ 10

Author(s):

Maurizio Mongiat ◽

Simone Buraschi ◽

Eva Andreuzzi ◽

Thomas Neill ◽

Renato V. Iozzo

Keyword(s):

Extracellular Matrix ◽

Tumor Angiogenesis ◽

Signaling Cascades ◽

Cancer Growth ◽

Cell Behavior ◽

Metastatic Progression ◽

Surface Receptors ◽

The Matrix ◽

Multiple Signaling

Abstract The extracellular matrix is a network of secreted macromolecules that provides a harmonious meshwork for the growth and homeostatic development of organisms. It conveys multiple signaling cascades affecting specific surface receptors that impact cell behavior. During cancer growth, this bioactive meshwork is remodeled and enriched in newly formed blood vessels, which provide nutrients and oxygen to the growing tumor cells. Remodeling of the tumor microenvironment leads to the formation of bioactive fragments that may have a distinct function from their parent molecules, and the balance among these factors directly influence cell viability and metastatic progression. Indeed, the matrix acts as a gatekeeper by regulating the access of cancer cells to nutrients. Here, we will critically evaluate the role of selected matrix constituents in regulating tumor angiogenesis and provide up-to-date information concerning their primary mechanisms of action.

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