A viscoelastic model of blood capillary extension and regression: derivation, analysis, and simulation
A viscoelastic model of blood capillary extension and regression: derivation, analysis, and simulation
复制标题
毛细血管扩张和回归的粘弹性模型：推导、分析和模拟
DOI：
10.1007/s00285-012-0624-8
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发表时间：
2012-11
影响因子：
1.9
通讯作者：
Chunjing Xie
中科院分区：
文献类型：
--
作者：
Xiaoming Zheng;Chunjing Xie
本文研究了毛细血管生长中的一个基本问题：细胞增殖或死亡如何引起应激反应和毛细血管的伸展或消退。我们开发了一个一维粘弹性模型的毛细血管的延伸/回归下与周围环境的非线性摩擦，分析其解决方案的性质，并模拟各种生长模式的血管生成。数学模型将细胞密度视为生长压力，引起细胞的粘弹性响应，这再次引起毛细管的延伸或消退。非线性分析捕获了存在生物学意义解时的两种情况：（1）细胞密度从根部到尖端降低，这可能发生在血管消退中;（2）细胞密度与时间无关，并且沿毛细血管沿着变化较小，这可能发生在毛细血管延伸而不增殖中。由于细胞增殖或死亡而引起的细胞密度扰动的线性分析预测，如果细胞密度的变化在时间上足够慢，则存在全局生物解。通过数值逼近捕捉到了爆破的例子，并通过慢增长过程恢复了全局解，验证了线性分析理论的正确性。数值模拟表明，该模型可以重现血管生成实验中的几个生物条件下，包括血管延伸没有增殖和血管退化。
This work studies a fundamental problem in blood capillary growth: how the cell proliferation or death induces the stress response and the capillary extension or regression. We develop a one-dimensional viscoelastic model of blood capillary extension/regression under nonlinear friction with surroundings, analyze its solution properties, and simulate various growth patterns in angiogenesis. The mathematical model treats the cell density as the growth pressure eliciting a viscoelastic response from the cells, which again induces extension or regression of the capillary. Nonlinear analysis captures two cases when the biologically meaningful solution exists: (1) the cell density decreases from root to tip, which may occur in vessel regression; (2) the cell density is time-independent and is of small variation along the capillary, which may occur in capillary extension without proliferation. The linear analysis with perturbation in cell density due to proliferation or death predicts the global biological solution exists provided the change in cell density is sufficiently slow in time. Examples with blow-ups are captured by numerical approximations and the global solutions are recovered by slow growth processes, which validate the linear analysis theory. Numerical simulations demonstrate this model can reproduce angiogenesis experiments under several biological conditions including blood vessel extension without proliferation and blood vessel regression.
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DOI：
10.1083/jcb.200601159
发表时间：
2006-09-11
期刊：
The Journal of cell biology
影响因子：
--
作者：
Prass M;Jacobson K;Mogilner A;Radmacher M
通讯作者：
Radmacher M
影响因子：
3.7
作者：
Travasso RD;Corvera Poiré E;Castro M;Rodríguez-Manzaneque JC;Hernández-Machado A
通讯作者：
Hernández-Machado A
影响因子：
3.1
作者：
Sheng Tong;Fan Yuan
通讯作者：
Sheng Tong;Fan Yuan
DOI：
10.1007/978-3-540-74331-6
发表时间：
2005
期刊：
--
影响因子：
--
作者：
A. Friedman
通讯作者：
A. Friedman
DOI：
10.1093/imammb/dqp015
发表时间：
2010-03-01
影响因子：
1.1
作者：
Fozard, J. A.;Byrne, H. M.;King, J. R.
通讯作者：
King, J. R.