High-throughput quantification of red blood cell deformability and oxygen saturation to probe mechanisms of sickle cell disease

Significance

Polymerization of deoxygenated hemoglobin was identified as the origin of sickle cell disease pathology over 70 y ago, yet our understanding of how this molecular event alters red blood cell mechanics and leads to downstream pathology remains incomplete. In this work, we present an assay capable of measuring the bulk mechanical changes that occur in HbS-containing RBCs over the full range of physiological oxygen tensions. Our results demonstrate that RBCs with detectable levels of HbS polymer are dramatically stiffer than those without polymer. The fraction of RBCs with detectable polymer increases with decreasing oxygen, but the measured stiffness of these cells is constant across oxygen tensions suggesting that very stiff RBCs could exist even in highly oxygenated tissues.

Abstract

The complex, systemic pathology of sickle cell disease is driven by multiple mechanisms including red blood cells (RBCs) stiffened by polymerized fibers of deoxygenated sickle hemoglobin. A critical step toward understanding the pathologic role of polymer-containing RBCs is quantifying the biophysical changes in these cells in physiologically relevant oxygen environments. We have developed a microfluidic platform capable of simultaneously measuring single RBC deformability and oxygen saturation under controlled oxygen and shear stress. We found that RBCs with detectable amounts of polymer have decreased oxygen affinity and decreased deformability. Surprisingly, the deformability of the polymer-containing cells is oxygen-independent, while the fraction of these cells increases as oxygen decreases. We also find that some fraction of these cells is present at most physiologic oxygen tensions, suggesting a role for these cells in the systemic pathologies. Additionally, the ability to measure these pathological cells should provide clearer targets for evaluating therapies.

Sickle cell disease (SCD) is a blood disorder that affects millions worldwide and causes systemic pathophysiology and decreased life expectancy (1, 2). The disease is caused by a single nucleotide base pair inversion in the β-globin gene leading to the production of a mutated hemoglobin, known as sickle hemoglobin or HbS. Deoxygenated HbS molecules bind together and, given sufficient concentration, aggregate into structured, polymer fibers (3). These macrostructures deform the red blood cell (RBC) and significantly change its mechanical properties (4). The evidence suggests that altered RBC biomechanics along with the increased endothelial adhesion and inflammatory response result in acute complications such as pain crises, vaso-occlusive crises, and acute chest syndrome as well as chronic complications including stroke, ischemia, and organ failure (5). Still, the specific role of these HbS-polymer-containing RBCs in the pathophysiology remains poorly understood. In pathologies that occur in small vessels and hypoxic tissues, such as vaso-occlusive crisis, it has been suggested that the stiffened, irregularly shaped RBCs play a significant role in initiation and propagation of the event (6–9). It is less clear whether these altered RBCs are also a major driver of SCD pathologies that occur in more oxygenated tissues, such as the brain or major organs. Moreover, we do not know how many of these cells are present in the various oxygen environments within the body or how mechanically altered they are. Thus, a first critical step in understanding the contribution of HbS polymerization to pathophysiology throughout the body is to know the distribution of RBC mechanical properties as they traverse the full range of physiologic oxygen environments.

Surprisingly, the RBC biomechanical changes resulting from intracellular polymerization and the oxygen dependence of these changes have not been fully quantified despite decades of work characterizing the biochemical and biophysical processes that drive HbS polymerization (10, 11), RBC sickling (12), and altered blood flow (13–16). Recent work from Di Caprio et al. has shown the presence of HbS polymer, as measured by reduced oxygen saturation, within a population of RBC even at relatively high oxygen tensions. Further, the fraction of RBCs with detectable polymer shows an inverse dependence on oxygen tension, highlighting the relationship between oxygen environment and polymer formation. However, measuring the presence or quantity of polymer does not tell us the mechanical properties of the cells, which is the pathologic mechanism. Stiffened RBCs have been shown to contribute to altered blood flow and potential endothelial damage through computational studies (13, 17) and experimental studies using chemically stiffened RBCs (18). However, these computational studies used estimates for the RBC stiffness as opposed to measured values, and the stiffness of glutaraldehyde-fixed cells used in experiments may or may not represent the actual stiffness of polymer-containing HbS. Moreover, neither approach provides an accurate picture of the distribution of cell stiffnesses under varying oxygen tensions, which is unlikely to be uniform given the distribution of underlying cellular properties. To provide an accurate picture of the effect of polymer-containing RBCs on SCD pathophysiology, it is necessary to know the distribution of stiffnesses of the RBC population, and how this distribution changes throughout the circulation.

