An investigation on the rheodynamics of human red blood cells using high performance computations

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Studies on the haemodynamics of human circulation are clinically and scientifically important. The flow of human blood is extremely complex due to the existence of the highly deformable red blood cells (RBCs), which are able to pass through capillaries smaller than their size. To investigate the effect of deformation and aggregation in blood flow, a computational technique has been developed by coupling the interaction between the fluid and the deformable solids. The flow of 49,512 RBCs at 45% concentration and under the influence of aggregating forces was examined to improve the existing knowledge on how to simulate and study the blood flow and its structural characteristics of blood at a large scale. The simulation was carried out with full parallelization of the coupled fluid-solid code using spatial decomposition and high performance supercomputers. The large scale feature of the simulation has enabled a macroscale verification and investigation of the overall characteristics of RBC aggregations to be carried out. The results are in excellent agreement with experimental studies and, more specifically, both the experimental and the simulation results show uniform RBC distributions under high shear rates (60-100/s) whereas large aggregations were observed under a lower shear rate of 10/s. The statistical analysis of the simulation data also shows that the shear rate has significant influence on both the flow velocity profiles and the frequency distribution of the RBC orientation angles. The flow under the low shear rate also tended to have bi-phasic velocity profile which is mainly due to the formation of large scale aggregation clusters

Evaluation of blood plasma flow around 2D erythrocytes with the use of computational fluid dynamics / Avaliação do escoamento de plasma sanguíneo ao redor de eritrócitos 2D com o uso de fluidodinâmica computacional

 Hemodynamic forces, such as Wall Shear Stress, are known to be one of the factors behind atherosclerotic plaque formation in blood vessels. Such plaque formation may lead to clinical conditions such as aneurysms and stenosis. Given the importance of understanding the hemodynamics inside blood vessels, CFD-based (Computational Fluid Dynamics) tools can be applied with Medical imaging techniques, in order to assist physicians. Although CFD simulations try to simulate cases as close as possible to their real physics, simplifications are often required. Furthermore, blood is usually taken as being a single-phase fluid, despite it being a suspension of blood cells in plasma. This is due to the focus of computational hemodynamics often being the whole blood flow or pathologies within the blood vessel. However, blood cells can account to more than half of the blood volume, depending on the patient. Hence, the present work aimed to study the behavior of plasma, flowing around a single erythrocyte, as well as a cluster of erythrocytes immersed in a 2D domain. In the simulations, parameters such as the Reynolds number and velocity profiles were analyzed. Results showed that erythrocyte geometry had an influence in the velocity profiles. Moreover, Reynolds numbers were considerably low, due to the micro scale utilized in the simulations, which was in accordance with literature. 

The buckling instability of aggregating red blood cells

Plasma proteins such as fibrinogen induce the aggregation of red blood cells (RBC) into rouleaux, which are responsible for the pronounced shear thinning behavior of blood, control the erythro- cyte sedimentation rate (ESR) a common hematological test and are involved in many situations of physiological relevance such as structuration of blood in the microcirculation or clot formation in pathological situations. Confocal microscopy is used to characterize the shape of RBCs within rouleaux at equilibrium as a function of macromolecular concentration, revealing the diversity of contact zone morphology. Three different configurations that have only been partly predicted before are identified, namely parachute, male-female and sigmoid shapes, and quantitatively recovered by numerical simulations. A detailed experimental and theoretical analysis of clusters of two cells shows that the deformation increases nonlinearly with the interaction energy. Models indicate a forward bifurcation in which the contacting membrane undergoes a buckling instability from a flat to a de- formed contact zone at a critical value of the interaction energy. These results are not only relevant for the understanding of the morphology and stability of RBC aggregates, but also for a whole class of interacting soft deformable objects such as vesicles, capsules or cells in tissues.Comment: 22 pages, 12 figure

Early stage of Erythrocyte Sedimentation Rate test: Fracture of a high-volume-fraction gel

Erythrocyte Sedimentation Rate (ESR) is a clinical parameter used as a non-specific marker for inflammation, and recent studies have shown that it is linked to the collapse of the gel formed by red blood cells (RBCs) at physiological hematocrits (i.e. RBC volume fraction). Previous research has suggested that the delay time before the sedimentation process is related to the formation of fractures in the gel. Moreover, RBC gels present specific properties due to the anisotropic shape and flexibility of the RBCs. Namely, the onset of the collapse is reached earlier and the settling velocity of the gel increases with increasing attraction between the RBCs, while gel of spherical particles show the opposite trend. Here, we report experimental observations of the gel structure during this onset and suggest an equation modeling this initial process as fracturing of the gel. We demonstrate that this equation provides a model for the motion of the interface between blood plasma and the RBC gel, along the whole time span. We also observe that the increase in the attraction between the RBCs modifies the density of fractures in the gel, which explains why the gel displays a decrease in delay time when the aggregation energy between the RBCs increases. Our work uncovers the detailed physical mechanism underlying the ESR and provides insights into the fracture dynamics of a RBC gel. These results can improve the accuracy of clinical measurements.Comment: 10 pages, 3 Figure

A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded in $\mathbb{R}^3$, these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions (RBFs) and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at "scattered" locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented

SPH-DEM approach to numerically simulate the deformation of three-dimensional RBCs in non-uniform capillaries

© 2016 The Author(s). Background: Blood continuously flows through the blood vessels in the human body. When blood flows through the smallest blood vessels, red blood cells (RBCs) in the blood exhibit various types of motion and deformed shapes. Computational modelling techniques can be used to successfully predict the behaviour of the RBCs in capillaries. In this study, we report the application of a meshfree particle approach to model and predict the motion and deformation of three-dimensional RBCs in capillaries. Methods: An elastic spring network based on the discrete element method (DEM) is employed to model the three-dimensional RBC membrane. The haemoglobin in the RBC and the plasma in the blood are modelled as smoothed particle hydrodynamics (SPH) particles. For validation purposes, the behaviour of a single RBC in a simple shear flow is examined and compared against experimental results. Then simulations are carried out to predict the behaviour of RBCs in a capillary; (i) the motion of five identical RBCs in a uniform capillary, (ii) the motion of five identical RBCs with different bending stiffness (K b ) values in a stenosed capillary, (iii) the motion of three RBCs in a narrow capillary. Finally five identical RBCs are employed to determine the critical diameter of a stenosed capillary. Results: Validation results showed a good agreement with less than 10% difference. From the above simulations, the following results are obtained; (i) RBCs exhibit different deformation behaviours due to the hydrodynamic interaction between them. (ii) Asymmetrical deformation behaviours of the RBCs are clearly observed when the bending stiffness (K b ) of the RBCs is changed. (iii) The model predicts the ability of the RBCs to squeeze through smaller blood vessels. Finally, from the simulations, the critical diameter of the stenosed section to stop the motion of blood flow is predicted. Conclusions: A three-dimensional spring network model based on DEM in combination with the SPH method is successfully used to model the motion and deformation of RBCs in capillaries. Simulation results reveal that the condition of blood flow stopping depends on the pressure gradient of the capillary and the severity of stenosis of the capillary. In addition, this model is capable of predicting the critical diameter which prevents motion of RBCs for different blood pressures

IMECE2008-67855 STUDY OF WHOLE BLOOD VISCOSITY USING A MICROFLUIDIC DEVICE

ABSTRACT Cardiovascular diseases include a wide range of disorders that affect heart and blood vessels, and are the leading cause of death in the Unite