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Biomedical Engineering

Hemorheological Approach to Improve Perfusion of Red Blood Cells with Reduced Deformability Using Drag-Reducing Polymer (In Vitro Study)

Crompton, Dan*,†; Gudla, Shushma*,†; Waters, Jonathan H.*,†,‡; Sundd, Prithu*,§,¶; Kameneva, Marina V.*,†,‖

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doi: 10.1097/MAT.0000000000001559
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Due in large part to their deformability, red blood cells (RBCs) naturally radially migrate toward the center of vessels and channels under 300 µm in diameter, creating an RBC-rich central core. This phenomenon, known as the Fåhraeus Effect leaves an RBC-poor fluid layer near the vessel wall, otherwise called the cell-free layer (CFL).1 The thickness of the CFL may vary between 1 and 10 µm and is dependent on vessel diameter, blood Ht, flow velocity, RBC aggregation, and RBC deformability.2 The formation of the RBC central core also results in the margination of less-deformable cells toward the vessel wall, such as platelets, leukocytes, and less-deformable RBCs.3 The margination of these cells increases their likelihood of being “skimmed” into smaller vessels at bifurcations, which increases their concentration within the microvasculature and may increase their tendency to obstruct flow due to their poor deformability or size.4 Further, as a result of the RBC-poor fluid layer at the vessel periphery, a larger proportion of plasma enters smaller vessels at bifurcations reducing the microcirculatory hematocrit (Ht) 20% to 50% than that of larger vessels.5 This work focuses on how the addition of blood soluble drag-reducing polymers (DRPs) alter the traffic and relative concentration of less-deformable RBCs and healthy RBCs within branched in vitro microchannel models of the microvasculature.

DRPs are a unique class of soluble long-chain, high-molecular-weight (MW > 106 Da) molecules that significantly reduce pressure losses within turbulent flow by up to 80% in low concentrations (Toms Effect).6 DRPs are routinely used in industrial applications as a means of increasing flow efficiency and cost savings.7 Generally, turbulent flow conditions are not present in the cardiovascular system with the exception of transitional flow in the ascending aorta at peak ejection. Despite turbulent flow being essential for the observation of the Toms Effect, DRPs still generate significant changes to blood flow in laminar regimes, indicating that there is a separate phenomenon occurring to cause the hemodynamic changes seen with the addition of DRP. Previous studies have shown that DRPs provide numerous beneficial hemorheological effects including increased capillary perfusion and oxygenation in animal models,8 reduced liver ischemia/reperfusion injury,9 improvement of cerebral blood flow following traumatic brain injury,10 increased survival following hemorrhagic shock,8 increased survival following severe myocardial ischemia,11 and inhibition of experimental metastases of human breast cancer cells in mice.12 Although not yet fully understood, the underlying mechanism of DRPs is theorized to originate from its ability to reduce flow separation and vortex size at bifurcations and significantly reduce or eliminate the width of the CFL.13 Additional studies have also shown that the DRP induced elimination of the CFL significantly reduces the margination of platelet-sized particles resulting in a more uniform distribution of rigid particles across the channel diameter.14 The use of DRP blood additives to alter the margination of less-deformable cells is of particular interest for its potential to influence and improve microcirculatory blood flow.

Reduced RBC deformability is well known in blood disorders such as malaria and spherocytosis but is especially well documented as a result of RBC aging and in the case of sickle cell disease (SCD),15 a recessively inherited autosomal hemoglobinopathy which affects over 100,000 individuals within the United States, and over 4 million worldwide.16,17 SCD is characterized by the formation of rigid sickle Hb fibers within RBCs, causing a decrease in deformability which directly impacts their tendency to initiate vaso-occlusion.18,19 In this work, we examine how the loss of RBC deformability affects the traffic patterns between healthy and less-deformable cells in microchannels, especially with the administration of DRP. We hypothesized that DRP additives to microchannel blood flow would lead to a reduction of marginating less-deformable RBCs. This action would decrease their susceptibility of being “skimmed” into daughter branches and may lead to an increase in normal (more deformable) RBCs found in daughter branches. The understanding of the microvascular effects DRPs have on blood flow, especially concerning populations of less-deformable RBCs has implications for the improvement of perfusion overall, as well as potential to maintain microvascular flow especially in the case of SCD. To test this hypothesis and improve our understanding of the mechanism(s) with which DRPs act upon small vessels, we conducted bifurcating microchannel flow studies using blood containing a mixture of both healthy and less-deformable RBCs.

