Graph analysis of cell clusters forming vascular networks

This manuscript describes the experimental observation of vasculogenesis in chick embryos by means of network analysis. The formation of the vascular network was observed in the area opaca of embryos from 40 to 55 h of development. In the area opaca endothelial cell clusters self-organize as a primitive and approximately regular network of capillaries. The process was observed by bright-field microscopy in control embryos and in embryos treated with Bevacizumab (Avastin®), an antibody that inhibits the signalling of the vascular endothelial growth factor (VEGF). The sequence of images of the vascular growth were thresholded, and used to quantify the forming network in control and Avastin-treated embryos. This characterization is made by measuring vessels density, number of cell clusters and the largest cluster density. From the original images, the topology of the vascular network was extracted and characterized by means of the usual network metrics such as: the degree distribution, average clustering coefficient, average short path length and assortativity, among others. This analysis allows to monitor how the largest connected cluster of the vascular network evolves in time and provides with quantitative evidence of the disruptive effects that Avastin has on the tree structure of vascular networks.

[1]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[2]  Piet Van Mieghem,et al.  Assortativity in complex networks , 2015, J. Complex Networks.

[3]  Roeland M. H. Merks,et al.  Particle-based simulation of ellipse-shaped particle aggregation as a model for vascular network formation , 2015, 1507.00298.

[4]  Bruce J. West Exact solution to fractional logistic equation , 2015 .

[5]  D. Chirio,et al.  Bevacizumab loaded solid lipid nanoparticles prepared by the coacervation technique: preliminary in vitro studies , 2015, Nanotechnology.

[6]  D. St Johnston The Renaissance of Developmental Biology , 2015, PLoS biology.

[7]  L. Berezansky,et al.  Effect of treatment on the global dynamics of delayed pathological angiogenesis models. , 2014, Journal of theoretical biology.

[8]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[9]  Periklis Pantazis,et al.  Advances in whole-embryo imaging: a quantitative transition is underway , 2014, Nature Reviews Molecular Cell Biology.

[10]  M. A. Herrero,et al.  Dynamics of VEGF matrix-retention in vascular network patterning , 2013, Physical biology.

[11]  L Preziosi,et al.  A review of mathematical models for the formation of vascular networks. , 2013, Journal of theoretical biology.

[12]  Christian Enzinger,et al.  Fractal Dimension and Vessel Complexity in Patients with Cerebral Arteriovenous Malformations , 2012, PloS one.

[13]  A. Czirók,et al.  Pattern formation during vasculogenesis. , 2012, Birth defects research. Part C, Embryo today : reviews.

[14]  Adam R. Navis,et al.  "A Series of Normal Stages in the Development of the Chick Embryo" (1951), by Viktor Hamburger and Howard L. Hamilton , 2012 .

[15]  D. Levinson Network Structure and City Size , 2012, PloS one.

[16]  Laure Gambardella,et al.  A Computational Tool for Quantitative Analysis of Vascular Networks , 2011, PloS one.

[17]  Andreas Deutsch,et al.  Early Embryonic Vascular Patterning by Matrix-Mediated Paracrine Signalling: A Mathematical Model Study , 2011, PloS one.

[18]  Marc Barthelemy,et al.  Spatial Networks , 2010, Encyclopedia of Social Network Analysis and Mining.

[19]  A. Czirók,et al.  Dynamic Analysis of Vascular Morphogenesis Using Transgenic Quail Embryos , 2010, PloS one.

[20]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[21]  Sylvie Lorthois,et al.  Fractal analysis of vascular networks: insights from morphogenesis. , 2010, Journal of theoretical biology.

[22]  R. Mark Henkelman,et al.  Three-Dimensional Analysis of Vascular Development in the Mouse Embryo , 2008, PloS one.

[23]  Andras Czirok,et al.  Network formation of tissue cells via preferential attraction to elongated structures. , 2006, Physical review letters.

[24]  R. Jain Normalization of Tumor Vasculature: An Emerging Concept in Antiangiogenic Therapy , 2005, Science.

[25]  A. Coniglio,et al.  Percolation and Burgers' dynamics in a model of capillary formation. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Kenneth J. Hillan,et al.  Discovery and development of bevacizumab, an anti-VEGF antibody for treating cancer , 2004, Nature Reviews Drug Discovery.

[27]  L. Preziosi,et al.  Modeling the early stages of vascular network assembly , 2003, The EMBO journal.

[28]  L Preziosi,et al.  Percolation, morphogenesis, and burgers dynamics in blood vessels formation. , 2003, Physical review letters.

[29]  M. Newman Assortative mixing in networks. , 2002, Physical review letters.

[30]  S. Chapman,et al.  Improved method for chick whole‐embryo culture using a filter paper carrier , 2001, Developmental dynamics : an official publication of the American Association of Anatomists.

[31]  H. Hinrichsen Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[32]  S. Brandt,et al.  TAL1/SCL is expressed in endothelial progenitor cells/angioblasts and defines a dorsal-to-ventral gradient of vasculogenesis. , 1997, Developmental biology.

[33]  Berk,et al.  Scale-invariant behavior and vascular network formation in normal and tumor tissue. , 1995, Physical review letters.

[34]  V. Hamburger,et al.  A series of normal stages in the development of the chick embryo , 1992, Journal of morphology.

[35]  Vicsek,et al.  Scaling in steady-state cluster-cluster aggregation. , 1985, Physical review. A, General physics.

[36]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[37]  Michael D. Abràmoff,et al.  Image processing with ImageJ , 2004 .