We present, to our knowledge, the first direct numerical simulation of 3D cellular-scale blood flow in physiologically realistic microvascular networks. The vascular networks are designed following in vivo images and data, and are comprised of bifurcating, merging, and winding vessels. Our model resolves the large deformation and dynamics of each individual red blood cell flowing through the networks with high fidelity, while simultaneously retaining the highly complex geometric details of the vascular architecture. To our knowledge, our simulations predict several novel and unexpected phenomena. We show that heterogeneity in hemodynamic quantities, which is a hallmark of microvascular blood flow, appears both in space and time, and that the temporal heterogeneity is more severe than its spatial counterpart. The cells are observed to frequently jam at vascular bifurcations resulting in reductions in hematocrit and flow rate in the daughter and mother vessels. We find that red blood cell jamming at vascular bifurcations results in several orders-of-magnitude increase in hemodynamic resistance, and thus provides an additional mechanism of increased in vivo blood viscosity as compared to that determined in vitro. A striking result from our simulations is negative pressure-flow correlations observed in several vessels, implying a significant deviation from Poiseuille's law. Furthermore, negative correlations between vascular resistance and hematocrit are observed in various vessels, also defying a major principle of particulate suspension flow. To our knowledge, these novel findings are absent in blood flow in straight tubes, and they underscore the importance of considering realistic physiological geometry and resolved cellular interactions in modeling microvascular hemodynamics.

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.

Generation 2 to generation 5 poly(amidoamine) (PAMAM) dendrimers having different terminal functionalities were analyzed by capillary electrophoresis (CE). Polyacrylamide gel electrophoresis was also used to assess the composition of the individual generations for comparison with the CE results. Separation of PAMAMs can be accomplished by either using uncoated silica or silanized silica capillaries, although reproducibility is poor using the uncoated silica capillary. To improve run-to-run reproducibility, silanized capillary was used and various internal standards were also tested. Relative and normalized migration times of primary amine terminated PAMAM dendrimers were then determined using 2,3-diaminopyridine (2,3-DAP) as an internal standard. Using silanized capillaries and internal standards, the relative and normalized migration times are fully reproducible and comparable between runs. Apparent dimensionless electrophoretic mobilities were determined and the results were compared to theoretical calculations. It is concluded that for PAMAMs a complex separation mechanism has to be considered in CE, where the movement of the ions is due to the electric field, but the separation is rather the consequence of the adsorption/desorption equilibria on the capillary wall ("electrokinetic capillary chromatography"). The described method may be used for quality control and may serve as an effective technique to analyze polycationic PAMAM dendrimers and their derivatives with different surface modifications.

Generation 5 ethylenediamine (EDA)-cored poly(amidoamine) (PAMAM) dendrimers (E5, E denotes the EDA core and 5 the generation number) with different degrees of acetylation and carboxylation were synthesized and used as a model system to investigate the effect of charge and the influence of dendrimer surface modifications on electrophoretic mobility (EM) and molecular distribution. The surface-modified dendrimers were characterized by size-exclusion chromatography, 1H NMR, MALDI-TOF-MS, PAGE, and CE. The focus of our study was to determine how EM changes as a function of particle charge and molecular mass, and how the molecular distribution changes due to surface modifications. We demonstrate that partially modified dendrimers have much broader migration peaks than those of fully surface functionalized or unmodified E5 dendrimers due to variations in the substitution of individual dendrimer surfaces. EM decreased nonlinearly with increases in surface acetylation for both PAMAM acetamides and PAMAM succinamic acids, indicating a complex migration activity in CE separations that is not solely due to charge/mass ratio changes. These studies provide new insights into dendrimer properties under an electric field, as well as into the characterization of dendrimer-based materials being developed for medical applications.

We present a computational methodology for modeling cellular-scale blood flow in arbitrary and highly complex geometry. Our approach is based on immersedboundary methods, which allow modeling flows in arbitrary geometry while resolving the large deformation and dynamics of every blood cell with high fidelity. The present methodology seamlessly integrates different modeling components dealing with stationary rigid boundaries of complex shape, moving rigid bodies, and highly deformable interfaces governed by nonlinear elasticity. Thus it enables us to simulate 'whole' blood suspensions flowing through physiologically realistic microvascular networks that are characterized by multiple bifurcating and merging vessels, as well as geometrically complex lab-on-chip devices. R2C1The focus of the present work is on the development of a versatile numerical technique that is able to consider deformable cells and rigid bodies flowing in three-dimensional arbitrarily complex geometries over a diverse range of scenarios. After describing the methodology, a series of validation studies are presented against analytical theory, experimental data, and previous numerical results. Then, the capability of the methodology is demonstrated by simulating flows of deformable blood cells and heterogeneous cell suspensions in both physiologically realistic microvascular networks and geometrically intricate microfluidic devices.It is shown that the methodology can predict several complex microhemodynamic phenomena observed in vascular networks and microfluidic devices. The present methodology is robust and versatile, and has the potential to scale up to very large microvascular networks at organ levels.

