Numerical simulation of red blood cells' deformation using SPH method

A numerical simulation method for the Red Blood Cells’ (RBC) deformation is presented in this study. The two-dimensional RBC membrane is modeled by the spring network, where the elastic stretch/compression energy and the bending energy are considered with the constraint of constant RBC surface area. Smoothed Particle Hydrodynamics (SPH) method is used to solve the Navier-Stokes equation coupled with the Plasma-RBC membrane and Cytoplasm- RBC membrane interaction. To verify the method, the motion of a single RBC is simulated in Poiseuille flow and compared with the results reported earlier. Typical motion and deformation mechanism of the RBC is observed.

Numerical simulation of red blood cells’ motion : a review

The micro-circulation of blood plays an important role in human body by providing oxygen and nutrients to the cells and removing carbon dioxide and wastes from the cells. This process is greatly affected by the rheological properties of the Red Blood Cells (RBCs). Changes in the rheological properties of the RBCs are caused by certain human diseases such as malaria and sickle cell diseases. Therefore it is important to understand the motion and deformation mechanism of RBCs in order to diagnose and treat this kind of diseases. Although, many methods have been developed to explore the behavior of the RBCs in micro-channels, they could not explain the deformation mechanism of the RBCs properly. Recently developed Particle Methods are employed to explain the RBCs’ behavior in micro-channels more comprehensively. The main objective of this study is to critically analyze the present methods, used to model the RBC behavior in micro-channels, in order to develop a computationally efficient particle based model to describe the complete behavior of the RBCs in micro-channels accurately and comprehensively

Packed red blood cells suppress myeloid dendritic cell and monocyte inflammatory responses in a whole blood model of transfusion

Purpose/Objective: The basis for poor outcomes in some patients post transfusion remains largely unknown. Despite leukodepletion, there is still evidence of immunomodulatory effects of transfusion that require further study. In addition, there is evidence that the age of blood components transfused significantly affects patient outcomes. Myeloid dendritic cell (DC) and monocyte immune function were studied utilising an in vitro whole blood model of transfusion. Materials and methods: Freshly collected (‘recipient’) whole blood was cultured with ABO compatible leukodepleted PRBC at 25% blood replacement-volume (6hrs). PRBC were assayed at [Day (D) 2, 14, 28and 42 (date-of expiry)]. In parallel, LPS or Zymosan (Zy) were added to mimic infection. Recipients were maintained for the duration of the time course (2 recipients, 4 PRBC units, n = 8).Recipient DC and monocyte intracellular cytokines and chemokines (IL-6, IL-10, IL-12,TNF-a, IL-1a, IL-8, IP-10, MIP-1a, MIP-1b, MCP-1) were measured using flow cytometry. Changes in immune response were calculated by comparison to a parallel no transfusion control (Wilcoxin matched pairs). Influence of storage age was calculated using ANOVA. Results: Significant suppression of DC and monocyte inflammatory responses were evident. DC and monocyte production of IL-1a was reduced following exposure to PRBC regardless of storage age (P < 0.05 at all time points). Storage independent PRBC mediated suppression of DC and monocyte IL-1a was also evident in cultures costimulated with Zy. In cultures co-stimulated with either LPS or Zy, significant suppression of DC and monocyte TNF-a and IL-6 was also evident. PRBC storage attenuated monocyte TNF-a production when co-cultured with LPS (P < 0.01 ANOVA). DC and monocyte production of MIP-1a was significantly reduced following exposure to PRBC (DC: P < 0.05 at D2, 28, 42; Monocyte P < 0.05 all time points). In cultures co-stimulated with LPS and zymosan, a similar suppression of MIP-1a production was also evident, and production of both DC and monocyte MIP-1b and IP-10 were also significantly reduced. Conclusions: The complexity of the transfusion context was reflected in the whole blood approach utilised. Significant suppression of these key DC and monocyte immune responses may contribute to patient outcomes, such as increased risk of infection and longer hospital stay, following blood transfusion.

