Name
Abstract | ||
|---|---|---|
Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoretical model of two-dimensional experimental vasculogenesis has been recently proposed, showing the relevance of percolation concepts and of cell cross-talk (chemotactic autocrine loop) to the understanding of this self-aggregation process. Here we study the natural 3D extension of the computational model proposed earlier, which is relevant for the investigation of the genuinely three-dimensional process of vasculogenesis in vertebrate embryos. The computational model is based on a multidimensional Burgers equation coupled with a reaction diffusion equation for a chemotactic factor and a mass conservation law. The numerical approximation of the computational model is obtained by high order relaxed schemes. Space and time discretization are performed by using TVD schemes and, respectively, IMEX schemes. Due to the computational costs of realistic simulations, we have implemented the numerical algorithm on a cluster for parallel computation. Starting from initial conditions mimicking the experimentally observed ones, numerical simulations produce network-like structures qualitatively similar to those observed in the early stages of in vivo vasculogenesis. We develop the computation of critical percolative indices as a robust measure of the network geometry as a first step towards the comparison of computational and experimental data. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.jcp.2007.03.030 | J. Comput. Physics |
Keywords | Field | DocType |
vasculogenesis simulations,chemotactic factor,relaxed schemes,percolative analysis,computational model,imex schemes,vivo vasculogenesis,chemotactic autocrine loop,numerical approximation,computational cost,early blood vessel formation,computational biology,two-dimensional experimental vasculogenesis,numerical algorithm,numerical simulation,successful theoretical model,cell migration,three dimensional,initial condition,embryos,mass conservation,burgers equation,computer model,parallel computer,reaction diffusion equation | Space time,Statistical physics,Discretization,Mathematical analysis,Vasculogenesis,Burgers' equation,Geometry,Reaction–diffusion system,Mathematics,Conservation of mass,Conservation law,Computation | Journal |
Volume | Issue | ISSN |
225 | 2 | Journal of Computational Physics |
Citations | PageRank | References |
2 | 0.68 | 2 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fausto Cavalli | 1 | 18 | 3.31 |
| A. Gamba | 2 | 2 | 0.68 |
| G. Naldi | 3 | 2 | 1.01 |
| Matteo Semplice | 4 | 64 | 8.16 |
| D. Valdembri | 5 | 2 | 0.68 |
| G. Serini | 6 | 2 | 1.01 |