Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of \(15\,\upmu \hbox {m}\) diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor–ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.     

Forces on a Wall-Bound Leukocyte in a Small Vessel Due to Red Cells in the Blood Stream

As part of the inflammation response, white blood cells (leukocytes) are well known to bind nearly statically to the vessel walls, where they must resist the force exerted by the flowing blood. This force is particularly difficult to estimate due to the particulate character of blood, especially in small vessels where the red blood cells must substantially deform to pass an adhered leukocyte. An efficient simulation tool with realistically flexible red blood cells is used to estimate these forces. At these length scales, it is found that the red cells significantly augment the streamwise forces that must be resisted by the binding. However, interactions with the red cells are also found to cause an average wall-directed force, which can be anticipated to enhance binding. These forces increase significantly as hematocrit values approach 25% and decrease significantly as the leukocyte is made flatter on the wall. For a tube hematocrit of 25% and a spherical protrusion with a diameter three-quarters that of the vessel, the average forces are increased by ∼40% and the local forces are more than double those estimated with an effective-viscosity-homogenized blood. Both the enhanced streamwise and wall-ward forces and their unsteady character are potentially important in regard to binding mechanisms.     

Norepinephrine promotes the β1-integrin-mediated adhesion of MDA-MB-231 cells to vascular endothelium by the induction of a GROα release

The migratory activity of tumor cells and their ability to extravasate from the blood stream through the vascular endothelium are important steps within the metastasis cascade. We have shown previously that norepinephrine is a potent inducer of the migration of MDA-MB-468 human breast carcinoma cells and therefore investigated herein, whether the interaction of these cells as well as MDA-MB-231 and MDA-MB-435S human breast carcinoma cells with the vascular endothelium is affected by this neurotransmitter as well. By means of a flow-through assay under physiologic flow conditions, we show that norepinephrine induces an increase of the adhesion of the MDA-MB-231 cells, but not of MDA-MB-468 and MDA-MB-435S cells to human pulmonary microvascular endothelial cells (HMVEC). The adhesion of MDA-MB-231 cells was based on a norepinephrine-mediated release of GROα from HMVECs. GROα caused a β1-integrin-mediated increase of the adhesion of MDA-MB-231 cells. Most interestingly, this effect of norepinephrine, similar to the aforementioned induction of migration in MDA-MB-468 cells, was mediated by β-adrenergic receptors and therefore abrogated by β-blockers. In conclusion, norepinephrine has cell line-specific effects with regard to certain steps of the metastasis cascade, which are conjointly inhibited by clinically established β-blockers. Therefore, these results may deliver a molecular explanation for our recently published retrospective data analysis of patients with breast cancer which shows that β-blockers significantly reduce the development of metastases.     

Computational investigation of blood cell transport in retinal microaneurysms

Microaneurysms (MAs) are one of the earliest clinically visible signs of diabetic retinopathy (DR). MA leakage or rupture may precipitate local pathology in the surrounding neural retina that impacts visual function. Thrombosis in MAs may affect their turnover time, an indicator associated with visual and anatomic outcomes in the diabetic eyes. In this work, we perform computational modeling of blood flow in microchannels containing various MAs to investigate the pathologies of MAs in DR. The particle-based model employed in this study can explicitly represent red blood cells (RBCs) and platelets as well as their interaction in the blood flow, a process that is very difficult to observe in vivo. Our simulations illustrate that while the main blood flow from the parent vessels can perfuse the entire lumen of MAs with small body-to-neck ratio (BNR), it can only perfuse part of the lumen in MAs with large BNR, particularly at a low hematocrit level, leading to possible hypoxic conditions inside MAs. We also quantify the impacts of the size of MAs, blood flow velocity, hematocrit and RBC stiffness and adhesion on the likelihood of platelets entering MAs as well as their residence time inside, two factors that are thought to be associated with thrombus formation in MAs. Our results show that enlarged MA size, increased blood velocity and hematocrit in the parent vessel of MAs as well as the RBC-RBC adhesion promote the migration of platelets into MAs and also prolong their residence time, thereby increasing the propensity of thrombosis within MAs. Overall, our work suggests that computational simulations using particle-based models can help to understand the microvascular pathology pertaining to MAs in DR and provide insights to stimulate and steer new experimental and computational studies in this area.     

