Analysis of red blood cell partitioning at bifurcations in simulated microvascular networks

Abstract

Partitioning of red blood cells (RBCs) at vascular bifurcations has been studied over many decades using in vivo, in vitro, and theoretical models. These studies have shown that RBCs usually do not distribute to the daughter vessels with the same proportion as the blood flow. Such disproportionality occurs, whereby the cell distribution fractions are either higher or lower than the flow fractions and have been referred to as classical partitioning and reverse partitioning, respectively. The current work presents a study of RBC partitioning based on, for the first time, a direct numerical simulation (DNS) of a flowing cell suspension through modeled vascular networks that are comprised of multiple bifurcations and have topological similarity to microvasculature in vivo. The flow of deformable RBCs at physiological hematocrits is considered through the networks, and the 3D dynamics of each individual cell are accurately resolved. The focus is on the detailed analysis of the partitioning, based on the DNS data, as it develops naturally in successive bifurcations, and the underlying mechanisms. We find that while the time-averaged partitioning at a bifurcation manifests in one of two ways, namely, the classical or reverse partitioning, the time-dependent behavior can cycle between these two types. We identify and analyze four different cellular-scale mechanisms underlying the time-dependent partitioning. These mechanisms arise, in general, either due to an asymmetry in the RBC distribution in the feeding vessels caused by the events at an upstream bifurcation or due to a temporary increase in cell concentration near capillary bifurcations. Using the DNS results, we show that a positive skewness in the hematocrit profile in the feeding vessel is associated with the classical partitioning, while a negative skewness is associated with the reverse one. We then present a detailed analysis of the two components of disproportionate partitioning as identified in prior studies, namely, plasma skimming and cell screening. The plasma skimming component is shown to under-predict the disproportionality, leaving the cell screening component to make up for the difference. The crossing of the separation surface by the cells is observed to be a dominant mechanism underlying the cell screening, which is shown to mitigate extreme heterogeneity in RBC distribution across the networks.

Neutrophil-mediated dynamic capillary stalls in ischemic penumbra: persistent traffic jams after reperfusion contribute to injury

“…By expanding our previous observations under physiological conditions (17), we see that the capillary RBC flow is extremely irregular and intermittent in the ischemic penumbra, with cells repeatedly getting stuck and released in the microcirculation. We already know that within brain tissue, capillary flow velocities are very different from each other, plasma and red blood cells are differentially partitioned at bifurcations (58), causing a spatial heterogeneity which can lower oxygen extraction efficiency (16,(59)(60)(61)(62). Simulations have revealed that the flow kinetics and partitioning in the tight lumen of capillaries are dominated by complex physical cell-cell interactions and rheological parameters which are influenced by temporal events affecting the incidental cell distributions (58).…”

“…We already know that within brain tissue, capillary flow velocities are very different from each other, plasma and red blood cells are differentially partitioned at bifurcations (58), causing a spatial heterogeneity which can lower oxygen extraction efficiency (16,(59)(60)(61)(62). Simulations have revealed that the flow kinetics and partitioning in the tight lumen of capillaries are dominated by complex physical cell-cell interactions and rheological parameters which are influenced by temporal events affecting the incidental cell distributions (58). Our findings introduce experimental data on the temporal heterogeneity in individual capillary segments, which can readily influence the upstream and downstream vessels in the network, and cumulatively in a chain-like fashion.…”

Deformation and sorting of capsules in a T-junction

“…Biological cells are examples of naturally occurring capsules. Haemodynamics in the capillary network (Popel & Johnson 2005;Balogh & Bagchi 2018) and porous media such as the placenta (Jensen & Chernyavsky 2019) involve the transport and deformation of discrete red blood cells, with diagnostic and treatment of micro-circulation conditions relying on advances in the understanding of the resulting rheology. There is also considerable diagnostic potential in isolating circulating cancer cells, which are typically of similar size but more deformable than healthy white blood cells (Geislinger & Franke 2013;Lim & Hoon 2014), or malaria-infected red blood cells, which stiffen by a factor of five due to the parasite that enters them (Bow et al 2011).…”

Effect of Cytoplasmic Viscosity on Red Blood Cell Migration in Small Arteriole-level Confinements

“…Due to the complexity of blood suspension dynamics, large scale simulation tools are required to understand much of the salient physics. Many approaches have been developed including the boundary integral method (Zhao et al, 2012;Sinha and Graham, 2015;Pozrikidis, 1992), the immersed boundary method coupled with the Lattice Boltzmann method (Shen et al, 2016;Krüger, 2012;Reasor et al, 2013;Závodszky et al, 2017;de Haan et al, 2018), and other immersed boundary approaches coupled to finite volume/difference/element solvers (Ye et al, 2016;Doddi, 2008;Balogh and Bagchi, 2018;Sigüenza et al, 2016;Saadat et al, 2018). The boundary integral method (BEM) has had great success in simulating smaller suspensions of cells, but poor scaling in particle number often reduces the ability to study larger suspensions via BEM.…”

“…The Lattice Boltzmann method has shown extremely good scaling in particle number and also the ability to study important features like the viscosity contrast -the viscosity ratio of inner cell cytoplasm to the outer plasma -which makes it a promising simulation technique (Shen et al, 2016;de Haan et al, 2018). In a similar manner, immersed boundary methods coupled to finite volume solvers or finite element solvers have also shown great promise in simulating these large suspensions and we will be utilizing this method to further elucidate the physics of these suspensions (Saadat et al, 2018;Balogh and Bagchi, 2018). Our method utilizes a finite volume flow solver and finite elements to model the physics of the RBCs.…”