To address this question, we have created an assay capable of simultaneously measuring mechanical properties and oxygen saturation of large populations of individual RBCs at different physiological oxygen tensions (Fig. 1A). To accomplish this, we have adapted well-characterized microfluidic methods of determining single-cell deformability (19–21) to handle the drastically different material properties of RBCs with and without polymer and the range of unstressed shapes polymer-containing RBCs can take (Fig. 1 B and C). We combined this method of determining single-cell mechanics with previously published techniques for controlling oxygen environment (15, 22, 23) and measuring single RBC oxygen saturation (Fig. 1 E and F) (24). We have simultaneously quantified the fraction of HbS polymer-containing RBCs and the stiffness of RBCs with and without detectable polymer in the entire range physiologically relevant of oxygen environments. Our results indicate that HbS polymer-containing RBCs are several orders of magnitude stiffer than RBCs without detectable HbS polymer. Surprisingly, we find that while the fraction of RBCs with detectable HbS polymer is inversely related to oxygen tension, the measured stiffness of these cells is independent of oxygen environment. This information will ultimately lead to a better understanding of the potential pathologic role of these cells throughout the circulation, help inform treatment strategies that aim to reduce the number of these cells, and provide a way to assess the potential efficacy of such therapies.

Fig. 1.

Experimental setup and deformability and saturation measurements. (A) Optical platform for imaging RBCs in the microfluidic device, alternating light-emitting diodes in the Soret band are synced to a high-speed camera to illuminate the sample flowing through the microfluidic device under controlled oxygen tension. (B) Single RBC deformation region demonstrating change in aspect ratio of the cell as it experiences increased shear forces. (C) Schematic of RBC deformation labeled with parameters used to calculate deformation. (D) Representative scatter plot of deformation versus cell cross-sectional area for an AA blood sample. (E) Representative images of a cell illuminated by a 405 nm light-emitting diode and a 430 nm light emitting diode, light absorption in the cell cross-section relative to the background is used to determine the mass of oxygenated and deoxygenated hemoglobin. (F) Molecular absorption spectra in the Soret band for oxygenated and deoxygenated hemoglobin. (G) Representative oxygen–hemoglobin disassociation curve constructed from single-cell measurements at eight different oxygen tensions ranging from 0 mmHg to 160 mmHg. All scale bars are 10 µm; error bars are standard deviation.

1. Results

1.1. HbSS, HbAS, and HbAA Genotypes Have Unique Distributions of RBC Oxygen Saturation and Deformability.

As the polymerization of hemoglobin and subsequent cell stiffening in SCD RBCs is initiated by hypoxia (25), measuring single-cell deformability and saturation at varying levels of oxygen can elucidate some of the mechanisms of SCD. To measure the distributions of single RBC saturations and mechanical phenotypes for diseased and healthy RBCs at a range of physiological oxygen tensions, we have developed a microfluidic platform capable creating a controlled oxygen environment and systematically, consistently shearing individual RBCs in high throughput while recording cell shape and calculating cell saturation (Fig. 1A). The oxygen saturation measurement is accomplished by illuminating RBCs with two alternating light-emitting diodes in the Soret band and imaging them while they pass through a constriction at high speed. The light-emitting diodess used correspond to the molecular absorption peaks of oxygenated and deoxygenated hemoglobin, and the light absorption at these two wavelengths allows for the measure of oxygenated and deoxygenated hemoglobin mass and thus single-cell oxygen saturation (Fig. 1 E–G). The shape of the RBC as it passes through and exits the constrictions can be used to estimate mechanical properties (Fig. 1 B–D). Fig. 2 shows representative data from experiments of a healthy AA control, an SCD patient, and a Sickle Cell Trait (SCT, also denoted AS) patient. For each patient sample, there is a scatter plot of saturation versus deformability at eight different oxygen tensions ranging from complete hypoxia to atmospheric oxygen tension. The oxygen tensions tested were chosen to emulate the environments in some key areas of the body such as the lungs, venules, and kidneys (26), as well as sample oxygen environments where we found SCD RBCs to exhibit highly dynamic behavior.

Fig. 2.

Effects of oxygen tension on RBC deformability and saturation for AA, SS, and AS patient blood. (A–C) Scatter plots of saturation versus measured deformability of RBCs under eight different oxygen tensions (0 mmHg to 160 mmHg) and representative cell images for AA, SS, and AS patients, respectively. The representative images show soft oxygenated (red border) and deoxygenated cells (blue border) and stiff deoxygenated cells (green border). The colored boxes on the scatter plots correspond to the populations the representative images with matching color border are taken from. All scale bars are 10 µm.

