Modeling of drug transport within capillaries and tissue remains a challenge, especially in tumors and cancers where the capillary network exhibits extremely irregular geometry. Recently introduced Composite Smeared Finite Element (CSFE) provides a new methodology of modeling complex convective and diffusive transport in the capillary-tissue system. The basic idea in the formulation of CSFE is in dividing the FE into capillary and tissue domain, coupled by 1D connectivity elements at each node. Mass transport in capillaries is smeared into continuous fields of pressure and concentration by introducing the corresponding Darcy and diffusion tensors. Despite theoretically correct foundation, there are still differences in the overall mass transport to (and from) tissue when comparing smeared model and a true 3D model. The differences arise from the fact that the smeared model cannot take into account the detailed non-uniform pressure and concentration distribution in the vicinity of capillaries. We introduced a field of correction function for diffusivity through the capillary walls of smeared models, in order to have the same mass accumulation in tissue as in case of true 3D models. The parameters of the numerically determined correction function are: ratio of thickness and diameter of capillary wall, ratio of diffusion coefficient in capillary wall and surrounding tissue; and volume fraction of capillaries within tissue domain. Partitioning at the capillary wall - blood interface can also be included. It was shown that the correction function is applicable to complex configurations of capillary networks, providing improved accuracy of our robust smeared models in computer simulations of real transport problems, such as in tumors or human organs.

中文翻译：

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用于生物组织系统中扩散传输的复合涂抹有限元精度提高的校正函数

毛细血管和组织内的药物运输建模仍然是一个挑战，尤其是在毛细血管网络表现出极不规则几何形状的肿瘤和癌症中。最近推出的复合涂抹有限元 (CSFE) 提供了一种新的方法来模拟毛细血管组织系统中的复杂对流和扩散传输。CSFE 公式的基本思想是将 FE 划分为毛细血管域和组织域，并通过每个节点的 1D 连接元素耦合。通过引入相应的达西张量和扩散张量，毛细血管中的质量传递被涂抹到连续的压力和浓度场中。尽管理论上是正确的，但在比较涂抹模型和真实 3D 模型时，进出组织的整体质量传输仍然存在差异。差异源于涂抹模型无法考虑毛细管附近详细的非均匀压力和浓度分布。我们通过涂抹模型的毛细血管壁引入了扩散率校正函数，以便在组织中具有与真实 3D 模型相同的质量积累。数值确定的校正函数的参数为​​：毛细血管壁的粗细比、毛细血管壁与周围组织的扩散系数比；和组织域内毛细血管的体积分数。还可以包括在毛细血管壁-血液界面处的分区。结果表明，修正函数适用于毛细管网络的复杂配置，