A coupled SPH-DEM approach to model the interactions between multiple red blood cells in motion in capillaries

Red blood cells (RBCs) are the most common type of blood cells in the blood and 99% of the blood cells are RBCs. During the circulation of blood in the cardiovascular network, RBCs squeeze through the tiny blood vessels (capillaries). They exhibit various types of motions and deformed shapes, when flowing through these capillaries with diameters varying between 5 10 µm. RBCs occupy about 45 % of the whole blood volume and the interaction between the RBCs directly influences on the motion and the deformation of the RBCs. However, most of the previous numerical studies have explored the motion and deformation of a single RBC when the interaction between RBCs has been neglected. In this study, motion and deformation of two 2D (two-dimensional) RBCs in capillaries are comprehensively explored using a coupled smoothed particle hydrodynamics (SPH) and discrete element method (DEM) model. In order to clearly model the interactions between RBCs, only two RBCs are considered in this study even though blood with RBCs is continuously flowing through the blood vessels. A spring network based on the DEM is employed to model the viscoelastic membrane of the RBC while the inside and outside fluid of RBC is modelled by SPH. The effect of the initial distance between two RBCs, membrane bending stiffness (Kb) of one RBC and undeformed diameter of one RBC on the motion and deformation of both RBCs in a uniform capillary is studied. Finally, the deformation behavior of two RBCs in a stenosed capillary is also examined. Simulation results reveal that the interaction between RBCs has significant influence on their motion and deformation.

Numerical modelling of deformation behaviour of red blood cells in microvessels using the coupled SPH-DEM method

This thesis developed an advanced computational model to investigate the motion and deformation properties of red blood cells in capillaries. The novel model is based on the meshfree particle methods and is capable of modelling the large deformation of red blood cells moving through blood vessels. The developed model was employed to simulate the deformation behaviour of healthy and malaria infected red blood cells as well as the motion of red blood cells in stenosed capillaries.

The effect of red blood cell orientation on the electrical impedance of pulsatile blood with implications for impedance cardiography

