In silico biophysics and hemorheology of blood hyperviscosity syndrome

Analysis of the Suitability of an Effective Viscosity to Represent Interactions Between Red Blood Cells in Shear Flow

Many methods to computationally predict red blood cell damage have been introduced, and among these are Lagrangian methods that track the cells along their pathlines. Such methods typically do not explicitly include cell-cell interactions. Due to the high volume fraction of red blood cells (RBCs) in blood, these interactions could impact cell mechanics and thus the amount of damage caused by the flow. To investigate this question, cell-resolved simulations of red blood cells in shear flow were performed for multiple interacting cells, as well as for single cells in unbounded flow at an effective viscosity. Simulations run without adjusting the bulk viscosity produced larger errors unilaterally and were not considered further for comparison. We show that a periodic box containing at least 8 cells and a spherical harmonic of degree larger than 10 are necessary to produce converged higher-order statistics. The maximum difference between the single-cell and multiple-cell cases in terms of peak strain was 3.7%. To achieve this, one must use the whole blood viscosity and average over multiple cell orientations when adopting a single-cell simulation approach. The differences between the models in terms of average strain were slightly larger (maximum difference of 6.9%). However, given the accuracy of the single-cell approach in predicting the maximum strain, which is useful in hemolysis prediction, and its computational cost that is orders of magnitude less than the multiple-cell approach, one may use it as an affordable cell-resolved approach for hemolysis prediction.

In silico modeling of patient-specific blood rheology in type 2 diabetes mellitus

Increased blood viscosity in type 2 diabetes mellitus (T2DM) is a risk factor for the development of insulin resistance and diabetes-related vascular complications; however, individuals with T2DM exhibit heterogeneous hemorheological properties, including cell deformation and aggregation. Using a multiscale red blood cell (RBC) model with key parameters derived from patient-specific data, we present a computational study of the rheological properties of blood from individual patients with T2DM. Specifically, one key model parameter, which determines the shear stiffness of the RBC membrane (μ) is informed by the high-shear-rate blood viscosity of patients with T2DM. At the same time, the other, which contributes to the strength of the RBC aggregation interaction (D0), is derived from the low-shear-rate blood viscosity of patients with T2DM. The T2DM RBC suspensions are simulated at different shear rates, and the predicted blood viscosity is compared with clinical laboratory-measured data. The results show that the blood viscosity obtained from clinical laboratories and computational simulations are in agreement at both low and high shear rates. These quantitative simulation results demonstrate that the patient-specific model has truly learned the rheological behavior of T2DM blood by unifying the mechanical and aggregation factors of the RBCs, which provides an effective way to extract quantitative predictions of the rheological properties of the blood of individual patients with T2DM.

Axial shear rate: A hemorheological factor for erythrocyte aggregation under Womersley flow in an elastic vessel based on numerical simulation

Erythrocyte aggregation (EA) is a highly dynamic, vital phenomenon to interpreting human hemorheology, which would be helpful for the diagnosis and prediction of circulatory anomalies. Previous studies of EA on erythrocyte migration and the Fåhraeus Effect are based on the microvasculature. They have not considered the natural pulsatility of the blood flow or large vessels and mainly focused on shear rate along radial direction under steady flow to comprehend the dynamic properties of EA. To our knowledge, the rheological characteristics of non-Newtonian fluids under Womersley flow have not reflected the spatiotemporal behaviors of EA or the distribution of erythrocyte dynamics (ED). Hence, it needs to interpret the ED affected by temporal and spatial flow variation to understand the effect of EA under Womersley flow. Here, we demonstrated the numerically simulated ED to decipher EA's rheological role in axial shear rate under Womersley flow. In the present study, the temporal and spatial variations of the local EA were found to mainly depend on the axial shear rate under Womersley flow in an elastic vessel, while mean EA decreased with radial shear rate. The localized distribution of parabolic or M-shape clustered EA was found in a range of the axial shear rate profile (-15 to 15s^-1) at low radial shear rates during a pulsatile cycle. However, the linear formation of rouleaux was realized without local clusters in a rigid wall where the axial shear rate is zero. In vivo, the axial shear rate is usually considered insignificant, especially in straight arteries, but it has a great impact on the disturbed blood flow due to the geometrical properties, such as bifurcations, stenosis, aneurysm, and the cyclic variation of pressure. Our findings regarding axial shear rate provide new insight into the local dynamic distribution of EA, which is a critical player in blood viscosity. These will provide a basis for the computer-aided diagnosis of hemodynamic-based cardiovascular diseases by decreasing the uncertainty in the pulsatile flow calculation.

Circulating cell clusters aggravate the hemorheological abnormalities in COVID-19

Microthrombi and circulating cell clusters (CCCs) are common microscopic findings in patients with COVID-19 at different stages in the disease course, implying that they may function as the primary drivers in disease progression. Inspired by a recent flow imaging cytometry study of the blood samples from patients with COVID-19, we perform computational simulations to investigate the dynamics of different types of CCCs, namely white blood cell (WBC) clusters, platelet clusters and red blood cell (RBC) clusters, over a range of shear flows and quantify their impact on the viscosity of the blood. Our simulation results indicate that the increased level of fibrinogen in patients with COVID-19 can promote the formation of RBC clusters at relatively low shear rates, thereby elevating the blood viscosity, a mechanism that also leads to an increase in viscosity in other blood diseases, such as sickle cell disease and type 2 diabetes mellitus. We further discover that the presence of WBC clusters could also aggravate the abnormalities of local blood rheology. In particular, the extent of elevation of the local blood viscosity is enlarged as the size of the WBC clusters grows. On the other hand, the impact of platelet clusters on the local rheology is found to be negligible, which is likely due to the smaller size of the platelets. The difference in the impact of WBC and platelet clusters on local hemorheology provides a compelling explanation for the clinical finding that the number of WBC clusters is significantly correlated with thrombotic events in COVID-19 whereas platelet clusters do not. Overall, our study demonstrates that our computational models based on dissipative particle dynamics can serve as a powerful tool to conduct quantitative investigation of the mechanism causing the pathological alterations of hemorheology and explore their connections to the clinical manifestations in COVID-19.

The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.

Recent advances in blood rheology: a review

Due to the potential impact on the diagnosis and treatment of various cardiovascular diseases, work on the rheology of blood has significantly expanded in the last decade, both experimentally and theoretically. Experimentally, blood has been confirmed to demonstrate a variety of non-Newtonian rheological characteristics, including pseudoplasticity, viscoelasticity, and thixotropy. New rheological experiments and the development of more controlled experimental protocols on more extensive, broadly physiologically characterized, human blood samples demonstrate the sensitivity of aspects of hemorheology to several physiological factors. For example, at high shear rates the red blood cells elastically deform, imparting viscoelasticity, while at low shear rates, they form "rouleaux" structures that impart additional, thixotropic behavior. In addition to the advances in experimental methods and validated data sets, significant advances have also been made in both microscopic simulations and macroscopic, continuum, modeling, as well as novel, multiscale approaches. We outline and evaluate the most promising of these recent developments. Although we primarily focus on human blood rheology, we also discuss recent observations on variations observed across some animal species that provide some indication on evolutionary effects.

Correction: Hemorheology: the critical role of flow type in blood viscosity measurements

Correction for 'Hemorheology: the critical role of flow type in blood viscosity measurements' by Elahe Javadi et al., Soft Matter, 2021, 17, 8446-8458, DOI: 10.1039/D1SM00856K.