Materials and Methods

Sample Preparation

Whole, fresh bovine blood obtained via venipuncture and anticoagulated in K2 EDTA was purchased from Lampire Biologic Laboratories (Pipersville, PA) by overnight shipment. Whole blood was received on ice less than 24 hour after the time of drawing, and used in experiments only if samples were not delayed during shipment, were still chilled from the ice packs, and if samples were not found to contain any thrombus or above normal plasma-free hemoglobin levels. Samples were consumed or discarded within 48 hours of receipt. Blood was filtered through a 40 µm blood transfusion filter (Haemonetics, Braintree, MA), and then washed 3× with phosphate-buffered saline (PBS) without Mg2+ or Ca2+ (Lonza, Switzerland) at 2,000 × g for 15 minutes and resuspended at 30% Ht in PBS with 1% bovine serum albumin (BSA) (Sigma Aldrich, St. Louis, MO). Fresh bovine blood suspensions at 30% Ht were used to verify the existence of the plasma skimming effect and were mixed with either the DRP polyethylene oxide (PEO) (molecular weight 4 × 106 Da, Sigma Aldrich, St. Louis, MO) at a final concentration of 10 ppm (10 µg/ml) or an equal volume of the vehicle (PBS).

In following experiments, a mixture containing equal amounts of both healthy and less-deformable RBCs was prepared for the purpose of identifying the traffic patterns of RBCs based on their deformability. Less-deformable RBCs were created via heat treatment, an established method to produce RBCs with irreversible loss of membrane deformability.20,21 Less-deformable RBCs were treated for 30 minutes at 52°C in a Neslab RTE-7 hot water bath (Thermo Fisher Scientific, Waltham, MA). This method was found to reliably produce less-deformable RBCs without significant increases in RBC destruction as measured by plasma-free hemoglobin release. RBC loss of deformability was verified visually under shear stress using a Linkam shearing stage (Linkam Scientific, Tadworth, United Kingdom), which is described in greater detail later in this text. A clear difference in RBC deformability between healthy and less-deformable RBCs is pictured in Figure 1. For use in microchannel experiments, the mixture of healthy and less-deformable RBCs was prepared by mixing equal volumes of 30% Ht healthy RBCs with 30% Ht less-deformable RBCs, which was then split into two pools, either receiving DRP for a final concentration of 10 ppm or an equal volume of PBS.

Figure 1.:
Demonstration of reduced RBC deformability following heat treatment. Healthy RBCs (A) and heat-treated less-deformable RBCs (B) subjected to 0 s−1 (top) and 1,000 s−1 (52 Pa shear stress). Imaged using the Linkam shearing stage, scale bar indicates 10 µm and applies to each inset image. RBCs, red blood cells.

Experimental Setup

Custom polydimethylsiloxane microchannels manufactured using soft lithography techniques from SynVivo Inc. (Huntsville, AL) were used in all experiments. Microchannels were designed with a height of 50 µm, 200 µm main channel diameter, and 100 µm daughter channel at a 45° bifurcation. PE-60 tubing (Braintree Scientific, Braintree, MA) was attached to inlet and outlet ports and their lengths minimized to prevent blood sedimentation. Channels were permanently bound to glass slides and passivated before experimentation with a 3% BSA solution. Blood was driven through the inlet of the channel via syringe pump (PhD Ultra Syringe Pump, Harvard Apparatus, Holliston, PA) in a syringe containing a miniature stirring rod with which blood was gently mixed by adjacent stir plate to prevent RBC sedimentation. Pressure drop across the microchannel was measured using a pressure transducer which was calibrated against atmospheric pressure and a known pressure using a calibrated manometer. Outlet blood samples were collected at the level of the microchannel (Δ height = 0) in small reservoirs open to the atmosphere. Schematics of the microchannel and experimental setup are pictured in Figure 2.

Figure 2.:
Schematic of custom polydimethylsiloxane microchannels. Main channel dimensions: 200 µm (width) × 50 µm (height), daughter branch dimensions: 100 µm (width) × 50 µm (height) (A); Experimental setup schematic (B).