Theoretical comparison of wall-derived and erythrocyte-derived mechanisms for metabolic flow regulation in heterogeneous microvascular networks

The objective of this study is to compare the effectiveness of metabolic signals derived from erythrocytes and derived from the vessel wall for regulating blood flow in heterogeneous microvascular networks. A theoretical model is used to simulate blood flow, mass transport, and vascular responses. The model accounts for myogenic, shear-dependent, and metabolic flow regulation. Metabolic signals are assumed to be propagated upstream along vessel walls via a conducted response. Arteriolar tone is assumed to depend on the conducted metabolic signal as well as local wall shear stress and wall tension, and arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model shows that under certain conditions metabolic regulation based on wall-derived signals can be more effective in matching perfusion to local oxygen demand relative to regulation based on erythrocyte-derived signals, resulting in higher extraction and lower oxygen deficit. The lower effectiveness of the erythrocyte-derived signal is shown to result in part from the unequal partition of hematocrit at diverging bifurcations, such that low-flow vessels tend to receive a reduced hematocrit and thereby experience a reduced erythrocyte-derived metabolic signal. The model simulations predict that metabolic signals independent of erythrocytes may play an important role in local metabolic regulation of vascular tone and flow distribution in heterogeneous microvessel networks.     

Hematocrit,viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel

Microscale blood flow is characterised by heterogeneous distributions of hematocrit, viscosity and velocity. In microvascular bifurcations, cells are unevenly distributed between the branches, and this effect can be amplified in subsequent branches depending on a number of parameters. We propose an approach to infer hematocrit profiles of human blood flowing through a bifurcating microchannel. The influence of aggregation, induced by the addition of Dextran 2000 to the samples, is also considered. Averaged values indicate plasma skimming, particularly in the presence of red blood cell (RBC) aggregation. Using an empirical model, the hematocrit profiles are used to estimate local relative viscosity distributions. Simulations are used to predict how the non-uniform viscosity influences the velocity profiles. Comparing these data to velocity profiles of RBCs measured using particle image velocimetry provides validation of the model. It is observed that aggregation blunts velocity profiles after a long straight section of channel. Downstream of the bifurcation, skewing of the velocity profiles is detected, which is enhanced by aggregation. The proposed methodology is capable of providing hitherto unreported information on important aspects of microscale blood rheology.     

Erythrocyte distribution in arterial blood flow: I. Basic equations and anisotropic effects

Equations are derived for the flow of an anisotropic fluid in a tube. It is argued that these provide a model for arterial blood flow. Particular attention is paid to the effect of radial differences in hematocrit. Sequels to this paper (Bull. Math. Biophysics,29, 565–574; forthcoming, 1967) will respectively demonstrate possible wall-directed forces on the erythrocyte and enlarge on the physiological consequence of hematocrit variations. The present article develops the basic equations and explores the possible role of anisotropic effects in blood flow.     

Tumor Cell Extravasation Mediated by Leukocyte Adhesion is Shear Rate Dependent on IL-8 Signaling^*

To complete the metastatic journey, cancer cells have to disseminate through the circulation and extravasate to distal organs. However, the extravasation process, by which tumor cells leave a blood vessel and invade the surrounding tissue from the microcirculation, remains poorly understood at the molecular level. In this study, tumor cell adhesion to the endothelium (EC) and subsequent extravasation were investigated under various flow conditions. Results have shown polymorphonuclear neutrophils (PMNs) facilitate melanoma cell adhesion to the EC and subsequent extravasation by a shear-rate dependent mechanism. Melanoma cell-PMN interactions are mediated by the binding between intercellular adhesion molecule-1 (ICAM-1) on melanoma cells andb2integrins on PMNs. In addition, the fluid convection affects the extent of activation ofb2integrins on PMNs by endogenously secreted interleukin 8 (IL-8) within the tumor microenvironment. Results also indicate that shear rate affects the binding kinetics between PMNs and melanoma cells, which may contribute to the shear-rate dependence of melanoma extravasation in a shear flow when mediated by PMNs.     

