A microfluidic platform for simultaneous quantification of oxygen-dependent viscosity and shear thinning in sickle cell blood

Abstract

The pathology of sickle cell disease begins with the polymerization of intracellular hemoglobin under low oxygen tension, which leads to increased blood effective viscosity and vaso-occlusion. However, it has remained unclear how single-cell changes propagate up to the scale of bulk blood effective viscosity. Here, we use a custom microfluidic system to investigate how the increase in the stiffness of individual cells leads to an increase in the shear stress required for the same fluid strain in a suspension of softer cells. We characterize both the shear-rate dependence and the oxygen-tension dependence of the effective viscosity of sickle cell blood, and we assess the effect of the addition of increasing fractions of normal cells whose material properties are independent of oxygen tension, a scenario relevant to the treatment of sickle patients with blood transfusion. For untransfused sickle cell blood, we find an overall increase in effective viscosity at all oxygen tensions and shear rates along with an attenuation in the degree of shear-thinning achieved at the lowest oxygen tensions. We also find that in some cases, even a small fraction of transfused blood cells restores the shape of the shear-thinning relationship, though not the overall baseline effective viscosity. These results suggest that untransfused sickle cell blood will show the most extreme relative rheologic impairment in regions of high shear and that introducing even small fractions of normal blood cells may help retain some shear-thinning capability though without addressing a baseline relative increase in effective viscosity independent of shear.

FIG. 1.

COMSOL oxygen transport modeling. (a) Cross-sectional and longitudinal device steady state views showing the device oxygen concentration profile. (b) Modeling probe at the crossview (x) location, showing that oxygen temporal response takes approximately 60 s to reach 0 mm Hg after switching off oxygen supply in the experimental section, while the bypass section remains unaltered at 160 mm Hg. (c) Spatial analysis shows device is at 0 mm Hg from approximately 7 mm to 15 mm length of the gas channel. (d) Experimental verification of oxygen temporal response using the oxygen sensitive dye Ru(bpy)3 shows the device reaches the 0 mm Hg Ru(bpy)3 SMS control after approximately 60 s but differs in the profile expected from the model. (e) Experimental verification of spatial oxygen response shows the device is at approximately 100 mm Hg at the location blood bends to enter the side view (y) section unlike the 160 mm Hg assumption in the model but still reaches 0 mm Hg for an approximately 8 mm length of the device experimental section. Oxygen tension was estimated using fluorescent calibrations at 0 mm Hg and 160 mm Hg using the oxygen-sensitive dye Ru(bpy)3.

FIG. 2.

Velocity response of sickle cell blood to oxygen. (a) Oxygen tension was cyclically modulated between 160 and 0 mm Hg and blood velocity tracked and analyzed. A representative SCD sample followed by a healthy control are shown. (b) Representative average velocity at 160 and 0 mm Hg oxygen tension for sickle and normal blood samples. The error bars represent the measurement standard deviation for the multiple oxygen cycles measured and used to determine the average relative velocity drop. (c) These values were then compared using Pearson's coefficient to assess linearity with respect to hemoglobin fraction values obtained using high performance liquid chromatography, but no significant linear correlation was found relating hemoglobin fractions to rheology (p > 0.05 for all metrics using Pearson correlation), n = 9 patients.

FIG. 3.

Blood viscosity measurement and quantification. (a) To acquire sample viscosity information at different oxygen levels, oxygen tension in the experimental zone is allowed to reach the steady state and then a series of pressure steps (top) are applied and velocity video data (bottom) collected. (b) Using our hydraulic circuit model (see Methods), viscosity vs average shear rate plots are generated for each oxygen tension analyzed. Error bars indicate the standard deviation of the measurement which on average was calculated using 18 video captures per pressure step. (c) For a set shear rate of 100/s, a significant increase in overall viscosity was found as the oxygen tension is decreased. (d) The flow behavior index is calculated by fitting the shear stress vs shear rate to a power law and extracting the exponent. Blood samples at 92 and 46 mm Hg oxygen tensions display similar flow behavior indices, despite the increased effective viscosity. At 0 mm Hg, flow behavior increases significantly, indicating reduced shear thinning. (e) This trend is further exemplified by decreased goodness of fit for the power law model at 0 mm Hg oxygen, indicating that blood no longer matches a conventional shear thinning model. All black bars in panels (c), (d), and (e) indicate the median in the distribution. Statistical significance was defined as: (^*) p value < 0.05, (^**) p value < 0.01, and (NS) no significance for p value > 0.05. The average shear rate is calculated as the maximum velocity at the channel midline divided by 7.5 μm, half the channel width, n = 9 patients.

FIG. 4.

Simulated transfusion therapy experiment reveals increasing normal to sickle blood ratios leads to a loss of blood viscosity dependence on oxygen tension. (a) The viscosity vs average shear rate qualitatively shows a decreasing hemoglobin S concentration via transfusions leads to a loss of the viscosity dependence on oxygen levels indicated by curves collapsing onto each other. (b) Comparison of 0 mm Hg oxygen tension responses for different hemoglobin mix ratios reveals the viscosity benefits transfusions can offer. In this sample, decreasing the HbS percentage to 52.4% decreased the 0 mm Hg viscosity (green curve) below the 46 mm Hg viscosity at 74.8% HbS (yellow curve). Further decreasing HbS to 22.4% (purple curve) shows a blood response of 0 mm Hg viscosity even below the 92 mm Hg viscosity for a sample with 74.8% HbS (red curve). (c) Quantification of transfusion 1. At approximately 25% HbS concentration, the 0 mm Hg flow behavior index (blue) shows values comparable to 46 mm Hg and 92 mm Hg oxygen tensions, indicating a fluid behavior recovery response. (d) Unlike transfusion 1, a fluid behavior index drop is observed as early as 50% hemoglobin S concentration indicating patient differences. Generally, the metric can be optimized to be used as a tool to characterize patients specifically and provide individualized treatment guidance. Error bars represent the max spread between 92, 46, and 0 mm Hg at 0% HbS percentage as this sample should show no dependency on oxygen due to being a healthy control, and any variation would exist due to experimental error found in the device or noise in recording equipment, n = 2 patients.

FIG. 5.

Device design and experimental setup. (a) The device is composed of three layers: a blood layer mimicking blood vessels (red), a hydration layer filled with phosphate-buffered saline to prevent blood dehydration (blue), and a gas layer used to control the partial pressure of oxygen in the oxygen layer (black). In addition, the device is subdivided into experimental and bypass zones. Controlled hypoxia in the experimental zone leads to the impairment of blood flow. The bypass zone, which is maintained at saturating oxygen partial pressures, mimics a cardiovascular branch and prevents red cell packing in the device when flow in the experimental zone is impaired. (b) A combination of control systems is utilized during experimental testing to perfuse blood (red), maintain blood hydrated (blue), mix and detect oxygen levels (black), and collect and analyze blood velocity data in real-time using custom MATLAB scripts.

FIG. 6.

Blood section of our device with (a) labeled resistances and pressures and (b) its analogous view as an electrical circuit assuming Re < 1.