Using a high‐fidelity, 3D computational model of blood flow in microvascular networks, we provide the full 3D distribution of wall shear stress ( WSS ), and its gradient ( WSSG ), and quantify the influence of red blood cells ( RBC s) on WSS and WSSG . The deformation and flow dynamics of the individual RBC s are accurately resolved in the model, while physiologically realistic microvascular networks comprised of multiple bifurcations, convergences, and tortuous vessels are considered. A strong heterogeneity in WSS and WSSG is predicted across the networks, with the highest WSS occurring in precapillary bifurcations and capillary vessels. 3D variations of WSS and WSSG are shown to occur due to both network morphology and the influence of RBC s. The RBC s increase the WSS by as much as three times compared to that when no RBC s are present, and the highest increase is observed in venules. WSSG also increases significantly, and high WSSG s occur over wider regions in the presence of RBC s. In most vessels, the circumferential component of WSSG is observed to be greater than the axial component in the presence of RBC s, while the opposite trend is observed when RBC s are not considered. These results underscore the important role of RBC s on WSS and WSSG that cannot be predicted by widely used 1D models of network blood flow. Furthermore, the subendothelium‐scale variations of WSS and WSSG predicted by the present model have implications in terms of endothelial cell functions in the microvasculature.

A computational study is presented on the flow of deformable red blood cells in stenosed microvessels. It is observed that the Fahraeus-Lindqvist effect is significantly enhanced due to the presence of a stenosis. The apparent viscosity of blood is observed to increase by several folds when compared to non-stenosed vessels. An asymmetric distribution of the red blood cells, caused by geometric focusing in stenosed vessels, is observed to play a major role in the enhancement. The asymmetry in cell distribution also results in an asymmetry in average velocity and wall shear stress along the length of the stenosis. The discrete motion of the cells causes large time-dependent fluctuations in flow properties. The root-mean-square of flow rate fluctuations could be an order of magnitude higher than that in non-stenosed vessels. Several folds increase in Eulerian velocity fluctuation is also observed in the vicinity of the stenosis. Surprisingly, a transient flow reversal is observed upstream a stenosis but not downstream. The asymmetry and fluctuations in flow quantities and the flow reversal would not occur in absence of the cells. It is concluded that the flow physics and its physiological consequences are significantly different in micro- versus macrovascular stenosis.

In the microcirculation, a plasma layer forms near the vessel walls that is free of red blood cells (RBCs). This region, often termed as the cell-free layer (CFL), plays important haemorheological and biophysical roles, and has been the subject of extensive research. Many previous studies have considered the CFL development in single, isolated vessels that are straight tubes or channels, as well as in isolated bifurcations and mergers. In the body, blood vessels are typically winding and sequentially bifurcate into smaller vessels or merge to form larger vessels. Because of this geometric complexity, the CFL in vivo is three-dimensional (3D) and asymmetric, unlike in fully developed flow in straight tubes. The three-dimensionality of the CFL as it develops in a vascular network, and the underlying hydrodynamic mechanisms, are not well understood. Using a high-fidelity model of cellular-scale blood flow in microvascular networks with in vivo-like topologies, we present a detailed analysis of the fully 3D and asymmetric nature of the CFL in such networks. We show that the CFL significantly varies over different aspects of the networks. Along the vessel lengths, such variations are predominantly non-monotonic, which indicates that the CFL profiles do not simply become more symmetric over the length as they would in straight vessels. We show that vessel tortuosity causes the CFL to become more asymmetric along the length. We specifically identify a curvature-induced migration of the RBCs as the underlying mechanism of increased asymmetry in curved vessels. The vascular bifurcations and mergers are also seen to change the CFL profiles, and in the majority of them the CFL becomes more asymmetric. For most bifurcations, this is generally observed to occur such that the CFL downstream narrows on the side of the vessel nearest the upstream bifurcation, and widens on the other side. The 3D aspects of such behaviour are elucidated. For many bifurcations, a discrepancy exists between the CFL in the daughter vessels, which arises from a disproportionate partitioning between the flow rate and RBC flux. For most mergers, the downstream CFL narrows in the plane of the merger, but widens away from this plane. The dominant mechanism by which such changes occur is identified as the geometric focusing of the two merging streams. To our knowledge, this work provides the first simulation-based analysis of the 3D CFL structure in complex in vivo-like microvascular networks, including the hydrodynamic origins of the observed behaviour.