An Experimental-Computational Approach to Quantify Blood Rheology in Sickle Cell Disease

Abstract

In sickle cell disease, aberrant blood flow due to oxygen-dependent changes in red cell biomechanics is a key driver of pathology. Most studies to date have focused on the potential role of altered red cell deformability and blood rheology in precipitating vaso-occlusive crises. Numerous studies, however, have shown that sickle blood flow is affected even at high oxygen tensions, suggesting a potentially systemic role for altered blood flow in driving pathologies, including endothelial dysfunction, ischemia, and stroke. In this study, we applied a combined experimental-computation approach that leveraged an experimental platform that quantifies sickle blood velocity fields under a range of oxygen tensions and shear rates. We computationally fitted a continuum model to our experimental data to generate physics-based parameters that capture patient-specific rheological alterations. Our results suggest that sickle blood flow is altered systemically, from the arterial to the venous circulation. We also demonstrated the application of this approach as a tool to design patient-specific transfusion regimens. Finally, we demonstrated that patient-specific rheological parameters can be combined with patient-derived vascular models to identify patients who are at higher risk for cerebrovascular complications such as aneurysm and stroke. Overall, this study highlights that sickle blood flow is altered systemically, which can drive numerous pathologies, and this study demonstrates the potential utility of an experimentally parameterized continuum model as a predictive tool for patient-specific care.

Significance

Efforts to understand the causes of vaso-occlusion in sickle cell disease have largely ignored the chronic mechanisms, such as systemically altered blood flow, that could increase the risk for acute pathologies. Here, we combine novel experimental tools with computational fluid dynamics to show how the non-Newtonian properties of sickle blood are altered over a wide range of physiologically relevant conditions. Our results suggest that sickle blood flow is altered throughout the vasculature compared with nonsickle blood. Such altered blood flow can cause vascular injury, vaso-occlusion, and even cerebral aneurysms. We also demonstrate how therapies such as transfusion can mitigate these effects and show a path for models to predict at-risk patients and evaluate treatment efficacy.

Introduction

Sickle cell disease (SCD) is a hereditary disorder in which a mutant hemoglobin molecule (sickle hemoglobin, HbS) polymerizes under hypoxic conditions (1,2). Complications associated with the disease include vaso-occlusive crisis, chronic organ damage, acute chest syndrome, aneurysm, and stroke (3). To date, our understanding of SCD pathophysiology has been centered around the proximal causes of vaso-occlusion, including altered red cell deformability (4,5), endothelial adhesion (6), and immune response (7). With the exception of free-heme-induced oxidative stress (8), much less attention has been paid to chronic mechanisms that promote endothelial inflammation and enhanced immune response and that precipitate acute complications including vaso-occlusion and stroke. One potentially significant but overlooked mechanism is systemically altered blood flow due to oxygen-dependent changes in red cell biomechanics and blood rheology (9,10). There is evidence that changes in red cell deformability and sickle blood rheology occur even at arterial oxygen tensions (11,12), suggesting that altered flow could arise throughout the circulation and could contribute to endothelial injury, tissue ischemia, inflammation, and other acute pathologies, including vaso-occlusive crisis, aneurysm, and stroke (13). Understanding the potential impact of altered flow will require us to predict important physiologic metrics—e.g., velocity, pressure, shear stress, etc.—in realistic vascular geometries. Making such predictions is complicated by the non-Newtonian nature of blood and the complex nonlinear changes that may occur in sickle blood as it transits the vasculature.

A number of experimental and computational approaches have been applied to understand the biophysical mechanisms of SCD at every scale from molecules to whole blood (14, 15, 16, 17). These methods have all provided new insights into factors that impact the erratic rheology that occurs in SCD and that drive the complex clinical behavior patients also exhibit. To describe how sickle blood rheology changes throughout the wide range of vessel sizes, oxygen tensions, and shear rates in the vasculature, however, requires a continuum model that predicts the blood’s non-Newtonian flow under a range of conditions using well-defined functions. Moreover, a sickle blood constitutive model should be parameterized using experiments that replicate the physiologic conditions under which altered flow is observed. A constitutive model so specified and validated could, in principle, be used to design patient-specific treatment regimens by understanding how, for example, a well-defined transfusion regimen will alter the patient’s rheological parameters. Moreover, such a model could be combined with patient-specific vascular models to predict patients at risk for complications such as cerebral aneurysm, which are common in SCD patients (18).