In the healthy patient sample (Fig. 2A), only the oxygen saturation changes as a function of oxygen tension, and the deformability is the same in completely saturated RBCs and completely desaturated RBCs. The representative images show a RBC within the constriction stitched to the image of that cell once it exits. The red bordered image shows a fully saturated AA cell and the image with the blue border a fully desaturated RBC with color-matched circles on the scatter plots. Unlike AA RBCs, SCD and SCT blood cells (Fig. 2 B and C) show both saturation and deformability dependence on environmental oxygen tension. At 160 mmHg oxygen, all the RBCs are fully saturated and show deformability similar to AA RBCs. As the oxygen tension in the environment decreases RBC saturation decreases and eventually a distinct second population emerges. These cells, first seen at 53 mmHg oxygen in the representative SCD dataset, present lower relative deformability and saturation. As oxygen tension is further decreased, the saturation of both subpopulations continues to decrease and the fraction of RBCs in the lower deformability, lower saturation subpopulation increases. The representative images again show saturated deformable cells in the red border, desaturated deformable cells in the blue border, and desaturated stiff cells in the green border. The representative images highlight the altered morphology of the stiffer cells.

In summary, measuring saturation and shear-induced deformation of RBCs under a range of physiological oxygen tensions can detect the presence of hemoglobin polymer in HbS containing RBCs; this phenomenon is not seen in RBCs only containing HbA.

1.2. The Fraction of Stiffened RBC and Their Oxygen Saturation Is Oxygen-Dependent, while the Stiffness of These Cells Is Oxygen-Independent.

To further study the behavior of the stiff RBC subpopulations, 11 SCD patient samples were tested. Every sample was run in the same conditions for the same eight oxygen tensions. K-means clustering using RBC saturation and deformability was carried out to isolate the stiff cells (described in Materials and Methods Section 3.5). To gain insight on the role of changing oxygen tension in the stiff cell subpopulation, the stiff cells were compared at normoxia and hypoxia using the methods described in Materials and Methods Section 3.5. Fig. 3 is the stiff cell fraction, stiff cell saturation, and stiff cell deformability at hypoxia and normoixa for all 11 SCD samples. The stiff RBCs showed a significant decrease in overall cell fraction (Fig. 3A) and a significant increase in saturation (Fig. 3B) between hypoxia and normoxia (***P value ≤ 0.001, Wilcoxon test). However, Fig. 3C shows there was no detectable change in the measured stiff cell deformability between hypoxia and normoxia (ns no significance, Wilcoxon test).

Fig. 3.

Hypoxic and normoxic stiff cell attributes. For each sample, stiff RBC populations were analyzed at complete hypoxia (0 mmHg) and normoxia which was determined to be the highest oxygen tensions that produces at least 15% stiff cells for a given sample (A) Stiff cell population fraction, (B) saturation, and (C) measured deformability at complete hypoxia and normoxia ***P value ≤ 0.001, ns no significance (Wilcoxon test). In C, the dotted line indicates the noise threshold for the deformability measurement.

These data suggest that decreasing oxygen environment will cause more HbS containing RBCs to form detectable levels of polymer and that while these polymer-containing RBCs still present oxygen environment-dependent saturation, their deformability only depends on the presence of detectable levels of polymer and not the oxygen environment.

1.3. Stiff and Soft RBCs Have Significantly Different Deformability and Oxygen–Hemoglobin Dissociation That Is Consistent across Genotypes.

In addition to the 11 SCD patient samples tested, 2 SCT and 3 AA patient samples were analyzed to compare stiff and soft cells across different samples (Fig. 4). For each sample, stiff and soft cells were clustered separately at every oxygen tension (this was not done for AA patient samples as these samples do not have stiff cells). For each sample, the P50 of both the soft cell and stiff cell subpopulation was computed using the methods described in Materials and Methods Section 3.5. Fig. 4A is per-sample P50s of the soft and stiff cell subpopulations which shows that the stiff cell P50s were significantly higher than the soft cell P50s (****P value ≤ 0.0001, Mann–Whitney U test). Further, the spread across samples was comparatively small with a SD of 2.50 mmHg and 4.45 mmHg for soft and stiff P50s, respectively. A per-sample deformability metric for stiff and soft RBCs shown in Fig. 4B was computed by pooling the deformability of each subpopulation across oxygen tensions since the measured deformability of the stiff cells was shown to be oxygen independent (Fig. 3C), and deoxygenation has been shown to have no significant effect on mechanics of RBCs without polymer (27). The overall deformability of stiff RBCs was significantly less than soft cells across the 15 samples (****P value ≤ 0.0001, Mann–Whitney U test). The spread of the deformability metric was also small with a SD of 0.028 and 0.016 for soft and stiff cell populations, respectively.