Impedance cardiography is an application of bioimpedance analysis primarily used in a research setting to determine cardiac output. It is a non invasive technique that measures the change in the impedance of the thorax which is attributed to the ejection of a volume of blood from the heart. The cardiac output is calculated from the measured impedance using the parallel conductor theory and a constant value for the resistivity of blood. However, the resistivity of blood has been shown to be velocity dependent due to changes in the orientation of red blood cells induced by changing shear forces during flow. The overall goal of this thesis was to study the effect that flow deviations have on the electrical impedance of blood, both experimentally and theoretically, and to apply the results to a clinical setting. The resistivity of stationary blood is isotropic as the red blood cells are randomly orientated due to Brownian motion. In the case of blood flowing through rigid tubes, the resistivity is anisotropic due to the biconcave discoidal shape and orientation of the cells. The generation of shear forces across the width of the tube during flow causes the cells to align with the minimal cross sectional area facing the direction of flow. This is in order to minimise the shear stress experienced by the cells. This in turn results in a larger cross sectional area of plasma and a reduction in the resistivity of the blood as the flow increases. Understanding the contribution of this effect on the thoracic impedance change is a vital step in achieving clinical acceptance of impedance cardiography. Published literature investigates the resistivity variations for constant blood flow. In this case, the shear forces are constant and the impedance remains constant during flow at a magnitude which is less than that for stationary blood. The research presented in this thesis, however, investigates the variations in resistivity of blood during pulsataile flow through rigid tubes and the relationship between impedance, velocity and acceleration. Using rigid tubes isolates the impedance change to variations associated with changes in cell orientation only. The implications of red blood cell orientation changes for clinical impedance cardiography were also explored. This was achieved through measurement and analysis of the experimental impedance of pulsatile blood flowing through rigid tubes in a mock circulatory system. A novel theoretical model including cell orientation dynamics was developed for the impedance of pulsatile blood through rigid tubes. The impedance of flowing blood was theoretically calculated using analytical methods for flow through straight tubes and the numerical Lattice Boltzmann method for flow through complex geometries such as aortic valve stenosis. The result of the analytical theoretical model was compared to the experimental impedance measurements through rigid tubes. The impedance calculated for flow through a stenosis using the Lattice Boltzmann method provides results for comparison with impedance cardiography measurements collected as part of a pilot clinical trial to assess the suitability of using bioimpedance techniques to assess the presence of aortic stenosis. The experimental and theoretical impedance of blood was shown to inversely follow the blood velocity during pulsatile flow with a correlation of -0.72 and -0.74 respectively. The results for both the experimental and theoretical investigations demonstrate that the acceleration of the blood is an important factor in determining the impedance, in addition to the velocity. During acceleration, the relationship between impedance and velocity is linear (r2 = 0.98, experimental and r2 = 0.94, theoretical). The relationship between the impedance and velocity during the deceleration phase is characterised by a time decay constant, ô , ranging from 10 to 50 s. The high level of agreement between the experimental and theoretically modelled impedance demonstrates the accuracy of the model developed here. An increase in the haematocrit of the blood resulted in an increase in the magnitude of the impedance change due to changes in the orientation of red blood cells. The time decay constant was shown to decrease linearly with the haematocrit for both experimental and theoretical results, although the slope of this decrease was larger in the experimental case. The radius of the tube influences the experimental and theoretical impedance given the same velocity of flow. However, when the velocity was divided by the radius of the tube (labelled the reduced average velocity) the impedance response was the same for two experimental tubes with equivalent reduced average velocity but with different radii. The temperature of the blood was also shown to affect the impedance with the impedance decreasing as the temperature increased. These results are the first published for the impedance of pulsatile blood. The experimental impedance change measured orthogonal to the direction of flow is in the opposite direction to that measured in the direction of flow. These results indicate that the impedance of blood flowing through rigid cylindrical tubes is axisymmetric along the radius. This has not previously been verified experimentally. Time frequency analysis of the experimental results demonstrated that the measured impedance contains the same frequency components occuring at the same time point in the cycle as the velocity signal contains. This suggests that the impedance contains many of the fluctuations of the velocity signal. Application of a theoretical steady flow model to pulsatile flow presented here has verified that the steady flow model is not adequate in calculating the impedance of pulsatile blood flow. The success of the new theoretical model over the steady flow model demonstrates that the velocity profile is important in determining the impedance of pulsatile blood. The clinical application of the impedance of blood flow through a stenosis was theoretically modelled using the Lattice Boltzman method (LBM) for fluid flow through complex geometeries. The impedance of blood exiting a narrow orifice was calculated for varying degrees of stenosis. Clincial impedance cardiography measurements were also recorded for both aortic valvular stenosis patients (n = 4) and control subjects (n = 4) with structurally normal hearts. This pilot trial was used to corroborate the results of the LBM. Results from both investigations showed that the decay time constant for impedance has potential in the assessment of aortic valve stenosis. In the theoretically modelled case (LBM results), the decay time constant increased with an increase in the degree of stenosis. The clinical results also showed a statistically significant difference in time decay constant between control and test subjects (P = 0.03). The time decay constant calculated for test subjects (ô = 180 - 250 s) is consistently larger than that determined for control subjects (ô = 50 - 130 s). This difference is thought to be due to difference in the orientation response of the cells as blood flows through the stenosis. Such a non-invasive technique using the time decay constant for screening of aortic stenosis provides additional information to that currently given by impedance cardiography techniques and improves the value of the device to practitioners. However, the results still need to be verified in a larger study. While impedance cardiography has not been widely adopted clinically, it is research such as this that will enable future acceptance of the method.

Deformation properties of single red blood cell in a stenosed microchannel

Red Blood Cells (RBCs) exhibit different types of motions and different deformed shapes, when they move through capillaries. RBCs can travel through capillaries having smaller diameters than RBCs’ diameter, due to the capacity of high deformability of the viscoelastic RBC membrane. The motion and the steady state shape of the RBCs depend on many factors, such as the geometrical parameters of the microvessel through which blood flows, the RBC membrane bending stiffness and the flow velocity. In this study, the effect of the RBC’s membrane stiffness on the deformation of a single RBC in a stenosed capillary is comprehensively examined. Smoothed Particle Hydrodynamics (SPH) in combination with the two-dimensional spring network membrane model is used to investigate the motion and the deformation property of the RBC. The simulation results demonstrate that the membrane bending stiffness of the RBC has a significant impact on the RBCs’ deformability.

