早期血管形成的3D模拟
3D simulations of early blood vessel formation
AI总结：
本研究通过将多维Burgers方程与趋化因子反应扩散方程及质量守恒定律耦合，建立了三维血管生成的数学模型，并采用高阶松弛格式和并行计算进行数值模拟，成功生成了与体内早期血管生成相似的网络结构，并计算了临界渗流指数以量化网络几何特征。
摘要：
血管网络通过单个细胞自发聚集形成，这些细胞向血管化位点迁移（血管发生）。最近，一个成功的二维实验性血管生成理论模型被提出，显示了渗流概念和细胞串扰（趋化自分泌环）对理解这一自聚集过程的相关性。在此，我们研究了早期提出的计算模型的自然三维扩展，这对于研究脊椎动物胚胎中真正三维的血管生成过程具有重要意义。该计算模型基于一个多维Burgers方程，耦合了趋化因子的反应扩散方程和质量守恒定律。计算模型的数值逼近通过高阶松弛格式获得。空间和时间离散化分别使用TVD格式和IMEX格式。由于实际模拟的计算成本，我们在并行计算集群上实现了数值算法。从模拟实验观察到的初始条件出发，数值模拟产生了与体内早期血管生成阶段定性相似的网络结构。我们开发了临界渗流指数的计算，作为网络几何的稳健度量，这是迈向计算与实验数据比较的第一步。
英文摘要：
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 threedimensional 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 \emph{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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
