Eckstein E C, Belgacem F
Department of Biomedical Engineering, University of Miami, Coral Gables, Florida 33124.
Biophys J. 1991 Jul;60(1):53-69. doi: 10.1016/S0006-3495(91)82030-6.
A drift term is added to the convective diffusion equation for platelet transport so that situations with near-wall excesses of platelets can be described. The mathematical relationship between the drift and the fully developed, steady-state platelet concentration profile is shown and a functional form of the drift that leads to concentration profiles similar to experimentally determined profiles is provided. The transport equation is numerically integrated to determine concentration profiles in the developing region of a tube flow. With the approximate drift function and typical values of augmented diffusion constant, the calculated concentration profiles have near-wall excesses that mimic experimental results, thus implying the extended equation is a valid description of rheological events. Stochastic differential equations that are equivalent to the convective diffusion transport equation are shown, and simulations with them are used to illustrate the impact of the drift term on platelet concentration profiles during deposition in a tube flow.
在血小板传输的对流扩散方程中添加了一个漂移项，以便能够描述血小板在近壁处过量的情况。展示了漂移与充分发展的稳态血小板浓度分布之间的数学关系，并给出了一种能产生与实验测定分布相似的浓度分布的漂移函数形式。对传输方程进行数值积分，以确定管流发展区域内的浓度分布。利用近似的漂移函数和增大扩散常数的典型值，计算得到的浓度分布在近壁处有过量情况，这与实验结果相似，从而意味着扩展后的方程是对流变学事件的有效描述。给出了与对流扩散传输方程等效的随机微分方程，并利用它们进行模拟，以说明漂移项对管流沉积过程中血小板浓度分布的影响。