A numerical study of the shape of the surface separating flow into branches in microvascular bifurcations.

The shape of the separating surface formed by the streamlines entering the branches of microvascular bifurcations plays a major role in determining the distribution of red blood cells and other blood constituents downstream from the bifurcation. Using the finite element method, we determined the shape of the surface through numerical solution of three dimensional Navier-Stokes equations for fluid flow at low Reynolds numbers in a T-type bifurcation of circular tubes. Calculations were done for a wide range of daughter branch to parent vessel diameter ratios and flow ratios. The effect of Reynolds number was also studied. Our numerical results are in good agreement with previously reported experimental data of Rong and Carr (Microvascular Research, Vol. 39, pp. 186-202, 1990). The numerical results of this study will be used to predict the concentration of blood constituents downstream from microvascular bifurcations providing that the inlet concentration profile is known.     

Numerical Simulation of Blood Flow Through Microvascular Capillary Networks

A numerical method is implemented for computing blood flow through a branching microvascular capillary network. The simulations follow the motion of individual red blood cells as they enter the network from an arterial entrance point with a specified tube hematocrit, while simultaneously updating the nodal capillary pressures. Poiseuille’s law is used to describe flow in the capillary segments with an effective viscosity that depends on the number of cells residing inside each segment. The relative apparent viscosity is available from previous computational studies of individual red blood cell motion. Simulations are performed for a tree-like capillary network consisting of bifurcating segments. The results reveal that the probability of directional cell motion at a bifurcation (phase separation) may have an important effect on the statistical measures of the cell residence time and scattering of the tube hematocrit across the network. Blood cells act as regulators of the flow rate through the network branches by increasing the effective viscosity when the flow rate is high and decreasing the effective viscosity when the flow rate is low. Comparison with simulations based on conventional models of blood flow regarded as a continuum indicates that the latter underestimates the variance of the hematocrit across the vascular tree.     

Rheological properties of the blood influencing selectin-mediated adhesion of flowing leukocytes

We studied how the rheological properties of blood influenced capture and rolling adhesion of leukocytes as well as their margination in the bloodstream. When citrated, fluorescently labeled blood was perfused through glass capillaries coated with P-selectin, leukocytes formed numerous rolling attachments. The number of attached leukocytes increased as the hematocrit was increased between 10% and 30% and was essentially constant from 30% to 50%. In EDTA-treated blood, adhesion was absent, and the flux of marginated cells varied little with increasing hematocrit. However, the velocity of marginated leukocytes increased monotonically, whereas the volumetric flow rate was constant, implying that the flow velocity profile became blunted and wall shear rate increased. Thus increasing hematocrit promoted attachment for a given total flow rate, without increasing margination, even though wall shear rate and blood viscosity increased. Blood was diluted to 20% hematocrit with plasma, 40-kDa dextran (to reduce red blood cell aggregation), or 500-kDa dextran (to enhance aggregation). Increasing aggregation correlated with increasing leukocyte adhesion and with more slow-flowing leukocytes near the wall. Thus flowing erythrocytes promote leukocyte adhesion, either by causing margination of leukocytes or by initiating and stabilizing attachments that follow.     