Deformation of a three-dimensional red blood cell in a stenosed micro-capillary

Red blood cells (RBCs) exhibit different types of motions and deformations when the blood flows through capillaries. Interestingly, due to the complex three-dimensional structure of the RBC membrane, RBCs show three-dimensional motions and deformations in the blood flow. These motions and deformations of the RBCs highly depend on the stiffness of the RBC membrane and on the geometrical parameters of the capillary through which blood flows. However, capillaries always do not have uniform cross sections and some capillaries have stenosed segments, where cross sectional area suddenly reduces. Further, some diseases can alter the stiffness of the RBC membrane drastically. In this study, the deformation behaviour of a single three-dimensional RBC is examined, when it moves through a stenosed capillary. A three-dimensional spring network is used to model the RBC membrane. The RBC’s inside and outside fluids are discretized into a finite number of mass points and treated by smoothed particle hydrodynamics (SPH) method. The capillary is considered as a rigid tube with a stenosed section. The deformation index, mean velocity and total energy of the RBC are analysed when it flows through the stenosed capillary. Further, motion and deformation of the RBCs with different membrane stiffness (KB) are compared when they flow through the stenosed segment of the capillary. The simulation results demonstrate the RBCs are subjected to a larger deformation when they move through the stenosed part of the capillary and the RBCs with lower KBvalues easily pass through the stenosed segment of the capillary. Further, RBCs having higher KBvalues have a lower mean velocity and it leads to slow down the overall blood flow rate

Deformation of a single red blood cell in a microvessel

Red blood cells (RBCs) are the most common type of cells in human blood and they exhibit different types of motions and deformed shapes in capillary flows. The behaviour of the RBCs should be studied in order to explain the RBC motion and deformation mechanism. This article presents a numerical simulation method for RBC deformation in microvessels. A two dimensional spring network model is used to represent the RBC membrane, where the elastic stretch/compression energy and the bending energy are considered with the constraint of constant RBC surface area. The forces acting on the RBC membrane are obtained from the principle of virtual work. The whole fluid domain is discretized into a finite number of particles using smoothed particle hydrodynamics concepts and the motions of all the particles are solved using Navier--Stokes equations. Minimum energy concepts are used to simulate the deformed shape of the RBC model. To verify the model, the motion of a single RBC is simulated in a Poiseuille flow and the characteristic parachute shape of the RBC is observed. Further simulations reveal that the RBC shows a tank treading motion when it flows in a linear shear flow.

Formation of the three-dimensional geometry of the red blood cell membrane

Red blood cells (RBCs) are nonnucleated liquid capsules, enclosed in deformable viscoelastic membranes with complex three dimensional geometrical structures. Generally, RBC membranes are highly incompressible and resistant to areal changes. However, RBC membranes show a planar shear deformation and out of plane bending deformation. The behaviour of RBCs in blood vessels is investigated using numerical models. All the characteristics of RBC membranes should be addressed to develop a more accurate and stable model. This article presents an effective methodology to model the three dimensional geometry of the RBC membrane with the aid of commercial software COMSOL Multiphysics 4.2a and Fortran programming. Initially, a mesh is generated for a sphere using the COMSOL Multiphysics software to represent the RBC membrane. The elastic energy of the membrane is considered to determine a stable membrane shape. Then, the actual biconcave shape of the membrane is obtained based on the principle of virtual work, when the total energy is minimised. The geometry of the RBC membrane could be used with meshfree particle methods to simulate motion and deformation of RBCs in micro-capillaries

Numerical investigation of motion and deformation of a single red blood cell in a stenosed capillary