Validation of the plasma skimming effect within microchannels was verified using the blood suspensions not containing heat-treated (less-deformable) RBCs. Samples were driven through microchannels at a rate of 5.9 µL/min and collected in triplicate from the parent and daughter outlets for Ht determination using micro-hematocrit glass capillary tubes (SurePrep heparinized capillary tubes; BD Clay Adams, Sparks, MD). A syringe pump-driven flow rate of 5.9 µL/min was chosen for all experiments in this study based on the size and direction of bifurcations (proportionately larger caliber vessel with smaller daughter branches), where a flow rate of 5.9 µL/min was chosen to represent blood flow within a medium to larger arteriole. This rate was decided upon using the dimensions of the main channel and having a mean flow velocity of approximately 1 cm/s, which is appropriate for the size of this microchannel and for the prevention of RBC sedimentation.

Blood suspensions containing a mixture of healthy and less-deformable cells were used for the determination of RBC traffic through microchannel bifurcations. Samples containing the mixture of both healthy and less-deformable RBCs were driven through microchannels at a rate of 5.9 µL/min and collected from the parent and daughter outlets. Collected blood samples were then diluted in a suspension of isotonic 5.6% polyvinylpyrrolidone (PVP) (Sigma Aldrich, St. Louis, MO) and imaged while subject to shear stress using a Linkam shearing stage (Linkam Scientific, Tadworth, United Kingdom). RBC suspension in viscous PVP solution allowed for a greater range of deliverable shear stresses using the Linkam shearing stage. All samples, including those containing DRP, were significantly diluted before deformability measurements by a 1:250 dilution (4 µl sample to 1 ml PVP solution) to prevent overlap of RBCs during image capture. The presence of ultra-dilute DRP in samples following PVP dilution and was not found to influence the results of deformability measurements or logistic regression analysis.

Image processing

Images of RBCs were captured while samples were exposed to 52 Pa of shear stress (shear rate 1,000 s−1) and analyzed using ImageJ,22 where individual cell height and widths were collected after thresholding and using the particle analyzing tool to omit overlapping cells, debris, or out of focus RBCs. Samples were measured in duplicate with upwards of 5,000 individual RBCs analyzed per sample to ensure consistency. Manual cell measurements were also performed using the ImageJ platform to check the accuracy of the particle analyzing tool and were found to be consistent.

Data Analysis

A logistic regression algorithm for binary classification was used to determine the proportion of healthy and less-deformable RBCs found in each sample using the cell height and width measurements collected during image processing. Less-deformable cells could then easily be differentiated from deformable RBCs in an automated method. Before each experiment, RBC measurements from samples containing exclusively healthy or rigidified RBCs were plotted as cell length versus cell width. Using these data, a decision boundary line or gate was drawn between the two groups of data. The slope and position of the decision boundary line were optimized to minimize the error found when separating the two binary classifications (healthy vs. less-deformable RBCs) using a logistic regression algorithm. Using this decision boundary line, the classification of unknown RBC mixtures could then be determined using their height and width measurements based on their position above (healthy) or below (less-deformable) the decision boundary line. A graphical interpretation of the algorithm is shown in Figure 3. The accuracy of the algorithm classifying cells as either healthy or less-deformable using training data were found to be >99%.

Figure 3.:
Flowchart of logistic regression algorithm. Healthy and less-deformable RBC length and width measurements are collected and plotted separately, with each point representing the measurements of a single RBC. A decision boundary gate is then created using a logistic regression algorithm, classifying points above the boundary as “healthy” and below the boundary as “less-deformable.” Following validation, the percentage of healthy or less-deformable heat-treated RBCs can be identified from sample mixtures containing unknown percentages of each. RBCs, red blood cells.

Following the classification of cells, the relative percent of healthy cells to less-deformable cells exiting the branch outlet was then normalized to the sample blood pool using the formula:

RelativePercent (%)=%HealthyRBCsBranch%HealthyRBCsMain%HealthyRBCsBloodPool*100Ht

where a positive relative percent value indicates more healthy RBCs exiting the daughter branch outlet than the main outlet when normalized by the blood pool. A negative relative percent values indicated a larger majority of less-deformable cell exiting the daughter branch outlet than the main outlet when normalized by the blood pool.

Statistical Analysis

The matched, paired Student’s t-test was used to evaluate differences between control and DRP groups. A value of p < 0.05 was assumed to indicate statistical significance.