In vitro Method to Observe E-selectin-mediated Interactions Between Prostate Circulating Tumor Cells Derived From Patients and Human Endothelial Cells

Metastasis is a process in which tumor cells shed from the primary tumor intravasate blood vascular and lymphatic system, thereby, gaining access to extravasate and form a secondary niche. The extravasation of tumor cells from the blood vascular system can be studied using endothelial cells (ECs) and tumor cells obtained from different cell lines. Initial studies were conducted using static conditions but it has been well documented that ECs behave differently under physiological flow conditions. Therefore, different flow chamber assemblies are currently being used to studying cancer cell interactions with ECs. Current flow chamber assemblies offer reproducible results using either different cell lines or fluid at different shear stress conditions. However, to observe and study interactions with rare cells such as circulating tumor cells (CTCs), certain changes are required to be made to the conventional flow chamber assembly. CTCs are a rare cell population among millions of blood cells. Consequently, it is difficult to obtain a pure population of CTCs. Contamination of CTCs with different types of cells normally found in the circulation is inevitable using present enrichment or depletion techniques. In the present report, we describe a unique method to fluorescently label circulating prostate cancer cells and study their interactions with ECs in a self-assembled flow chamber system. This technique can be further applied to observe interactions between prostate CTCs and any protein of interest.     

Determining beta2-integrin and intercellular adhesion molecule 1 binding kinetics in tumor cell adhesion to leukocytes and endothelial cells by a gas-driven micropipette assay

Interactions between polymorphonuclear neutrophils (PMNs) and tumor cells have been reported to facilitate the adhesion and subsequent extravasation of tumor cells through the endothelium under blood flow, both of which are mediated by binding β(2)-integrin to intercellular adhesion molecule 1 (ICAM-1). Here the adhesions between human WM9 metastatic melanoma cells, PMNs, and human pulmonary microvascular endothelial cells (HPMECs) were quantified by a gas-driven micropipette aspiration technique (GDMAT). Our data indicated that the cellular binding affinity of PMN-WM9 pair was 3.9-fold higher than that of the PMN-HPMEC pair. However, the effective binding affinities per molecular pair were comparable between the two cell pairs no matter whether WM9 cells or HPMECs were quiescent or cytokine-activated, indicating that the stronger adhesion between PMN-WM9 pair is mainly attributed to the high expression of ICAM-1 on WM9 cells. These results proposed an alternative mechanism, where WM9 melanoma cells adhere first with PMNs near vessel-wall regions and then bind to endothelial cells via PMNs under blood flow. In contrast, the adhesions between human MDA-MB-231 metastatic breast carcinoma cells and PMNs showed a comparable cellular binding affinity to PMN-HPMEC pair because the ICAM-1 expressions on MDA-MB-231 cells and HPMECs are similar. Furthermore, differences were observed in the intrinsic forward and reverse rates of the β(2)-integrin-ICAM-1 bond between PMN-TC and PMN-EC pairs. This GDMAT assay enables us to quantify the binding kinetics of cell adhesion molecules physiologically expressed on nucleated cells. The findings also further the understanding of leukocyte-facilitated tumor cell adhesion from the viewpoint of molecular binding kinetics.     

Self-sustained Oscillations in Blood Flow Through a Honeycomb Capillary Network

Numerical simulations of unsteady blood flow through a honeycomb network originating at multiple inlets and terminating at multiple outlets are presented and discussed under the assumption that blood behaves as a continuum with variable constitution. Unlike a tree network, the honeycomb network exhibits both diverging and converging bifurcations between branching capillary segments. Numerical results based on a finite difference method demonstrate that as in the case of tree networks considered in previous studies, the cell partitioning law at diverging bifurcations is an important parameter in both steady and unsteady flow. Specifically, a steady flow may spontaneously develop self-sustained oscillations at critical conditions by way of a Hopf bifurcation. Contrary to tree-like networks comprised entirely of diverging bifurcations, the critical parameters for instability in honeycomb networks depend weakly on the system size. The blockage of one or more network segments due to the presence of large cells or the occurrence of capillary constriction may cause flow reversal or trigger a transition to unsteady flow.     