Fig. 4.

Comparisons between stiff and soft cell population attributes. (A) P50 of soft and stiff cells for all samples. For every sample, cell populations were separated into soft and stiff at each oxygen tension to create an oxygen saturation curve for stiff and soft cell population of that sample. SO2 curves were fit with a Hill function to determine P50. ****P value ≤ 0.0001 (Mann–Whitney U test). (B) Measured deformability of soft and stiff cells for all samples. Soft and stiff populations at every oxygen tension were pooled for each sample to determine an overall measured deformability. ****P value ≤ 0.0001 (Mann–Whitney U test). In B, the dotted line indicates the noise threshold for the deformability measurement.

Comparing the saturation and deformability of different genotype RBCs demonstrates the quantitative differences between RBCs with and without detectable amounts of polymer. SCD and SCT RBCs without detectable amounts of polymer present similar oxygen affinity and deformability to healthy HbA containing RBCs, and polymer containing RBCs are similar across patient samples, but markedly different from RBCs without detectable amounts of polymer.

2. Discussion

Sickle cell pathology is driven in part by stiffened, HbS polymer-containing RBCs leading to rheological changes and endothelial damage (5). Prior studies have explored the processes involved in hemoglobin S polymerization (28, 29), and there have been a multitude of in-vitro studies recreating the pathological flow behavior and vascular damage introduced by polymer-containing RBCs (16, 30, 31). What is not well understood is how these results can extend to the complex, in-vivo pathophysiology. We need to measure the fraction of polymer-containing RBCs and their stiffness in oxygen environments found throughout the body. Without this knowledge, it is impossible to understand the role of polymer-containing RBCs on the different pathologies. Our study analyzed the stiffness and oxygen saturation of SCD patient RBC populations at a physiological range of oxygen tension. In doing this, we have identified that red blood cells containing HbS polymer can be separated from those without by both oxygen saturation and stiffness, with the stiffness of the polymer-containing RBCs being orders of magnitude larger than RBCs without polymer. Further, we have found that the population fraction of polymer-containing RBCs increases with decreasing oxygen in the environment suggesting a threshold of desaturated HbS monomers necessary to induce cell stiffening.

Our results indicate that SCD RBCs exist in one of two subpopulations: one with high relative saturation and high deformability and another with low relative saturation and low deformability. Red blood cells in the low deformability subpopulation contain polymerized HbS fibers that stiffen the cell and lock a portion of the hemoglobin in the low affinity, T-state. The decreased saturation at intermediate oxygen tensions (15 mmHg to 90 mmHg) is an easily measurable marker of hemoglobin polymerization (32). Regardless of polymer content, RBC oxygen saturation changes monotonically with soluble oxygen concentration (Figs. 3B and 5B). Polymer-containing RBCs have a significantly right shifted P50 relative to RBCs without detectable levels of polymer (Fig. 4A). RBC stiffness, while also being a continuous variable, shows a step change between RBCs with and without delectable polymer, and appears to only depend on the presence of polymer and not the oxygen environment. Average cell stiffness of polymer-containing RBCs is significantly higher than that of RBCs without detectable polymer at every oxygen tensions (Fig. 4B), but across oxygen values, the stiffness of these cells does not vary significantly (Fig. 3C). Measuring both saturation and deformability highlights how the mechanical behavior and oxygen-carrying capacity of SCD RBCs are affected in different ways by the formation of HbS polymer.

Fig. 5.

Patient sample stiff cell fraction and oxygen–hemoglobin dissociation curves. (A) Fraction of cells clustered in the stiff, low saturation subpopulation as a function of oxygen tension. The horizontal line at 0.15 corresponds to the cutoff threshold for normoxic stiff cells. The red data point is the highest oxygen tension to present greater than 15% stiff cells and is used as the normoxic data point; the blue data point is the hypoxic data point. (B) Oxygen-hemoglobin dissociation curves for the soft and stiff RBC subpopulations. The data points represent the mean saturation values of each subpopulation at the eight oxygen tensions, and the curves are the corresponding Hill fits to those values. The horizontal line at 0.5 indicates 50% saturation and the red diamonds mark the soft and stiff subpopulation P50s as calculated by the Hill fit. The red data point is the saturation value of the normoxic stiff cells in this sample, and the blue data point is the hypoxic saturation value of the stiff cells in the sample. Error bars are standard deviation.

