Harmonic Solutions of a Mixed Boundary Problem Arising in the Modeling of Macromolecular Transport into Vessel Walls.
Harmonic Solutions of a Mixed Boundary Problem Arising in the Modeling of Macromolecular Transport into Vessel Walls.
复制标题
大分子输运进入血管壁的建模中出现的混合边界问题的调和解。
DOI：
10.1016/j.camwa.2008.11.020
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Rumschitzki,David
中科院分区：
文献类型：
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作者：
Balsim,Igor;Neimark,MathewA;Rumschitzki,David
导致动脉粥样硬化的最早事件涉及LPW密度脂蛋白(LDL)胆固醇从血液通过排列在动脉壁上的内皮细胞的运输。拉普拉斯方程描述了示踪剂在血管壁上的稳态扩散分布。这就产生了一个具有混合Dirichlet和Robin条件的边值问题。我们构造了一个线性积分方程组，它近似于解的级数展开的系数。我们利用Gershgorin关于相应矩阵的特征值位置的定理，解析地证明了该问题解的存在性。我们利用Miranda定理给出了一个唯一性证明[C.Miranda，P.D.E.of椭圆型，Springer-Verlag，柏林，1970]。解析构造法构成了数值计算算法的基础。我们将我们的结果应用于上面的输运问题，并用它们解释了示踪剂局部渗漏斑点随示踪剂循环时间增长的实验观测。
The earliest events leading to atherosclerosis involve the transport of lpw density lipooprotein (LDL) cholesterol from the blood across endothelial cells that line the artery wall. Laplace’s equation describes the steady state diffusion profile of a tracer through the vessel wall. This gives rise to a boundary value problem with mixed Dirichlet and Robin conditions. We construct a linear system of integral equations that approximate the coefficients of the series expansion of the solution. We prove the existence of the solution to this problem analytically by using Gershgorin’s theorem on the location of the eigenvalues of the corresponding matrix. We give a uniqueness proof using Miranda’s theorem [C. Miranda, P.D.E. of Elliptic Type, Springer-Verlag, Berlin, 1970]. The analytical construction method forms the basis for a numerical calculation algorithm. We apply our results to the transport problem above, and use them to interpret experimental observations of the growth of localized tracer leakage spots with tracer circulation time.