el-Kareh A W, Braunstein S L, Secomb T W
Department of Physiology, University of Arizona, Tucson 85724.
Biophys J. 1993 May;64(5):1638-46. doi: 10.1016/S0006-3495(93)81532-7.
We present theoretical calculations relating the effective diffusivity of monoclonal antibodies in tissue (Deff) to the actual diffusivity in the interstitium (Dint) and the interstitial volume fraction phi. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio Deff/Dint is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. Deff/Dint is found to generally be between (2/3) phi and phi for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on Deff/Dint is examined by varying the arrangement of the cells, and found to be slight. Also, the estimates of Deff/Dint are shown to be insensitive to typical nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity of an IgG polyclonal antibody both in water and in tumor tissue, we deduce that the diffusivity of this molecule in the interstitium is one-tenth to one-twentieth its diffusivity in water. We also conclude that exclusion of molecules from cells (an effect independent of molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%). This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular-weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.
我们给出了将单克隆抗体在组织中的有效扩散系数（Deff）与间质中的实际扩散系数（Dint）以及间质体积分数φ相关联的理论计算。测量的扩散系数值是有效值，是从将组织视为连续介质的浓度分布推导出来的。通过使用均匀化理论，计算了间质体积分数在10%至65%范围内的Deff/Dint比值。假设只有细胞间间隙中的扩散对有效扩散系数有贡献。所考虑的几何结构是周期性排列的长方体细胞，细胞间有均匀的间隙。对于这些几何结构，发现Deff/Dint通常在(2/3)φ和φ之间。一般来说，细胞间的扩散路径不是直的。通过改变细胞排列来研究弯曲路径对Deff/Dint的影响，发现影响很小。此外，结果表明Deff/Dint的估计值对细胞间间隙宽度的典型不均匀性不敏感。根据我们的计算以及已发表的关于IgG多克隆抗体在水和肿瘤组织中的有效扩散系数的实验测量结果，我们推断该分子在间质中的扩散系数是其在水中扩散系数的十分之一到二十分之一。我们还得出结论，对于小的间质体积分数（约20%），细胞对分子的排斥（一种与分子量无关的效应）对有效扩散系数降低的贡献与间质阻碍一样大。这表明使用较小分子量的分子（如抗体片段或双功能抗体）导致的向组织递送速率的增加可能小于预期。
