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

e22121 Background: To investigate the prognostic values of putative hepatic stem/progenitor cells (HSCs/HPCs) biomarkers in hepatocellular carcinoma (HCC) patients. Methods: Fourteen biomarkers related with HSCs/HPCs or tumor angiogenesis were assessed by qRT-PCR and then validated by tissue microarrays (TMAs) in three independent cohorts of HCC patients underwent curative resection (n=67, 314 and 73). Results: Most of the biomarkers were found over-expressed in recurrent HCC patients by qRT-PCR. HSCs/HPCs biomarkers cytokeratin 19, ABCG2, CD133, Nestin, CD44 and angiogenesis agents CD34, VEGF and PD-ECGF, were confirmed as significant predictors for overall survival (OS) and/or relapse-free survival (RFS) in TMAs analysis. Compared with the low HSCs/HPCs profile group, patients with high HSCs/HPCs profile had significantly lower OS and RFS (p<0.0001), expressed higher VEGF levels (p = 0.012) and microvessel density (MVD, determined by CD34 immunostaining, p = 0.030). Based on Cox regression, a simplified model including CD133, CD44, Nestin, and MVD was constructed and confirmed as an independent predictor for OS (p<0.0001) and RFS (p<0.0001), regardless of alpha-fetoprotein level, tumor stage and recurrence time (p<0.0001 for all). Conclusions: High expression levels of HSCs/HPCs biomarkers are related to tumor angiogenesis and poor prognosis of HCC. The simplified model based on HSCs/HPCs and tumor angiogenesis profile can be used to classify HCC patients with high risk of tumor recurrence after operation. No significant financial relationships to disclose.

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

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2021028 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Xueli Bai ◽

Wenji Zhang

Keyword(s):

Tumor Angiogenesis ◽

Generalized Solutions ◽

Chemotaxis Model ◽

Sprout Growth

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Explicit solutions to a free interface model for the static/flowing transition in thin granular flows

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2020042 ◽

2020 ◽

Author(s):

Christelle Lusso ◽

Francois Bouchut ◽

Alexandre Ern ◽

Anne Mangeney

Keyword(s):

Free Surface ◽

Source Term ◽

Granular Flows ◽

Analytical Description ◽

Time Dependent ◽

Simplified Model ◽

Normal Space ◽

Explicit Solutions ◽

Asymptotic Model ◽

Starting Point

This work is devoted to an analytical description of the dynamics of the static/flowing interface in thin dry granular flows. Our starting point is the asymptotic model derived by Bouchut et al. (2016) from a free surface incompressible model with viscoplastic rheology including a Drucker--Prager yield stress. This asymptotic model is based on the thin-layer approximation (the flow is thin in the direction normal to the topography compared to its down-slope extension), but the equations are not depth-averaged. In addition to the velocity, the model includes a free surface at the top of the flow and a free time-dependent static/flowing interface at the bottom. In the present work, we simplify this asymptotic model by decoupling the space coordinates, and keeping only the dependence on time and on the normal space coordinate $Z$. We introduce a time- and $Z$-dependent source term, assumed here to be given, which represents the opposite of the net force acting on the flowing material, including gravity, pressure gradient, and internal friction. We prove several properties of the resulting simplified model that has a time- and $Z$-dependent velocity and a time-dependent static/flowing interface as unknowns. The crucial advantage of this simplified model is that it can provide explicit solutions in the inviscid case, for different shapes of the source term. These explicit inviscid solutions exhibit a rich behaviour and qualitatively reproduce some physical features observed in granular flows.

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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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