Kim D, Armenante P M, Durán W N
Department of Chemical Engineering, Chemistry, and Environmental Science, New Jersey Institute of Technology, Newark 07102.
Microvasc Res. 1990 Nov;40(3):358-78. doi: 10.1016/0026-2862(90)90033-n.
A one-dimensional, unsteady-state mathematical model was developed to describe the transfer of macromolecules across a microvascular wall and into the interstitial space. The proposed theoretical model accounts for both molecular diffusion and convective transfer through the microvascular wall as well as in the interstitial space. The resulting partial differential equations were simultaneously solved using the Laplace transform method. The inversion of the Laplace transformed equations was obtained by using contour integration in the complex region. The final solution is represented by two equations expressing the macromolecule concentration in the microvascular wall region and in the interstitial space, respectively, as functions of time, spatial coordinate, macromolecule concentration in the microvascular wall at the plasma-wall interface, wall thickness, wall-interstitial space equilibrium constant for the macromolecules, ratio of the cross-sectional area of the two regions, sieving coefficients, diffusivity coefficients, and average fluid velocity terms in the two regions. Plots of the macromolecule concentration in both regions as a function of time are presented and discussed for selected values of the parameters. An analytical expression for the total amount of mass which has accumulated in a portion of the interstitial space at any given time was also derived and used to determine the average fluid velocity term and the diffusivity coefficient for each of the two regions from published experimental data (A. Y. Bekker, A. B. Ritter, and W. N. Durán, 1989, Microvasc. Res. 34, 200-216). A numerical nonlinear regression method was used for this purpose. The values for the diffusivity coefficients found in this work for this particular data set compare favorably with the results previously obtained by other workers in similar systems. It is expected that our model will be used in the future to describe the dynamics of mass transfer across a microvascular wall and into the interstitial space, on the basis of the molecular diffusion and/or convective transport mechanisms, thus contributing to the solution of the controversy regarding the nature of the transfer mechanism controlling macromolecule transport in living systems.
开发了一个一维非稳态数学模型，用于描述大分子穿过微血管壁并进入间质空间的传输过程。所提出的理论模型考虑了分子扩散以及通过微血管壁和间质空间的对流传输。使用拉普拉斯变换法同时求解所得的偏微分方程。通过在复区域中进行围道积分获得拉普拉斯变换方程的反演。最终解由两个方程表示，分别将微血管壁区域和间质空间中的大分子浓度表示为时间、空间坐标、血浆 - 壁界面处微血管壁中的大分子浓度、壁厚度、大分子的壁 - 间质空间平衡常数、两个区域的横截面积之比、筛分系数、扩散系数以及两个区域中的平均流体速度项的函数。针对选定的参数值，给出并讨论了两个区域中大分子浓度随时间变化的曲线。还推导了在任何给定时间在间质空间的一部分中积累的总质量的解析表达式，并用于根据已发表的实验数据（A. Y. 贝克尔、A. B. 里特和 W. N. 杜兰，1989 年，《微血管研究》34 卷，200 - 216 页）确定两个区域各自的平均流体速度项和扩散系数。为此使用了数值非线性回归方法。在这项工作中针对该特定数据集找到的扩散系数值与其他研究人员在类似系统中先前获得的结果相比具有优势。预计我们的模型未来将用于基于分子扩散和/或对流传输机制描述大分子穿过微血管壁并进入间质空间的传质动力学，从而有助于解决关于控制生物系统中大分子传输的传输机制性质的争议。