In this study, we applied a combined experimental/computational approach to examine sickle blood rheology under a range of physiologically relevant conditions. We took advantage of recent advances in blood flow imaging and analysis to measure submicron-resolution velocity fields, and we constructed a computational model of the channel flow and regressed model parameters to the measured velocity fields. This approach leverages the richer information content contained in the experimental velocity fields, and it provides simple parameters for a constitutive equation that can be used to translate the data to other geometries and flow conditions. By creating constitutive models, we obviate the need to iterate experimentally the limitless variability in vascular geometries needed to characterize the rheological behavior. In this work, we 1) developed a protocol for the experimental/computational approach proposed in the previous paragraph, 2) used that approach to analyze the rheological behavior of blood from healthy and SCD donors under varying oxygen tension and perfusion level, 3) incorporated an experimental and computational approach to assess transfusion treatment efficacies, and 4) incorporated the derived parameters into an illustrative finite-element simulation of blood flow in a realistic vessel geometry.

Materials and Methods

Blood sample collection

Blood samples from SCD patients and from normal, healthy donors were collected at the University of Minnesota Medical Center and Massachusetts General Hospital under Institutional Review Board approved protocols. All blood samples were stored for a few hours and up to 3 days before testing in the microfluidic device setup (Fig. 1 A). Additional blood sample testing and data collection details are given in the Supporting Materials and Methods.

Figure 1.

Schematic of the combined experimental-computational method. (A) Blood is pumped through a microfluidic system with controlled pressure drop and oxygen tension. (B) Blood flow is recorded by a high-speed camera (top), analyzed to identify trackable features (middle), and tracked to generate a velocity profile (bottom). (C) An experimental profile of velocity versus position across the channel is generated. (D) Concurrently, a rectangular finite-difference model is generated of the flow in the channel using an initial guess for the Carreau-Yasuda model parameters. (E) Solution of the model equations gives a full velocity profile (i.e., v_z vs. x and y). (F) The velocity profile is averaged through the channel height to give a velocity profile comparable to the experimental profile in (C). The model parameters are adjusted iteratively to minimize the sum of squared error between the model profile and the experimental profile. To see this figure in color, go online.

Combined experimental-computational approach

The essence of our approach is shown in Fig. 1. Briefly, the experimental component consists of a microfluidic system (Fig. 1 A), described previously (19), that allows control of flow rate and oxygen tension, with simultaneous pressure-drop monitoring (allowing pressure-drop control) and high-speed, high-resolution video recording of the blood flow (Fig. 1 B). Taking the flow direction to be z, the channel width to be x, and the channel height to be y, the video recording allows generation of a height-averaged velocity profile v_z(x), as in Fig. 1 C. The same profile is generated computationally via a finite-difference model of Carreau-Yasuda flow (Fig. 1, D and E) in the channel and appropriate averaging of the finite-difference solution. The model equation is

$$\eta ={\eta }_{\infty }+\left({\eta }_0-{\eta }_{\infty }\right){\left[1+{\left(\lambda \dot{\gamma }\right)}^a\right]}^{\frac{n-1}{a}},$$ (1)

where η is the apparent viscosity as a function of shear rate $\dot{\gamma }$, η₀ is the zero-shear-rate viscosity, η_∞ is the infinite-shear-rate viscosity, n is an exponent that determines the steepness of the viscosity curve, a is a dimensionless parameter that describes the transition from the zero-shear-rate region to the power-law region, and λ is a time constant associated with the critical shear rate ${\dot{\gamma }}_{cr}$ ∝ 1/λ where the power-law region starts. The parameters η_∞, η₀, n, a, and λ are iterated to minimize the error between the experimental and model profiles (Fig. 1 F). A slip velocity is introduced along the wall to match the apparent slip observed experimentally (cf. (19,20)). Further methodological details are given in the Supporting Materials and Methods.