There have been few studies measuring changes in bulk RBC stiffness brought about by formation of intercellular hemoglobin polymer. In our assay, the cell geometry and speed of each RBC can be used in conjunction with the known channel geometry and carrier fluid viscosity to estimate the order of magnitude of an elastic shear modulus of each cell using methods described by Hochmuth et al. and Mancuso et al. (33, 34). This method and representative data are presented in detail in the Materials and Methods of this text. From this calculation, we estimate the elastic shear modulus of the soft RBCs to be ~5 μN/m and the elastic shear modulus of polymer-containing RBCs to be at least 2,000 μN/m. The shear modulus of the soft RBCs matches results from the literature (35). The shear modulus of the RBC with polymer is a lower limit as the small deformations measured in these cells are close to the noise level of the measurement due to pixel size and minimal motion blurring. While there is a lack of experimental work on the bulk mechanical properties of individual polymer-containing RBCs, their markedly increased stiffness has been measured on the population scale using ektacytometry (36) and pore-clogging assays (37), and computational work by Lei et al. has estimated the stiffness of RBCs containing HbS polymer to be upward of 100 times that of soft cells, which is consistent with our findings here (13).

The incredible stiffness of the polymer-containing RBCs appears to be constant with changing oxygen tension, but this fraction of these RBCs increases monotonically with decreasing oxygen (Fig. 3A). Every SCD patient sample tested showed a roughly sigmoidal relationship between stiff cell fraction and decreasing oxygen tension (SI Appendix, Fig. S1). RBCs becoming detectably stiffer at different oxygen tensions could be explained by a threshold concentration of deoxygenated hemoglobin S monomer necessary to form sufficient polymer to stiffen the cells. Intracellular hemoglobin concentration varies across an RBC population and the hemoglobin variants have been shown to have a heterocellular distribution (38), which has been suggested to impact polymerization behavior (39). Both of these variables along with more dynamic cellular aspects such as 2,3-diphosphoglycerate concentration could lead to a distribution of intracellular deoxygenated hemoglobin S concentration resulting in a range of oxygen tensions for RBCs to form detectable levels of HbS polymer rather than a single value.

Stiff, polymer-containing RBCs present at almost all physiological oxygen tensions combined with an increasing percentage of these cells in more oxygen demanding tissues could help explain the unique, systemic pathologies of SCD. Vaso-occlusive crisis, the hallmark of SCD, often occurs in the capillaries and postcapillary venules (40), where tissue oxygen tension is low and our assay would predict a high percentage of stiff cells. In high oxygen tissues such as the cranial arteries or major organs, we would expect less RBCs with detectable polymer, but not a complete absence of them. Previous studies have shown stiffened RBCs present even in small population fractions to have a drastic impact on blood rheology (4, 15). Moreover, these cells have been shown to interact more strongly with the vascular walls, which could lead to chronic vascular injury even in more highly oxygenated tissues (17, 41–43). This suggests that stiffened cells could be partially responsible for the pathologies seen in highly oxygenated tissues as well as low oxygen tissues.

In summary, we have measured single-cell saturation and deformability of SCD RBCs at a range of physiological oxygen tensions and determined that polymer-containing RBCs are distinct from RBCs without detectable polymer cells by lower saturation and much greater stiffness. We have also found, within the measurement abilities of this assay, the stiffness of the polymer-containing RBCs to be far greater than those without detectable polymer and to not change as a function of oxygen tension. However, the amount of polymer-containing RBCs does increase with decreasing oxygen levels. These results can help to explain some of the pathophysiology of SCD and increase our understanding of the role of oxygen environment in the mechanical changes of RBCs.

3. Materials and Methods

3.1. Blood Handling and Preparation.

Blood samples from healthy donors and donors with SCD or SCT were collected at the Massachusetts General Hospital and Children’s Hospital and Clinics of Minnesota. This study was approved by the Massachusetts General Hospital Institutional Review Board and the Children’s Hospital and Clinics of Minnesota Institutional Review Board. All human subjects gave informed consent before participating in this study, or discarded specimens were used under an IRB-approved waiver of consent. Complete blood count (CBC) and hemoglobin variant tests for all samples were conducted using a Sysmex XN-9000 automated analyzer and capillary electrophoresis, respectively, to measure hematocrit, hemoglobin fractions, and other blood count indices for each sample. Patient blood samples were collected in vacuum-sealed citrate tubes, and all blood samples tested were stored for a few hours and up to 3 d at 4 °C prior to testing. These storage conditions have been shown to cause minimal changes in RBC mechanics (44, 45). Whole blood was rinsed with 1× phosphate buffered saline solution and spun at 400 × g for 2 min to remove plasma. Then, 2.7 µL of packed RBCs were added to 192 µL of 25% HSA solution (Gemini Bio) and 8 µL 1× phosphate buffered saline.