Microchannel Parameter Calculation

At a flow rate of 5.9 µL/min, the calculated wall shear rate found in the main channel was 1180 s−1, with a Reynolds number of 0.34. The flow rate within the daughter channel branch was estimated using the volume of the blood sample collected divided by the running time of the experiment and was found to be approximately 2 µL/min, with no differences found between control and samples containing DRP. The calculated wall shear rate of the daughter branch was found to be 900 s−1, with a Reynolds number of 0.25. Similarly to previous work performed by Marhefka et al, the pressure drop across the entire microchannel was elevated in samples containing 10 ppm DRP (10.9 ± 4.2 mm Hg) as compared to control blood samples (5.6 ± 1.5 mm Hg), due to the increased near-wall viscosity caused by the elimination of the near-wall CFL.23

Microchannel Validation/Verification of the Plasma Skimming Effect

The presence of the plasma skimming effect and the existence of the CFL in our microchannel model was found using healthy blood at 30% Ht driven through our bifurcating microchannels. Control blood samples were found to have a statistically significant drop in Ht between the parent branch and that of the daughter branch efflux (p = 0.02). The Ht of samples exiting the main outlet was 31.6 ± 1.0%, while the Ht of the blood exiting the daughter branch was 28.3 ± 2.2%. Conversely, the addition of 10 ppm of the DRP PEO demonstrated the elimination of the plasma skimming effect, which led to nonsignificant differences between the parent and daughter branch efflux Ht (Figure 4). The Ht of samples containing 10 ppm DRP exiting the main outlet was 29.7 ± 0.6%, while the Ht of the blood exiting the daughter branch was 28.5 ± 1.4%.

Figure 4.:
The plasma skimming effect, showing a decreased Ht in the daughter outlet as compared to the main (n = 5, p = 0.017). “*” indicates statistical significance between main and daughter branch outlet Ht (p < 0.05) (top). Nonsignificant Ht changes between main and daughter outlets with the addition of DRP, indicating the elimination of the CFL and the plasma skimming effect (n = 7, p > 0.05) (bottom). CFL, cell-free layer; DRP, drag-reducing polymers.

Distribution of Less-deformable RBC Traffic Through Daughter Branch Outlets

It was found that the 50:50 mixture of healthy and less-deformable RBCs exhibited asymmetrical RBC flow patterns when driven through our bifurcating microchannels. In control experiments (without DRP), the relative percent of healthy RBCs exiting the daughter branch was found to be 8.5 ± 2.5%, indicating an increased proportion of less-deformable RBCs exiting the daughter branch. Conversely, with the addition of 10 ppm DRP, it was found that relative percent was increased to +12.1 ± 5.4%, indicating more healthy RBCs exiting the daughter branch (Figure 5).

Figure 5.:
The percent differences of healthy RBCs between branch and main outlets. In control groups, an average of 8.5 ± 2.5% fewer healthy RBCs exited the branch outlet than less-deformable RBCs. In groups with 10 ppm DRP, an average of +12.1 ± 5.4% more healthy RBCs exited the branch outlet than less-deformable RBCs (n = 6 Control, n = 6 DRP, p = 0.02). “*” indicates statistical significance between control and experimental groups (p < 0.05). DRP, drag-reducing polymers; RBCs, red blood cells.


In this study, the elimination of the plasma skimming effect through a single microchannel bifurcation was confirmed by a nonsignificant Ht difference between main and daughter branch outlets following the addition of DRP. We theorized that this effect is due to the ability of DRPs to reduce the width of the near-wall CFL,24 which was further confirmed in our experimentation through a significant increase in the pressure drop across the channel. At the level of nanomolar concentrations of DRPs used in this work, the increase in pressure drop cannot solely be explained by a change in fluid density with the addition of DRP, nor has the addition of such concentrations of DRP been found to significantly or appreciably increase either the density or viscoelasticity of the blood suspension.8,23 While the increase in pressure drop across a single microchannel is not intuitively beneficial, previous in vivo work has found that DRPs improve the number of functioning capillaries through recruitment of the capillary reserve due to an increase in precapillary pressures.25 As a result, overall tissue perfusion is increased through hydrodynamic modulation of the microvascular resistance independent of vasoactivity.8,26,27 As such, the work requirement from the heart or other blood pumping devices such as mechanical circulatory support devices would theoretically not be increased. Additional studies to test this hypothesis are warranted, especially in the case of patient populations vulnerable to alteration in hemodynamics or hemodynamic instability. Ultimately, the observed elimination of the plasma skimming effect is suggestive of the mechanism for the improvement of perfusion of blood cells within individual and especially, small vascular branches.