Results

Model validation: pressure-drop sweep on healthy blood

Initial validation was performed by conducting a study of healthy blood samples (n = 5) over a range of pressure drops (Fig. S2, A and B). For the approach to be valid, the model parameters should be the same or nearly so for the same blood under different flow conditions. All parameters showed a variation of less than 5% over three different oxygen levels (0, 45, and 90 mmHg, oxygen level defined as the partial pressure of gas), and five different pressure drops (0.2, 1, 2, 3, and 4 psi). In addition to providing a good validation test, the calculated parameter values established a healthy blood baseline used in the other studies described in this work (Table S2). Detailed results from the validation study are provided in the Supporting Materials and Methods.

Healthy versus sickle cell disease, high versus low oxygen tension

In light of the well-established sensitivity of SCD blood to changes in oxygen tension, we compared parameter values determined at high (90 mmHg) and low (0 mmHg) oxygen tension for both SCD blood (>70% HbS) and healthy blood (0% HbS); all experiments were performed at 1.0 psi pressure drop. The gross observations were as expected and consistent with previous studies (17,19); at high oxygen tension, the flow rate of SCD blood was lower than that of healthy blood at the same pressure drop, indicating a higher viscosity, and at low oxygen tension, the difference was amplified considerably as the healthy blood remained unchanged but the SCD blood thickened. The blunting of the velocity profile near the center of the channel (Fig. 2, A and B) is indicative of high low-shear viscosity. The model was able to fit the data quite well for all cases.

Figure 2.

Healthy versus SCD blood at high and low oxygen tensions at 1 psi pressure drop. (A) Four dimensional velocities are shown for four cases: healthy at 90 mmHg oxygen tension (1), healthy at 0 mmHg oxygen tension (2), sickle at 90 mmHg oxygen tension (3), and sickle at 0 mmHg oxygen tension (4). Even at 0 mmHg oxygen tension, the healthy blood (2) shows a much higher flow rate than the SCD blood at 90 mmHg oxygen tension (3), and the thickening of the SCD blood at 0 mmHg oxygen tension is even more pronounced. (B) Experimental (circles) and model (lines) velocity profiles for the four cases shown in (A) are given. (C) Viscosity-shear-rate plot constructed using the fitted model parameters is shown. The SCD blood shows a high degree of shear thinning and a very large low-shear modulus. (D) Comparison of the specific model parameter values shows no significant change for any parameter with oxygen tension for the healthy blood. For the SCD blood, in contrast, both viscosities increase sharply at low oxygen tension, and the other parameters also change. Error bars represent sample standard deviation for each fitted parameter. To see this figure in color, go online.

Because the entire profile was fitted, not just the total flow rate, a single experiment was sufficient to generate a viscosity versus shear-rate curve (Fig. 2 C), in which the extreme thickening of the SCD blood at low oxygen tension is seen. It is also clear from Fig. 2 C that the amount of shear thinning exhibited by the SCD blood at low oxygen tension was higher than that for high oxygen tension or healthy blood.

Turning to the model details, the most striking feature of the curves in Fig. 2 C is supported by the first two plots in Fig. 2 D. Both the low-shear (η₀) and high-shear (η_∞) viscosity rose sharply for the low-oxygen SCD case. Other, more subtle changes also occurred. A decrease in λ corresponds to an increase in the transition shear rate, indicating that the SCD blood not only has a higher viscosity at high and low shear but also tends more strongly toward the (higher) zero-shear viscosity, further increasing its resistance to flow. The increase in a for the low-oxygen SCD blood suggests a sharper transition to the power-law regime, and the decrease in n suggests a stronger dependence on the shear rate at high viscosity. Taken together, these results indicate that the SCD blood becomes more resistant to flow via multiple different effects.

Transfusion effects on the blood rheology

Blood transfusion is a primary treatment method for severe SCD (21), with two main goals: 1) to provide healthy red blood cells to the patient to increase oxygen capacity, and 2) to lower the blood viscosity, allowing the blood to flow more freely (22). Although chronic transfusion is beneficial in the treatment of the disease, there are many risks associated with the procedure, such as alloimmunization and excess iron, which leads to damage in the liver, heart, and other organs. At present, the target levels of chronic transfusion therapy aim for a hemoglobin level of 10 g/dL and <30% HbS cells (23). These target levels, however, are not patient dependent, and less aggressive targets could still prove beneficial while easing the burden on blood supply and limiting transfusion-associated risks. To study the effect of transfusion, we applied our analytical procedure to blood from an SCD patient mixed with healthy blood to create HbS fractions from 0% (pure healthy blood) to 74.8% (pure SCD blood). Again, oxygen tensions of 0, 45, and 90 mmHg were used, with a focus on the 0-mmHg-oxygen case because the effect of SCD is most pronounced at low oxygen tension.