3.2. Microfluidic Design and Fabrication.

All studies were conducted using a polydimethylsiloxane (PDMS) device and microfluidic system. The microfluidic device was composed of two distinct PDMS layers separated by 100 µm of PDMS. The upper layer consists of a snaking gas channel, 150 µm in height and 1,000 µm in width, which can be supplied with a controlled mixture of air and nitrogen to control the oxygen environment of the device. The lower layer is 5.5 µm in height and consists of an inlet, resistor section, constriction section, and outlet. The constriction (Fig. 1B) is a 100-µm-long, 8-µm-by-5.5-µm rectangular channel with tapered entrance and exit.

The upper and lower layers of the microfluidic device were fabricated using soft lithography techniques from silicon wafer molds. The silicon wafer molds were fabricated using negative resist photolithography at the indicated feature geometries. The upper, gas layer was fabricated using traditional PDMS (Sylgard 184, Dow Corning) soft lithography to a targeted PDMS thickness of 4 mm. The lower layer was fabricated using a compression molding technique described previously (15) with a targeted height of 100 μm above the features, which created a 100 μm thick PDMS membrane separating the upper and lower layers. Each layer was plasma bonded at 100 cc min⁻¹ oxygen flow rate, 100 W power, and 60-s exposure time settings (PE-50, PlasmaEtch). The merged layers were then plasma bonded to a clean glass coverslip using the same plasma settings to finalize device fabrication.

3.3. Experimental Setup.

To analyze each blood sample, the microfluidic device described previously was placed in a Zeiss Axio Observer microscope encased in a 37 °C environmental incubation chamber. The region of interest was illuminated by two alternating light-emitting diodes synced to the trigger of the high-speed camera (Fig. 1A). The light-emitting diodes had wavelengths of 405 nm and 430 nm (M405L4, M430L4, Thorlabs) and were centered at the molecular absorption peaks of oxygenated and deoxygenated hemoglobin (Fig. 1F) using a 410-nm band-pass filter and 430-nm band-pass filter, respectively (FB410-10, FB430-10, Thorlabs). The high-speed camera (Phantom Miro C110, Vision Research Inc.) synchronized to the alternating light-emitting diodes captured images at a frame rate of 1,000 fps with 300 µs exposure; a 40×/0.75NA objective was used to magnify the ROI (Fig. 1A).

The oxygen environment of the microfluidic device was controlled by supplying the channel of the upper layer with a specified concentration of oxygen using a solenoid valve gas mixer reported previously (15, 22, 23). The mixer works by combining air (21% O₂, balance N₂) and 0% oxygen gas (N₂) in a solenoid valve-controlled chamber to generate gas at user-specified concentrations then perfused through the gas layers. Compressed air (21% O₂, balance N₂) and compressed nitrogen (N₂) are regulated to 1 psi (PRG200-25, omega) and their gas lines connected to a manifold (Manifold, 3× HDI, 3-port, face mount, The Lee Co.) equipped with eight solenoid valves (3 port face mount solenoid valves, The Lee Co.). The oxygen concentration was set by the duty cycle of the solenoid valves operated by a control system. The control system includes a control board (MCP23008 8-Channel 8 W Open Collector FET Driver I2C Shield with IoT Interface, NCD), an Arduino (Arduino Uno, Arduino), and custom Python scripts. The oxygen tension at the device gas outlet was monitored for the duration of the experiment using a fiber optic oxygen sensor (NeoFox-GT, Ocean Optics).

The prepped sample was perfused into the lower layer of the device at a fixed pressure of 800 mbar using an electronic pressure regulator (Flow EZ, Fluigent). The resistor section of this layer allows for greater control over cell velocity and ensures adequate time for RBCs to reach steady state saturation before reaching the constriction. Within the constriction cells reach speeds of 8,000 µm/s. The high-speed camera visualized individual RBCs passing through the constriction section of the microfluidic device. The ROI encompasses the entire constriction and the extent of the tapered exit. This region of interest was chosen as it was sufficient to image the RBCs in the extent of their deformation and relaxation. The exposure time was necessary to ensure adequate signal capture from the two narrow band light-emitting diodes to calculate saturation. The 300 µs exposure results in a five percent motion blurring that has been accounted for by introducing a noise floor that corresponds to the smallest measurable deformation possible using this system. The optical platform was able to image 30 to 50 cells passing through the constriction per second. Between 4,000 and 5,000 RBCs was recorded per experiment.

