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

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.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 da...

[1]  Jens Harting,et al.  Inversion of hematocrit partition at microfluidic bifurcations. , 2016, Microvascular research.

[2]  Dominik Obrist,et al.  Red blood cell phase separation in symmetric and asymmetric microchannel networks: effect of capillary dilation and inflow velocity , 2016, Scientific Reports.

[3]  C. Ellis,et al.  Heterogeneity of red blood cell perfusion in capillary networks supplied by a single arteriole in resting skeletal muscle. , 1994, Circulation research.

[4]  T. Skalak,et al.  Hemodynamic Systems Analysis of Capillary Network Remodeling During the Progression of Type 2 Diabetes , 2011, Microcirculation.

[5]  G. Karniadakis,et al.  Blood–plasma separation in Y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study , 2012, Physical biology.

[6]  R. Carr.  Estimation of hematocrit profile symmetry recovery length downstream from a bifurcation. , 1989, Biorheology.

[7]  A. Pries,et al.  Biophysical aspects of blood flow in the microvasculature. , 1996, Cardiovascular research.

[8]  B. Fenton,et al.  Nonuniform red cell distribution in 20 to 100 μm bifurcations , 1985 .

[9]  B. W. Roberts,et al.  The distribution of freely suspended particles at microfluidic bifurcations , 2006 .

[10]  Andreas A Linninger,et al.  Hematocrit Distribution and Tissue Oxygenation in Large Microcirculatory Networks , 2015, Microcirculation.

[11]  Aleksander S Popel,et al.  Microcirculation and Hemorheology. , 2005, Annual review of fluid mechanics.

[12]  Céline Fouard,et al.  A Novel Three‐Dimensional Computer‐Assisted Method for a Quantitative Study of Microvascular Networks of the Human Cerebral Cortex , 2006, Microcirculation.

[13]  R. Carr,et al.  Plasma Skimming in Vascular Trees: Numerical Estimates of Symmetry Recovery Lengths , 1995, Microcirculation.

[14]  A. Pries,et al.  Red cell distribution at microvascular bifurcations. , 1989, Microvascular research.

[15]  A. Pries,et al.  Microvascular blood viscosity in vivo and the endothelial surface layer. , 2005, American journal of physiology. Heart and circulatory physiology.

[16]  G. Schmid-Schönbein,et al.  Model studies on distributions of blood cells at microvascular bifurcations. , 1985, The American journal of physiology.

[17]  Prosenjit Bagchi,et al.  Direct Numerical Simulation of Cellular-Scale Blood Flow in 3D Microvascular Networks. , 2017, Biophysical journal.

[18]  H. H. Lipowsky,et al.  The Distribution of Blood Rheological Parameters in the Microvasculature of Cat Mesentery , 1978, Circulation research.

[19]  A. Krogh.  Studies on the physiology of capillaries , 1921, The Journal of physiology.

[20]  R. Skalak,et al.  Strain energy function of red blood cell membranes. , 1973, Biophysical journal.

[21]  John B. Geddes,et al.  Oscillations in a Simple Microvascular Network , 2005, Annals of Biomedical Engineering.

[22]  G Enden,et al.  A numerical study of plasma skimming in small vascular bifurcations. , 1994, Journal of biomechanical engineering.

[23]  Ying Song,et al.  Direct labeling and visualization of blood vessels with lipophilic carbocyanine dye DiI , 2008, Nature Protocols.

[24]  A. Acrivos,et al.  A three-dimensional analysis of plasma skimming at microvascular bifurcations. , 1991, Microvascular research.

[25]  A. Undar,et al.  A microfluidic device for continuous, real time blood plasma separation. , 2006, Lab on a chip.

[26]  Shayn M. Peirce,et al.  Agent-Based Model of Therapeutic Adipose-Derived Stromal Cell Trafficking during Ischemia Predicts Ability To Roll on P-Selectin , 2009, PLoS Comput. Biol..

[27]  W. Helfrich,et al.  Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. , 1989, Physical review. A, General physics.

[28]  J. Restrepo,et al.  Simulated Red Blood Cell Motion in Microvessel Bifurcations: Effects of Cell–Cell Interactions on Cell Partitioning , 2011, Cardiovascular engineering and technology.

[29]  G. Cokelet,et al.  Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms. , 1994, The American journal of physiology.

[30]  Prosenjit Bagchi,et al.  A computational approach to modeling cellular-scale blood flow in complex geometry , 2017, J. Comput. Phys..

[31]  P. Johnson,et al.  Capillary network geometry and red cell distribution in hamster cremaster muscle. , 1982, The American journal of physiology.

[32]  Stephan Gekle,et al.  On the bending algorithms for soft objects in flows , 2016, Comput. Phys. Commun..

[33]  D. Holmes,et al.  Spatial Distributions of Red Blood Cells Significantly Alter Local Haemodynamics , 2014, PloS one.

[34]  Toru Hyakutake,et al.  Numerical simulation of red blood cell distributions in three-dimensional microvascular bifurcations. , 2015, Microvascular research.

[35]  Y. Sui,et al.  Motion of a spherical capsule in branched tube flow with finite inertia , 2016, Journal of Fluid Mechanics.

[36]  A. Acrivos,et al.  Fluid skimming and particle entrainment into a small circular side pore , 1991, Journal of Fluid Mechanics.

[37]  V. Doyeux,et al.  Spheres in the vicinity of a bifurcation: elucidating the Zweifach–Fung effect , 2010, Journal of Fluid Mechanics.

[38]  Axel R Pries,et al.  Angioadaptation: keeping the vascular system in shape. , 2002, News in physiological sciences : an international journal of physiology produced jointly by the International Union of Physiological Sciences and the American Physiological Society.

[39]  R T Carr,et al.  Plasma skimming in serial microvascular bifurcations. , 1990, Microvascular research.

[40]  Juan M. Restrepo,et al.  Simulated Two-dimensional Red Blood Cell Motion, Deformation, and Partitioning in Microvessel Bifurcations , 2008, Annals of Biomedical Engineering.

[41]  S. Gekle,et al.  Theory and algorithms to compute Helfrich bending forces: a review , 2017, Journal of physics. Condensed matter : an Institute of Physics journal.

[42]  Alireza Yazdani,et al.  Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Junfeng Zhang,et al.  Multiple red blood cell flows through microvascular bifurcations: cell free layer, cell trajectory, and hematocrit separation. , 2013, Microvascular research.

[44]  W. Olbricht,et al.  The motion of model cells at capillary bifurcations. , 1987, Microvascular research.

[45]  K. Svanes,et al.  Variations in small blood vessel hematocrits produced in hypothermic rats by micro-occlusion , 1968 .

[46]  R. Skalak,et al.  Cell distribution in capillary networks. , 1980, Microvascular research.

[47]  Y. Fung.  Stochastic flow in capillary blood vessels. , 1973, Microvascular research.