The novel findings that DRP additives alter the local traffic of blood cells based on their deformability also poses great clinical significance. Although reduced deformability is a natural phenomenon of RBC aging, the loss of RBC deformability such as in SCD is a well-known contributor toward increased microvessel transit times and decreased perfusion of the microvascular system28,29 and is considered to be a primary factor leading toward vaso-occlusion.19 The use of DRPs to increase the traffic of healthy, more deformable RBCs into vessel bifurcations may help to maintain higher levels of microvascular flow to preserve or improve tissue oxygenation.

Finally, the ancillary observation of elevated wall shear stresses may also prevent immune surveillance cells from creating strong adhesions with the endothelium. In specific-disease states such as SCD where rampant inflammation is a major contributor toward vaso-occlusion,30 this effect may interfere with immune cell rolling, activation, and extravasation. Although warranting further study, this effect may help to suppress the proinflammatory state, which leads to vascular dysfunction in SCD. This theory has been partially observed in vivo, where following liver ischemic/reperfusion injury, DRPs were shown to reduce neutrophil extracellular trap formation and platelet microthrombi.9 Similarly, the administration of DRP has been shown to inhibit the extravasation and metastasis of human breast cancer cells in mice,12 where the interaction and adhesion between endothelial, immune, and circulating tumor cells are known to play an important role in the development of metastases. The potential disruption of adhesion interactions between circulating blood cells produced by DRP is likely the cause of attenuation of the incidence of vaso-occlusion of SCD in vivo, as demonstrated in a recent study.31 Furthermore, in the same manner, it has also been speculated that the use of DRPs in mechanical circulatory support systems and other blood-wetted medical devices may help to reduce the risk of thrombosis through the demargination and disaggregation of near-wall circulating immune cells.14 While the entire mechanistic effect of DRP is not fully understood, this work takes a step toward their understanding using a bifurcating microchannel model. The conclusions drawn in this study demonstrate the potential of DRPs to alter the traffic of blood cells based on their deformability and improve the microvascular flow of blood also containing less-deformable cells through daughter branches. Many questions remain unanswered surrounding the clinical use of DRPs. Future studies in both microchannel and animal models will help to further elucidate their mechanisms and would serve to identify both clinical applications and potential contraindications.

Study Limitations and Future Applications

The labeling and visualization of flowing RBCs within our microchannel model could provide additional information on their margination and flow patterns. Future work is planned using multiphoton microscopy to circumvent these problems in later studies. A potential source of experimental error may have been introduced via the logistic regression algorithm used to identify healthy versus less-deformable RBCs; however, the training data used to validate this measurement system was found to show a high degree of accuracy and data replication was achieved when using blinded measurements also taken by hand. While a specific minimum difference in cellular deformability was not identified in this work, it is presumable that with adequate sample size and training data, these same image processing and data analysis techniques could be used to identify small differences in cell deformability between samples. Future applications of this platform may include segregation of RBC populations due to the loss of deformability characteristic to RBC aging32 or identifying differences in RBC deformability as a potential diagnostic tool such as in chronic fatigue syndrome.33 Finally, the same platform may also be adapted to include deformability-based identification of more than two subpopulations of cells or cell mixtures but is not within the scope of this particular study.


This study demonstrates the novel finding that nanomolar additives of DRPs alter the traffic of less-deformable RBCs through bifurcations of branched microchannels. We hypothesized that the mechanism behind this effect was related to the documented ability of DRPs to reduce the size of the near-wall CFL. This effect caused less-deformable RBCs, which were previously more likely to be skimmed into bifurcations to be replaced with normal RBCs and increased the proportion of normal cells flowing through daughter branches. The conclusions of this study implicate the use of DRPs in the future as a means of improving microcirculatory blood flow in vivo.


The authors thank Dr. Maritza Jimenez-Montanez for assistance with microchannel design.


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Microcirculation; RBCs; rigid RBCs; cell-free layer; margination; microchannel branch

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