Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation

Gamba, A.; Ambrosi, Davide Carlo; Coniglio, Antonio; Candia, A. de; Talia, Stefano Di; Giraudo, Enrico; Serini, Guido; Preziosi, Luigi; Bussolino, Federico

doi:10.1103/physrevlett.90.118101

Cited by 256 publications

(349 citation statements)

References 18 publications

Supporting

Mentioning

318

Contrasting

Order By: Relevance

“…These structures cannot be explained by the Patlak/KellerSegel parabolic model (or the variants) which generically lead to pointwise blow-up. As shown in [59,28,24] they can be recovered by numerical experiments on the following hyperbolic model proposed in [59,28] …”

Section: Initiation Of Angiogenesismentioning

confidence: 99%

See 1 more Smart Citation

PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic

Perthame

2004

Appl Math

116

View full text Add to dashboard Cite

Modeling the movement of cells (bacteria, amoeba) is a long standing subject and Partial Differential equations have been used several times. The most classical and successful system was proposed by Patlak [55] and Keller & Segel [39] and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on bacteria like Escherichia Coli or amoeba like Dictyostelium Discoïdeum exhibiting pointwise concentrations.For human endothelial cells, several experiments show the formation of networks that can be interpreted as the initiation of angiogenesis. To recover such patterns a hydrodynamical model seems better adapted.The two systems can be unified by a kinetic approach that was proposed for Escherichia Coli, based on more precise experiments showing a movement by 'jump and tumble'. This nonlinear kinetic model is interesting by itself and the existence theory is not complete. It is also interesting from a scaling point of view; in a diffusion limit one recovers the Keller-Segel model and in a hydrodynamical limit one recovers the model proposed for human endothelial cells.We also mention the mathematical interest of a analyzing another degenerate parabolic system (exhibiting different properties) proposed to describe the angiogenesis phenomena i.e. the formation of capillary blood vessels. 1

show abstract

Section: Initiation Of Angiogenesismentioning

confidence: 99%

“…Their movements lead to the formation of networks that are interpreted as the beginning of a vasculature ( [59,28]). This phenomenon is important since it is responsible for angiogenesis, a major factor for the growth of tumors [14,44].…”

Section: Introductionmentioning

confidence: 99%

PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic

Perthame

2004

Appl Math

116

View full text Add to dashboard Cite

show abstract

“…Virtual cells in the CPM typically undergo a random walk with relatively short persistence lengths, while microfluidics experiments show that ECs have longer persistence lengths or even retrace their own paths [59]. Indeed, in vitro vasculogenesis may require endothelial cell persistence [2,48,15]. A number of authors have proposed CPM extensions for making cells directionally persistent [6,5,26].…”

Section: Quantitative Cell-based Modeling Of Vasculogenesismentioning

confidence: 99%

“…They developed a series of continuum models [2,48,15] whose results they compared to HUVEC-Matrigel cultures. The Preziosi model assumes that a) endothelial cells secrete a chemoattractant which attracts other endothelial cells, b) the chemoattractant diffuses in the extracellular matrix which gradually inactivates it, and c) endothelial cell motion is direction persistent.…”

Section: Chemotaxis-based Modelsmentioning

confidence: 99%

Modeling Morphogenesisin silicoandin vitro: Towards Quantitative, Predictive, Cell-based Modeling

Merks

Koolwijk

2009

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract. Cell-based, mathematical models help make sense of morphogenesis-i.e. cells organizing into shape and pattern-by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in vitro. This review discusses two cell culture models of morphogenesis that have been studied using this combined experimental-mathematical approach: chondrogenesis (cartilage patterning) and vasculogenesis (de novo blood vessel growth). In both these systems, radically different models can equally plausibly explain the in vitro patterns. Quantitative descriptions of cell behavior would help choose between alternative models. We will briefly review the experimental methodology (microfluidics technology and traction force microscopy) used to measure responses of individual cells to their micro-environment, including chemical gradients, physical forces and neighboring cells. We conclude by discussing how to include quantitative cell descriptions into a cell-based model: the Cellular Potts model.

show abstract

“…It is necessary to add a term related to cell polarization and persistence, in conjunction with a chemotactic response, which were shown to be key ingredients also in the formation of vascular networks [10,25,28].…”

Section: Discussionmentioning

confidence: 99%

Individual cell-based models of cell scatter of ARO and MLP-29 cells in response to hepatocyte growth factor

Scianna

Merks

Preziosi

et al. 2009

Journal of Theoretical Biology

View full text Add to dashboard Cite

The different behaviours of colonies of two cell lines, ARO and MLP-29, in response to Hepatocyte Growth Factor (HGF) are described deducing suitable Cellular Potts Model (CPM). It is shown how increased motility and decreased adhesiveness are responsible for cellcell dissociation and tissue invasion in the ARO cells. On the other hand, it is shown that, in addition to the biological mechanisms above, it is necessary to include cell persistence in motion and HGF diffusion to describe the scattering and the branching processes characteristic of MLP-29 cells.

show abstract

Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation

Cited by 256 publications

References 18 publications

PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic

PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic

Modeling Morphogenesisin silicoandin vitro: Towards Quantitative, Predictive, Cell-based Modeling

Individual cell-based models of cell scatter of ARO and MLP-29 cells in response to hepatocyte growth factor

Contact Info

Product

Resources

About