LaBS, Dipartimento di Chimica, Materiali e Ingegneria Chimica "Giulio Natta", Politecnico di Milano, Milan, Italy.
MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy.
Int J Numer Method Biomed Eng. 2019 Mar;35(3):e3165. doi: 10.1002/cnm.3165. Epub 2018 Nov 20.
We present a two-phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one-dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation, and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus-Lindqvist, plasma skimming, and capillary leakage effects on the distribution of flow in a microvascular network.
我们提出了一个描述血浆与红细胞相互作用的微循环两阶段模型。该模型考虑了典型的微循环特征，如 Fahraeus-Lindqvist 效应和血浆撇除。除了这些特征，该模型还描述了毛细血管与周围组织的相互作用。更准确地说，该模型描述了毛细血管跨壁流动与周围间质压力的相互作用。此外，毛细血管被表示为具有任意、可能弯曲配置的一维通道。后两个特征依赖于该模型根据局部微分形式的质量和动量守恒来沿毛细血管轴计算流量和压力变化的独特能力。事实上，该模型建立在坚实的数学基础上，这也是本文所关注的。特别是，我们提出了模型推导、变分公式及其使用有限元方法的近似。最后，我们通过对 Fahraeus-Lindqvist、血浆撇除和毛细血管渗漏效应对微血管网络中血流分布的重要性进行比较计算研究来结束这项工作。
