Triebold Carlson, Barber Jared
Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, Indianapolis, USA.
Biomech Model Mechanobiol. 2022 Jun;21(3):771-796. doi: 10.1007/s10237-022-01560-x. Epub 2022 Feb 10.
Red blood cells (RBCs) make up 40-45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5-1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL's resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell-cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL's resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.
红细胞（RBCs）占血液的40 - 45%，在氧气运输中发挥着重要作用。这种运输取决于红细胞在全身的分布，而这种分布是高度不均匀的。反过来，这种分布又取决于红细胞在血液从一根血管流入两根血管的分叉血管处如何分布或分配。一些研究使用数学模型来考虑红细胞在这种分叉处的分配，以便得出有用的见解。然而，这些研究假设血管壁是一个平坦、不可渗透的均匀表面。虽然这是一个很好的初步近似，特别是对于较大的血管，但血管壁通常被一层厚度约为0.5 - 1微米的柔性多孔内皮糖萼或内皮表面层（ESL）所覆盖。为了更好地理解这一层对红细胞分配的可能影响，使用一个柔性二维模型分析了一个分叉的毛细血管。此外，当ESL特性发生变化时，该模型还用于研究红细胞变形和红细胞对ESL区域的穿透。红细胞用相互连接的粘弹性元件表示。斯托克斯流方程（粘性流）对周围流体进行建模。ESL中的流动使用具有相应水力阻力的多孔介质的布林克曼近似进行建模。ESL对压缩的阻力使用渗透压差异进行建模。一次有一个细胞通过分叉，因此不存在细胞间相互作用。探索了一系列生理相关的水力阻力和渗透压差异。降低水力阻力和/或降低渗透压差异（ESL对压缩的阻力）产生了四种行为：（1）红细胞分配不均匀性略有增加；（2）红细胞变形减少；（3）红细胞速度相对于血流速度降低；（4）红细胞更深入地穿透ESL。将ESL的流动阻力和/或压缩阻力降低到病理水平可能会导致更频繁的细胞粘附和凝血，以及由于ATP和一氧化氮释放减弱而导致的血管调节受损。还讨论了可能导致这些行为的潜在机制。