It is generally assumed that influence of the red blood cells (RBCs) is predominant in blood rheology. The healthy RBCs are highly deformable and can thus easily squeeze through the smallest capillaries having internal diameter less than their characteristic size. On the other hand, RBCs infected by malaria or other diseases are stiffer and so less deformable. Thus it is harder for them to flow through the smallest capillaries. Therefore, it is very important to critically and realistically investigate the mechanical behavior of both healthy and infected RBCs which is a current gap in knowledge. The motion and the steady state deformed shape of the RBCs depend on many factors, such as the geometrical parameters of the capillary through which blood flows, the membrane bending stiffness and the mean velocity of the blood flow. In this study, motion and deformation of a single two-dimensional RBC in a stenosed capillary is explored by using smoothed particle hydrodynamics (SPH) method. An elastic spring network is used to model the RBC membrane, while the RBC's inside fluid and outside fluid are treated as SPH particles. The effect of RBC's membrane stiffness (kb), inlet pressure (P) and geometrical parameters of the capillary on the motion and deformation of the RBC is studied. The deformation index, RBC's mean velocity and the cell membrane energy are analyzed when the cell passes through the stenosed capillary. The simulation results demonstrate that the kb, P and the geometrical parameters of the capillary have a significant impact on the RBCs' motion and deformation in the stenosed section.

Neutrophil oxidative burst is primed by supernatant from stored red cells : implications for Transfusion-Related Acute Lung Injury (TRALI)

Aim/Background: Transfusion-related acute lung injury (TRALI) is a potentially fatal adverse transfusion reaction. It is hypothesised to occur via a two-insult mechanism: the recipient’s underlying co-morbidity in addition to the transfusion of blood products activate neutrophils in the lung resulting in damaged endothelium and capillary leakage. Neutrophil activation may occur by antibody or non-antibody related mechanisms, with the length of storage of cellular blood products implicated in the latter. This study investigated non-antibody mediated priming and/or activation of neutrophil oxidative burst. Methods: A cytochrome C reduction assay was used to assess priming and activation of neutrophil oxidative burst by pooled supernatant (SN) from day 1 (D1; n=75) and day 42 (D42; n=113) packed red blood cells (PRBC). Pooled PRBC-SN were assessed in parallel with PAF (priming), fMLP (activating), PAF + fMLP (priming + activating) and buffer only (negative) controls. Cytochrome C reduction was measured over 30min at 37oC (inclusive of 10min priming). Neutrophil activation by PRBC-SN was assessed cf. buffer only and neutrophil priming by PRBC-SN was assessed by co-incubation with fMLP cf. fMLP alone. One-way ANOVA; Newman-Keuls post-test; p<0.05; n=10 independent assays. Results: Neither D1- nor D42- PRBC-SN alone activated neutrophil oxidative burst. In addition, D1-PRBC-SN did not prime fMLP-activated neutrophil oxidative burst. D42-PRBC-SN did, however, prime neutrophils for subsequent activation of oxidative burst by fMLP, the magnitude of response being similar to PAF (a known neutrophil priming agonist). Conclusion: These findings are consistent with the two-insult mechanism of TRALI. Factors released into the SN during PRBC storage contributed to neutrophil priming synergistically with other neutrophil stimulating agonists. This implicates PRBC storage duration as a key factor contributing to non-immune neutrophil activation in the development of TRALI in patients with pre-disposing inflammatory conditions.

Age of blood and recipient factors determine the severity of transfusion-related acute lung injury (TRALI)