As can be seen in Fig. 3, there was a dose-dependent response, with the velocity profile becoming faster and steeper (i.e., less blunted) as the fraction of healthy blood was increased (Fig. 3, A and B). The wall slip velocity increases as the HbS fraction increases from 22.4 to 74.8% HbS (Fig. 3 B, line (2)–(4)) but is nearly identical for lower HbS fraction (Fig. 3 B, line (1) versus (2)). Viscosity-shear-rate curves showed an increase in viscosity and more pronounced shear-thinning behavior, with an increase in the HbS fraction at all shear rates (Fig. 3 C).

Figure 3.

Dose-dependent effect of transfusion on low-oxygen-tension SCD blood flow. (A) The velocity profile for the highest-transfused case (1) is slightly lower than that observed for healthy blood, as seen in Fig. 2A above. As the sickle cell fraction is increased, the blood becomes increasingly more viscous, leading to reduced velocity and a blunter velocity profile. HbS levels: 1) 7.4%, 2) 22.4%, 3) 52.8%, and 4) 74.8%. (B) The velocity profile becomes lower and flatter with increased sickle cell fraction (numbers correspond to A). (C) The calculated viscosity increases with sickle cell fraction at all shear rates; the curve for 52.4% sickle cells (black) is very close to that for 74.8% sickle cells (red). (D) The individual model parameters show little oxygen dependence at low HbS% but diverge at higher HbS%. To see this figure in color, go online.

The dose dependency was explored in further detail by plotting the different model parameters versus HbS at different oxygen tensions (Fig. 3 D). There are two striking results. First, even very low HbS fractions (7.4%) lead to changes in the blood rheology, which are quantifiable in terms of the model parameters. Second, the lack of dependence of the model parameters on oxygen tension, seen in the healthy blood case in Fig. 2 D, is maintained for 7.4% HbS and for 22.4% HbS for all parameters except for some change in λ; that is, the different curves in the plots of Fig. 3 D nearly overlap for 0, 7.4, and 22.4% HbS and then start to spread for larger HbS levels. At low levels of HbS (up to 22.4%), the presence of the sickle cells alters the blood rheology but in an oxygen-independent manner. As the HbS fraction increases, however, the oxygen dependence emerges and intensifies.

Further analysis (Fig. S3, A and B; details in Supporting Materials and Methods) showed a strong correlation among the model parameters, especially at low oxygen tensions. In particular, the low-shear and high-shear viscosities, η₀ and η_∞, were highly correlated (r² = 0.96), whereas the correlation between η₀ and λ was less strong (r² = 0.69). Thus, we focused on the parameters η₀ and λ as descriptors of blood rheology. As can be seen in Fig. 4 A, the viscosity change with pO2 and HbS% was quite smooth, with the highest viscosity in the low pO2-high HbS% region in the upper left corner of the contour plot. Fig. 4 A also shows the relatively small effect of oxygen tension on viscosity at low HbS fraction, transitioning to a large effect at high HbS fraction. Fig. 4 B shows similar behavior, with the lowest λ-value (i.e., the highest transition shear rate) in the low-oxygen, high-HbS region.

Figure 4.

Contours plots for non-Newtonian model parameters. Each black dot represents one blood sample at one oxygen tension. Contours for (A) η₀ and (B) λ for the transfusion study of a single patient show that non-Newtonian parameters change smoothly with sickle cell fraction and oxygen tension. Contour plots for (C) η₀ and (D) λ based on blood from 12 different patients suggest that other individual factors can affect blood viscosity in different patients. To see this figure in color, go online.