Integrin VLA-4 enhances sialyl-Lewisx/a-negative melanoma adhesion to and extravasation through the endothelium under low flow conditions

During their passage through the circulatory system, tumor cells undergo extensive interactions with various host cells including endothelial cells. The capacity of tumor cells to form metastasis is related to their ability to interact with and extravasate through endothelial cell layers, which involves multiple adhesive interactions between tumor cells and endothelium (EC). Thus it is essential to identify the adhesive receptors on the endothelial and melanoma surface that mediate those specific adhesive interactions. P-selectin and E-selectin have been reported as adhesion molecules that mediate the cell-cell interaction of endothelial cells and melanoma cells. However, not all melanoma cells express ligands for selectins. In this study, we elucidated the molecular constituents involved in the endothelial adhesion and extravasation of sialyl-Lewis(x/a)-negative melanoma cell lines under flow in the presence and absence of polymorphonuclear neutrophils (PMNs). Results show the interactions of alpha(4)beta(1) (VLA-4) on sialyl-Lewis(x/a)-negative melanoma cells and vascular adhesion molecule (VCAM-1) on inflamed EC supported melanoma adhesion to and subsequent extravasation through the EC in low shear flow. These findings provide clear evidence for a direct role of the VLA-4/VCAM-1 pathway in melanoma cell adhesion to and extravasation through the vascular endothelium in a shear flow. PMNs facilitated melanoma cell extravasation under both low and high shear conditions via the involvement of distinct molecular mechanisms. In the low shear regime, beta(2)-integrins were sufficient to enhance melanoma cell extravasation, whereas in the high shear regime, selectin ligands and beta(2)-integrins on PMNs were necessary for facilitating the melanoma extravasation process.     

Numerical Simulation of Unsteady Blood Flow through Capillary Networks

A numerical method is implemented for computing unsteady blood flow through a branching capillary network. The evolution of the discharge hematocrit along each capillary segment is computed by integrating in time a one-dimensional convection equation using a finite-difference method. The convection velocity is determined by the local and instantaneous effective capillary blood viscosity, while the tube to discharge hematocrit ratio is deduced from available correlations. Boundary conditions for the discharge hematocrit at divergent bifurcations arise from the partitioning law proposed by Klitzman and Johnson involving a dimensionless exponent, q≥1. When q=1, the cells are partitioned in proportion to the flow rate; as q tends to infinity, the cells are channeled into the branch with the highest flow rate. Simulations are performed for a tree-like, perfectly symmetric or randomly perturbed capillary network with m generations. When the tree involves more than a few generations, a supercritical Hopf bifurcation occurs at a critical value of q, yielding spontaneous self-sustained oscillations in the absence of external forcing. A phase diagram in the m–q plane is presented to establish conditions for unsteady flow, and the effect of various geometrical and physical parameters is examined. For a given network tree order, m, oscillations can be induced for a sufficiently high value of q by increasing the apparent intrinsic viscosity, decreasing the ratio of the vessel diameter from one generation to the next, or by decreasing the diameter of the terminal vessels. With other parameters fixed, oscillations are inhibited by increasing m. The results of the continuum model are in excellent agreement with the predictions of a discrete model where the motion of individual cells is followed from inlet to outlet.     

Plasmodium falciparum-induced CD36 clustering rapidly strengthens cytoadherence via p130CAS-mediated actin cytoskeletal rearrangement

The adhesion of infected red blood cells (IRBCs) to microvascular endothelium is critical in the pathogenesis of severe malaria. Here we used atomic force and confocal microscopy to examine the adhesive forces between IRBCs and human dermal microvascular endothelial cells. Initial contact of the cells generated a mean ± sd adhesion force of 167 ± 208 pN from the formation of single or multiple bonds with CD36. The strength of adhesion increased by 5- to 6-fold within minutes of contact through a signaling pathway initiated by CD36 ligation by live IRBCs, or polystyrene beads coated with anti-CD36 or PpMC-179, a recombinant peptide representing the minimal binding domain of the parasite ligand PfEMP1 to CD36. Engagement of CD36 led to localized phosphorylation of Src family kinases and the adaptor protein p130CAS, resulting in actin recruitment and CD36 clustering by 50-60% of adherent beads. Uninfected red blood cells or IgG-coated beads had no effect. Inhibition of the increase in adhesive strength by the Src family kinase inhibitor PP1 or gene silencing of p130CAS decreased adhesion by 39 ± 12 and 48 ± 20%, respectively, at 10 dyn/cm(2) in a flow chamber assay. Modulation of adhesive strength at PfEMP1-CD36-actin cytoskeleton synapses could be a novel target for antiadhesive therapy.     