Introduction Critical care patients frequently receive blood transfusions. Some reports show an association between aged or stored blood and increased morbidity and mortality, including the development of transfusion-related acute lung injury (TRALI). However, the existence of conflicting data endorses the need for research to either reject this association, or to confirm it and elucidate the underlying mechanisms. Methods Twenty-eight sheep were randomised into two groups, receiving saline or lipopolysaccharide (LPS). Sheep were further randomised to also receive transfusion of pooled and heat-inactivated supernatant from fresh (Day 1) or stored (Day 42) non-leucoreduced human packed red blood cells (PRBC) or an infusion of saline. TRALI was defined by hypoxaemia during or within two hours of transfusion and histological evidence of pulmonary oedema. Regression modelling compared physiology between groups, and to a previous study, using stored platelet concentrates (PLT). Samples of the transfused blood products also underwent cytokine array and biochemical analyses, and their neutrophil priming ability was measured in vitro. Results TRALI did not develop in sheep that first received saline-infusion. In contrast, 80% of sheep that first received LPS-infusion developed TRALI following transfusion with "stored PRBC." The decreased mean arterial pressure and cardiac output as well as increased central venous pressure and body temperature were more severe for TRALI induced by "stored PRBC" than by "stored PLT." Storage-related accumulation of several factors was demonstrated in both "stored PRBC" and "stored PLT", and was associated with increased in vitro neutrophil priming. Concentrations of several factors were higher in the "stored PRBC" than in the "stored PLT," however, there was no difference to neutrophil priming in vitro. Conclusions In this in vivo ovine model, both recipient and blood product factors contributed to the development of TRALI. Sick (LPS infused) sheep rather than healthy (saline infused) sheep predominantly developed TRALI when transfused with supernatant from stored but not fresh PRBC. "Stored PRBC" induced a more severe injury than "stored PLT" and had a different storage lesion profile, suggesting that these outcomes may be associated with storage lesion factors unique to each blood product type. Therefore, the transfusion of fresh rather than stored PRBC may minimise the risk of TRALI.

Shorter telomere length in peripheral blood cells associated with migraine in women

Objective To evaluate relative telomere length of female migraine patients. Background Migraine is a debilitating disorder affecting 6-28% of the population. Studies on the mechanisms of migraine have demonstrated genetic causes but the pathophysiology and subcellular effects of the disease remain poorly understood. Shortened telomere length is associated with age-related or chronic diseases, and induced stresses. Migraine attacks may impart significant stress on cellular function, thus this study investigates a correlation between shortening of telomeres and migraine. Methods Relative telomere length was measured using a previously described quantitative polymerase chain reaction method. A regression analysis was performed to assess differences in mean relative telomere length between migraine patients and healthy controls. Results The leukocyte telomeres of a cohort of 142 Caucasian female migraine subjects aged 18-77 years and 143 matched 17-77-year-old healthy control Caucasian women were examined.A significantly shorter relative telomere length was observed in the migraine group compared with the control group after adjusting for age and body mass index (P = .001). In addition, age of onset was observed to associate with the loss of relative telomere length, especially at early age of onset (<17 years old). No association was observed between relative telomere length and the severity and frequency of migraine attacks and the duration of migraine. Conclusion Telomeres are shorter in migraine patients and there is more variation in telomere length in migraine patients.

Stored blood products augment inflammation in a two-event model of Transfusion Related Acute Lung Injury (TRALI)

Aim/Background TRALI is hypothesised to develop via a two-event mechanism involving both the patieint's underlying morbidity and blood product factors. The storage of cellular products has been implicated in cases of non-antibody mediated TRALI, however the pathophysiological mechanisms are undefined. We investigated blood product storage-related modulation of inflmmatory cells and medicators involved in TRALI. Methods In an in vitro mode, fresh human whole blood was mixed with culture media (control) or LPS as a 1st event and "transfused" with 10% (v/v) pooled supernatant (SN) from Day 1 (d1, n=75) or Day 42 (D42, n=113) packed red blood cells (PRBCs) as a 2nd event. Following 6hrs, culture SN was used to assess the overall inflammatory response (cytometric bead array) and a duplicate assay containing protein transport inhibitor was used to assess neutrophil- and monocyte-specific inflmamatory responses using multi-colour flow cytometry. Panels: IL-6, IL-8, IL-10, IL-12, IL-1, TNF, MCP-1, IP-10, MIP-1. One-way ANOVA 95% CI. Results In the absence of LPS, exposure to D1 or D42 PRBC-SN reduced monocyte expression of IL-6, IL-8 and Il-10. D42 PRBC-SN also reduced monocyte IP-10, and the overall IL-8 production was increased. In the presence of LPS, D1-PRBC SN only modified overall IP-10 levels which were reduced. However, cf LPS alone, the combination of LPS and D42 PRBC-SN resulted in increased neutrophil and monocyte productionof IL-1 and IL-8 as well as reduced monocyte TNF production. Additionally, LPS and D42 PRBC-SN resulted in overall inflmmatory changes: elevated IL-8,