PO2 effects on the blood rheology for multiple patients

The data of Fig. 4, A and B were combined with additional data on blood from 12 different SCD patients (HbS range 18–88.6%), leading to the contour plots of Fig. 4, C and D. Despite the fact that numerous other individual factors may affect blood viscosity in different patients (4), the contour plots show consistent trends, with the most severe features (high η₀ and low λ) arising at high HbS% and low pO2, as expected. Fitting the data with a simple biquadratic model yields the expressions

$${\eta }_0=2.44+60.8x+24.4y-116xy-32.2x^2-853y^2$$ (2)

and

$$\lambda =1.27-3.59x-4.40y-3.04xy+2.54x^2-11.2y^2,$$ (3)

where x is the HbS fraction from 0.18 to 0.886 and y is the oxygen tension from 0.02 to 0.08. The goodness of fit was found to be r² = 0.92 for λ and r² = 0.91 for η₀.

Non-Newtonian effects on simulated blood flow in a realistic geometry

Studies have associated SCD with cerebrovascular health problems such as intracranial aneurysm and aneurysm subarachnoid hemorrhage (24,25). Patients with SCD have presented with multiple intracranial aneurysms, generally located in the posterior cerebrovascular circulation and not associated with traditional risk factors such as systemic hypertension, hypercholesterolemia, renal insufficiency, or arteriosclerosis (26). Changes in blood rheology can lead to altered wall shear stress (WSS), which can ultimately lead to endothelial injury, a possible triggering event in the development of aneurysms (27). Finite-element modeling of cerebrovascular blood flow provides a useful platform to explore the potential consequences of the observed changes in blood rheology.

To explore how rheological changes in the blood due to SCD could alter the WSS profile in a realistic geometry, we used a three-dimensional model of the vertebrobasilar system, constructed from a magnetic resonance MR scan of a 23-year-old female subject (Fig. 5 A) and provided by the Open Source Medical Software Corporation (28). The hemodynamics problem was solved using the open-source SimVascular (29) biofluid mechanics software for Newtonian and non-Newtonian blood rheology, assuming rigid vessel walls. For the non-Newtonian model, parameters found previously for healthy blood and 74.5% HbS blood were used as inputs. In the SCD cases, 90 and 45 mmHg oxygen tensions were selected to represent a range of possible oxygen levels in the brain arteries. For the Newtonian model, a constant viscosity of 3 cP was used. Resistance boundary conditions were used on the smaller vessels and mean flow input for the larger ones. Values for the boundary conditions were obtained from (30). Although there is an observable pressure pulse in the cerebral arteries, steady flow was used for this illustrative study. It is emphasized that this computation was made to demonstrate the potential impact of rheological changes on a relevant vascular mechanics problem, not to make any specific clinical conclusion—the MR subject was healthy, and the blood rheology was from different individuals.

Figure 5.

(A) Three-dimensional model of the vertebrobasilar system constructed based on MR scan from a 23-year-old female subject. Blood flow dynamics were calculated assuming either a (B) Newtonian or (C–E) non-Newtonian viscosity model. For the non-Newtonian model, a shear-dependent viscosity was used. The viscosity parameters were based on results obtained in Fig. 2 for an oxygen tension of 90 mmHg. Wall shear stress (WSS) distribution along the wall is calculated for (B) the Newtonian model for healthy blood and the non-Newtonian model for (C) healthy blood, (D) sickle blood (>70%), and (E) transfused blood (22.4% HbS). The arrows mark the high WSS region with values provided on top of the figure. The Newtonian model showed the largest local WSS because the model fails to account for the shear thinning of the blood. For the non-Newtonian model, changes in the non-Newtonian parameters with increased sickle cell fraction leads to an increases WSS in the vessel wall. The transfused blood with lower sickle cell fraction is less viscous, leading to a lower WSS when compared to the sickle blood. To see this figure in color, go online.

Fig. 5, B–E show the calculated WSS along the vessels for the different parameter values studied, with the maximal value marked with an arrow and provided at the top of each panel. All of the results shown are at 90 mmHg oxygen tension. The Newtonian model (Fig. 5 B) overpredicts the WSS badly compared to the other models because it fails to account for the shear thinning of the blood, which is most pronounced near the wall and thus has a large effect on WSS in a controlled-flow-rate model. The healthy blood model (Fig. 5 C) had the lowest WSS over most of the domain and had the lowest peak WSS. The SCD model for a sickle blood fraction higher than 70% showed elevated WSS even at high oxygen tension (Fig. 5 D), the result of the SCD blood being more viscous than the healthy blood (Figs. 2, 3, and 4). The transfused blood model (22.4% HbS) showed a reduced WSS compared to the sickle model. The transfusion reduced sickle cell fraction in the blood decreases the blood viscosity and thus lowers WSS when compared to the sickle blood. These effects were exaggerated when oxygen tension was reduced to 45 mmHg (Fig. S4, A–D).