Dynamics of blood flow: modeling of the Fåhræus–Lindqvist effect

To model the Fåhræus–Lindqvist effect, Haynes’ marginal zone theory is used, following previous works, i.e., a core layer of uniform red blood cells (RBCs) is assumed to be surrounded by an annular plasma layer in which no RBCs are present. A simplified trial-and-error solution procedure is provided to determine the size of the core region and the hematocrit level in that zone in addition to the apparent viscosity, given the (upstream) large vessel hematocrit level and the average hematocrit level in the (downstream) small vessel. To test the model, a set of experimental data is selected to provide not only apparent viscosity data but also the average hematocrit levels in small tubes of different diameters. The results are found to support Haynes’ marginal theory, with no fitting parameters used in the computations. Viscous dissipation is determined. The use of the mechanical energy balance is found to lead to results that are consistent with those based on the momentum balance, while leaving the average hematocrit level undetermined and required by either experimental data or an additional equation based on further theoretical work. The present analysis is used to model bifurcation using published empirical correlations quantifying the Fåhræus effect and phase separation. The model equations are extended to microvascular networks with repeated bifurcations.     

Adhesive interactions between CD34<Superscript>+</Superscript>-derived dendritic cell precursors and dermal microvascular endothelial cells studied by scanning electron microscopy

Dendritic cells are migratory cells. Before they extravasate from the circulation into the skin across capillary blood vessel walls, they have to interact with endothelial cells. Using a fluorimetric adhesion assay, we have recently shown that CD34⁺-derived dendritic cell precursors are able to bind to resting and stimulated dermal microvascular endothelial cells. In the present study, we attempted to visualize this process at an ultrastructural level. CD34⁺ progenitor cells were purified from human cord blood samples by means of immunomagnetic beads, and dendritic cells were generated by culture in the presence of GM-CSF, TNF- and hSCF for 5 days. Immature CD83^– CD86^low dendritic cells were added to human dermal microvascular endothelial cells grown to confluence on membrane chambers. After 2 h, unbound dendritic cell precursors were removed, and bound cells were prepared for routine scanning electron microscopy. We found that (1) dendritic cell precursors firmly adhere to microvascular endothelial cells, enveloping them with their surface processes; (2) dendritic cell precursors are extremely deformable as they squeeze through the dense network of microvascular endothelial cells; (3) microvascular endothelial cells form, in part, a multi-layered network rather than the typical cobblestone pattern as seen by phase-contrast microscopy. The morphology of dendritic cell precursors and of human dermal microvascular endothelial cells was examined here, for the first time, by scanning electron microscopy. These data further emphasize that CD34⁺-derived dendritic cells efficiently adhere to dermal microvascular endothelial cells.     

Modeling the effect of blood vessel bifurcation ratio on occlusive thrombus formation

Vascular geometry is a major determinant of the hemodynamics that promote or prevent unnecessary vessel occlusion from thrombus formation. Bifurcations in the vascular geometry are repeating structures that introduce flow separation between parent and daughter vessels. We modelled the blood flow and shear rate in a bifurcation during thrombus formation and show that blood vessel bifurcation ratios determine the maximum shear rate on the surface of a growing thrombus. We built an analytical model that may aid in predicting microvascular bifurcation ratios that are prone to occlusive thrombus formation. We also observed that bifurcation ratios that adhere to Murray’s law of bifurcations may be protected from occlusive thrombus formation. These results may be useful in the rational design of diagnostic microfluidic devices and microfluidic blood oxygenators.