3.4. Single-Cell Deformation and Saturation Calculations.

As a cell passed through the constrictions and exited the tapered exit, it was tracked using a custom python software package. The image processing software labeled each RBC and measured shape, saturation, area, and velocity of the cell at each frame to observe the changes that occur as the cell was constricted and relaxed. The cell shape at each frame was fit to an ellipse and used to calculate the Taylor deformation. The deformability parameter of each RBC was calculated by taking the absolute change in Taylor Deformation of the cell when it was in the constriction and after it exited (Eq. 1), any rotation as the cell exits is accounted for in the image processing. The parameters a′ and b′ are the semi-major and semi-minor axis of the ellipse fit to the cell shape in the constriction, and a and b are the same axis once the cell exited the constriction (Fig. 1C).

$$\text{Deformability}=\left|\left(\frac{a\mathit{\text{'}}-b\mathit{\text{'}}}{a\mathit{\text{'}}+b\mathit{\text{'}}}\right)-\left(\frac{a-b}{a+b}\right)\right|.$$ [1]

It is necessary to compare the constricted and unconstricted geometry for SCD blood cells. While RBCs without detectable polymer will present a circular cross-section at rest, polymer-containing RBCs can take on many different morphologies at rest, so any deviation from a Taylor deformation value of zero may or may not mean shape change. To accurately determine the amount of deformation, it is required to look at the absolute change in shape. Change in Taylor deformation was chosen as the deformation parameter because it has been shown to be less sensitive to noise compared to other deformation metrics such as circularity or eccentricity (46). The deformability measurement has a slight correlation with cell area and cell speed, which has been adjusted for (Fig. 1D).

The saturation of each cell was determined using the alternating light-emitting diodes in the Soret band following the protocol of Di Caprio et al. (24) (Fig. 1E). The two light-emitting diodes, with nominal wavelengths of 405 nm and 430 nm, were fitted with 10-nm FWHM band-pass filters centered at 410 nm and 430 nm which correspond to absorption peaks of oxygenated and deoxygenated hemoglobin, respectively (Fig. 1F). By taking the average pixel value within the contour of the cell and comparing it to the background pixel value under each light emitting diode, it is possible to calculate the mass of oxygenated and deoxygenated hemoglobin and from this calculate saturation value. It was necessary to have a small FWHM for both light-emitting diodes fully to decouple the signal from the two hemoglobin species and get an accurate saturation calculation, but this meant the experiment required a in a slighter longer exposure time to get adequate signal as the hemoglobin absorbed a significant amount of light. The average single-cell saturation recorded across a range of oxygen tensions can provide an oxygen–hemoglobin dissociation curve (Fig. 1G).

3.5. K-means Clustering to Separate Cell Subpopulations and Derive Sample Metrics.

The marked differences in deformability and saturation between soft and stiff cells make possible effective grouping of two subpopulations using k-means clustering. To analyze the raw data collected from each patient sample, we clustered cells by their deformability and saturation at each oxygen tensions into a stiff cell subpopulation and soft cell subpopulation. From this, we can observe how the two subpopulations change as a function of oxygen tension. Fig. 5, which shows the results of this clustering for the SCD patient data in Fig. 2B, highlights the role of oxygen tension on key population metrics. In this representative patient dataset, the relative fraction of stiff cells increases monotonically with decreasing oxygen tension. Fig. 5A shows the stiff cell fraction versus oxygen tension for this sample. The measurement of stiff cell fraction allows us to identify the highest oxygen tension with a distinct, measurable fraction of stiff cells. This threshold was chosen to be 15% stiff cells (indicated by the red data point above the dotted line in Fig. 5A) to ensure all patient samples had enough normoxic stiff cells to achieve a 95% confidence level using Fisher’s sampling formula. The stiff cells at this highest measured oxygen tension are denoted normoxic stiff cells. These can be compared with stiff cells at 0 mmHg, which are denoted hypoxic stiff cells (blue data point in Fig. 3A). Along with decreased deformability in the stiff cell subpopulation, the oxygen saturation is also decreased. Fig. 5B is the stiff and soft subpopulations saturation measurements at each oxygen tension and the Hill fits of these data points. The red diamonds overlaid on the two curves are the corresponding P50s derived from the Hill fits; the stiff cell subpopulation has a right-shifted P50 relative to the soft cell subpopulation. The red and blue data points on the stiff cell curve are the normoxic stiff cell saturation and hypoxic stiff cell saturation, respectively.