Discussion

The most important contribution of this work is the development and demonstration of a combined microfluidic and computational approach that allows us 1) to make rheological measurements that are relevant to the patients’ likely in vivo experience and 2) to extract physically meaningful parameters from the rheology to improve our understanding of the complexities of sickle cell blood flow. The resulting parameterization of a full constitutive model for blood under given conditions (HbS fraction and oxygen tension) allows us to begin exploring and pinpointing alterations in SCD blood flow under the full range of physiologic conditions and to compare blood rheology across patients quantitatively. The resulting constitutive equation can also be applied to other complex geometries without the need for lengthy experimentation and variable changes, enabling realistic simulations of blood flow in the vascular system and forming the basis for potential future patient-specific treatment design. Although behavior in capillaries is too complex to be described by a continuous model such as the Carreau-Yasuda model, the higher risk of SCD patients for vascular anomalies (31) points to the need for and potential benefit of the approach described here.

The experimental and computational components of our approach are both essential. Unlike traditional rheometric tools, our microfluidic device can characterize the unique non-Newtonian aspects of SCD blood flow and explore them systematically at a series of shear rates and oxygen tensions. This capability is a strength in our system, as the ability to generate high-quality data sets has been limited, which, in turn, has restricted the availability and utility of data for computational models. Experimentally, we found that SCD blood rheology responds to oxygen tension, which we observed as a decreasing average velocity and increasingly blunted flow profile as oxygen tension was decreased. The more blunted profile is consistent with a rise in low-shear viscosity, as seen by an increase in η₀ and a decrease in λ in the analysis. The response was notably different among patients with different levels of HbS, and there was even variation in the response among patients with similar HbS levels, consistent with the patient phenotypic heterogeneity observed in the clinic (32,33). Although our methods are designed to limit some of the interpatient variability, there remain parameters that vary among the blood samples that can affect the rheological profile. Most of the subjects in our study are receiving hydroxyurea therapy with the goal of increasing HbF, which can inhibit polymerization of HbS within red blood cells. However, response to hydroxyurea varies dramatically among patients, as can be seen by the HbF fractions in Table S1. Additionally, red cells accumulate membrane damage over time, increasing the stiffness of the cells and altering cell-cell adhesion, thus altering the rheological behavior in our microchannels. Patient-specific differences can arise from differences in red cell turnover rates as well as sources of membrane damage within the circulation, which will be patient-specific. Even with this variation, the plots of Fig. 4 indicate that general trends emerge—the blood properties become farther from healthy values as the HbS level increases and as the oxygen tension decreases—and that for an individual patient, a relatively simple curve fit of the overall data could be used to describe the patient’s HbS-level-dependent blood rheology.

For our computational analysis, we used the Carreau-Yasuda model, describing sickle blood as a shear-thinning fluid. The Carreau-Yasuda model has been used to characterize the known shear-dependent viscosity of normal, healthy blood in past studies; the approach described herein could be applied with any of the models normally used for blood rheology (see reviews (34,35)). Also, the detailed velocity profile could be used as a test of mesoscale models that account for individual cell-cell interactions (20). Unlike most mesoscale simulations, our methods are computationally inexpensive and thus easily scalable. The simulations reported here used a Dell desktop, Intel Core i7 8700 with six core up to 4.60 GHz. Using 10 different pressures, it took roughly 9.14 s, and solving three parameters (by keeping two fixed) took roughly 8.44 s. We found that, as expected, normal blood shear thins, and the associated model parameters are independent of oxygen tension. For sickle blood, however, the results show a high dependence on oxygen tension with all fitting parameters η_∞, η₀, n, a, and λ exhibiting a significant change between 0 and 90 mmHg (Fig. 3). The change in λ is of particular note in that it suggests not only an overall increase in blood viscosity (via increases in η₀ and η_∞) but also a shift toward the (higher) low-shear viscosity. That is, not only is the sickle blood more viscous at all shear rates, it requires a larger shear rate to shift into the presumably less dangerous high-shear viscosity regime. One major implication of our findings is that SCD blood flow is likely to be altered throughout the vasculature, from the low-shear, low-oxygen venous circulation to the high-shear, high-oxygen arterial circulation, including the pulmonary and cerebral vasculatures, where the most severe complications occur. Thus, the vascular endothelium is chronically exposed to aberrant shear stress, potentially causing vascular inflammation, increasing red cell adhesion, and promoting leukocyte accumulation. The overall result is increased likelihood of vaso-occlusion throughout the vasculature and severe complications such as acute chest syndrome, cerebral aneurysm, and stroke.

To explore the potential utility of our approach in a clinical setting, we examined how the model parameters would change via a simulated transfusion experiment. Transfusions are common clinically and work by diluting the unhealthy red blood cells with healthy transfused ones, but transfusions do not come without their issues. Iron overload, circulatory overload, and alloimmunization symptoms can be expressed by patients (21,23), and limiting the need and amount of transfusions by detailing a patient-specific treatment method could be beneficial. Moreover, decreasing the blood needed for transfusions would free up this precious resource for other health care needs. We found that all model parameters changed as expected when SCD blood was diluted with healthy blood, but not all to the same degree. At a 22.4% HbS concentration or lower, η_∞, η₀, n, and a stopped showing any oxygen-dependent differences, whereas λ continued to show differences even at a small HbS concentration of 7.5%. We demonstrated that a simple curve fit can be performed to estimate the model parameters for a patient as a function of HbS level and oxygen tension.

The availability of an HbS- and pO2-dependent model points to a potential opportunity for patient-specific transfusion strategy decisions. Clinically, a common target for chronic transfusion therapy is a hemoglobin level of 10 g/dL and <30% HbS cells recurring every 3–4 weeks (23). This amount of blood transfused, however, may be unnecessary, and smaller or less frequent transfusions could be sufficient, limiting complication risk and saving blood and personnel resources. It may be possible to identify target rheological parameters rather than target HbS levels; an initial test of the patient’s blood could be used to specify model parameters as in Eqs. 2 and 3, which in turn could be used to tune an individual patient’s target HbS level. Such an approach, if successful, would improve both patient care and resource management. Importantly, sickle cell disease complications depend heavily on blood rheology, so a successful model could provide enough information to aid the patient even with minimal inclusion of biological factors that also contribute to disease pathology.

The role of blood rheology in cerebral aneurysm formation is an active research area, and there is a recognized association between SCD and some cerebrovascular anomalies (18,31). These observations suggest that an effective approach to treatment design for SCD patients could include both patient-specific blood rheology and patient-specific cerebrovascular geometry (via, e.g., magnetic resonance angiography). We demonstrated in this work (Fig. 5) that the changes in blood properties we observed were sufficient to produce substantial changes in the hemodynamic outcomes (e.g., WSS) in a realistic biofluid dynamic model. The altered hemodynamics of sickle blood provide a likely biophysical mechanism behind the observation that patients with high transcranial Doppler velocities are at greater risk for stroke. Given the multiple challenges involved in identifying at-risk patients, especially before an aneurysm forms, the ideas put forward herein for a patient-specific approach must be seen as exploratory rather than prescriptive; the concept is worth further investigation but requires considerable work before it might be of clinical use.

Conclusions

In summary, the combined experimental and computational approach in our study affords the opportunity to develop a physics-based understanding of sickle cell disease complexities. The model can be used as both an explorational tool to understand the impact certain physical parameters have on sickle cell disease as well as a potential clinical tool to aid in the diagnosis and prognosis of patients. Our study was limited in tracking clinical course, so there is still a need for future studies to determine the utility of our model predictive capabilities among patient populations, as well as exploring additional fluid models that may better describe the disease. Regardless, this work highlights the important need for integrated experimental and computational approaches and the potential utility of model-based indicators to better understand and treat disease. This approach, combined with growing biological characterization modalities, could provide an improved clinical framework to better understand and treat a patient’s disease.

Author Contributions

Designed research, performed research, analyzed data, wrote the manuscript: M.S.B.; designed research, performed research, analyzed data, wrote the manuscript: J.M.V.; designed research, wrote the manuscript: V.H.B.; designed research, wrote the manuscript: D.K.W.

Editor: Guy Genin.