3.6. RBC Shear Modulus and Viscous Modulus Calculation.

To estimate the shear elastic and viscous moduli of soft and stiff SCD RBCs, a separate experiment was performed with adjusted experimental parameters. In this experiment, a high powered white light was used instead of alternating light-emitting diodes in the Soret band. Using this brighter light source allowed for shorter exposure times and higher perfusion pressures at the expense of the saturation measurement. The high-speed camera was set to 2,000 fps with a 30-μs exposure. Perfusion pressure was set to 1,200 mbar, which led to a maximum cell velocity of 15,000 μm/s. The perfusion pressure was increased for this experiment to increase deformation of the stiff cells and create a larger dynamic range. These experimental parameters led to measureable deformations in all cells and motion blurring of less than 1%. The shear elastic moduli and viscous moduli for each RBC were estimated using methods described by Hocumuth et al. (33) and recently demonstrated in similar experiential protocol to this study by Mancuso et al. (34). In this procedure, the uniaxial tension force on the cell, presented in Eq. 2, is calculated using the viscosity of the carrier fluid, the strain rate, du/dx, and the length scale of the cell. The viscosity of the carrier fluid was measured as 8.26 cP using a Brookfield LVDVII+ cone and plate viscometer (SI Appendix), and the length scale was set as the semi-major axis of the cell.

$$T=\frac{\sigma A}{L_o}=\frac{3A{\eta }_s\frac{\mathit{du}}{\mathit{dx}}}{L_o}.$$ [2]

The shape of the RBC was recorded as it passed through the constriction to calculate the stretch ratio, λ, which is defined as the length of the deformed axis in the direction of extension divided by the length of that same axis in the undeformed state. For our experiment, this was the axis of the cell in the direction of flow in the constriction and that same axis once the cell had exited the constriction. Planar rotation was accounted for in the image processing. The RBCs were modeled as Kelvin–Voigt materials in a similar fashion to both Hochmuth and Mancuso. Eq. 3 is the Kelvin–Voigt model; T is the uniaxial tension force, λ is the stretch ration, μ is the elastic shear modulus, and η is the viscous modulus.

$$T=\frac{\mathrm{\mu }}{2}\left({\lambda }^2-{\lambda }^{-2}\right)+\frac{2\eta }{\lambda }\frac{\partial \lambda }{\partial t}.$$ [3]

Representative images of soft and stiff cells passing through the constriction and plots of stretch ratio, time derivative of stretch ratio, cell velocity, and spatial derivative of cell velocity as a function of position are shown in Fig. 6. The stretch ratio and cell velocity were measured in both time and space making fitting Eq. 3 for each RBC a straightforward process. The fitting was performed using the Python SciPy package. Using this method, we estimate the average elastic shear modulus of the soft cells to be 4.33 μN/m (±1.52 μN/m) and the viscous modulus to be 7.57 μN-s/m (±2.57 μN-s/m), and the elastic shear modulus of the stiff cells to be 2.26 mN/m (±2.85 mN/m) and the viscous modulus to be 8.12 μN-s/m (±13.3 μN-s/m). The large standard deviates for the stiff cell moduli are most likely partially due to small deformation producing noise in the measurement.

Fig. 6.

Representative behavior of soft and stiff cells and associated parameters used to estimate shear elastic modulus and viscous modulus (A) Representative images of a soft cell passing through the constriction. (B) A plot of the stretch ratio as a function of position along the constriction and exit. (C) A plot of the time derivative of the stretch ratio as a function of position along the constriction and exit. (D) Velocity of the cell as a function of position along the constriction and exit. (E) Velocity derivative of the cell in the direction of flow along the constriction and exit. (F) Representative image of a stiff cell passing through the constriction. (G–J) Plots of stretch ratio, time derivative of stretch ratio, cell velocity, and spatial derivative of cell velocity along the constriction and exit, respectively. Arrows indicate flow direction; scale bars are 10 µm.

3.7. Statistical Analysis.

Statistics were performed using Prism9 GraphPad software. The test used in each case was reported in the figure captions. For comparing the means across different conditions, we used a Wilcoxon test; for comparing the means between sample groups, we used a Mann–Whitney U test.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Anonymized (Python Code and Excel Files) data have been deposited in Github (https://github.com/dillonwilliams890/SingleCell) (47).