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

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.

Characterization of ENU-induced mutations in red blood cell structural proteins

Murine models with modified gene function as a result of N-ethyl-N-nitrosourea (ENU) mutagenesis have been used to study phenotypes resulting from genetic change. This study investigated genetic factors associated with red blood cell (RBC) physiology and structural integrity that may impact on blood component storage and transfusion outcome. Forward and reverse genetic approaches were employed with pedigrees of ENU-treated mice using a homozygous recessive breeding strategy. In a “forward genetic” approach, pedigree selection was based upon identification of an altered phenotype followed by exome sequencing to identify a causative mutation. In a second strategy, a “reverse genetic” approach based on selection of pedigrees with mutations in genes of interest was utilised and, following breeding to homozygosity, phenotype assessed. Thirty-three pedigrees were screened by the forward genetic approach. One pedigree demonstrated reticulocytosis, microcytic anaemia and thrombocytosis. Exome sequencing revealed a novel single nucleotide variation (SNV) in Ank1 encoding the RBC structural protein ankyrin-1 and the pedigree was designated Ank1EX34. The reticulocytosis and microcytic anaemia observed in the Ank1EX34 pedigree were similar to clinical features of hereditary spherocytosis in humans. For the reverse genetic approach three pedigrees with different point mutations in Spnb1 encoding RBC protein spectrin-1β, and one pedigree with a mutation in Epb4.1, encoding band 4.1 were selected for study. When bred to homozygosity two of the spectrin-1β pedigrees (a, b) demonstrated increased RBC count, haemoglobin (Hb) and haematocrit (HCT). The third Spnb1 mutation (spectrin-1β c) and mutation in Epb4.1 (band 4.1) did not significantly affect the haematological phenotype, despite these two mutations having a PolyPhen score predicting the mutation may be damaging. Exome sequencing allows rapid identification of causative mutations and development of databases of mutations predicted to be disruptive. These tools require further refinement but provide new approaches to the study of genetically defined changes that may impact on blood component storage and transfusion outcome.

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 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 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.

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.

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

Bridging the biology of the ovine TRALI model – human inflammatory cell responses to TRALI inducing supernatants

Background Transfusion-related acute lung injury (TRALI) is a serious and potentially fatal consequence of transfusion. A two-event TRALI model demonstrated date-of-expiry - day (D) 5 platelet (PLT) and D42 packed red blood cell (PRBC) supernatants (SN) induced TRALI in LPS-treated sheep. We have adapted a whole blood transfusion culture model as an investigative bridge between the ovine TRALI model human responses to transfusion. Methods A whole blood transfusion model was adapted to replicate the ovine model - specifically +/- 0.23μg/mL LPS as the first event and 10% SN volume (transfusion) as the second event. Four pooled SN from blood products, previously used in the TRALI ovine model, were investigated: D1-PLT, D5-PLT, D1-PRBC, and D42-PRBC. Fresh human whole blood (recipient) was mixed with combinations of LPS and BP-SN stimuli and incubated in vitro for 6 hrs. Addition of golgi plug enabled measurement of monocyte cytokine production (IL-6, IL-8, IL-10, IL-12, TNF-α, IL-1α, CXCL-5, IP-10, MIP-1α, MCP-1) using multi-colour flow cytometry. Responses for 6 recipients were assessed. Results In the presence of LPS, D42-PRBC-SN significantly increased monocyte IL-6 (P=0.031), IL-8 (P=0.016) and IL-1α (P=0.008) production compared to D1-PRBC-SN. This response to D42-PRBC-SN was LPS-dependent, and was not evident in non-LPSstimulated controls. This response was also specific to D42-PRBC-SN, as similar changes were not evident for the D5-PLT-SN, compared to the D1-PLT-SN, regardless of the presence of LPS. D5-PLT-SN significantly increased IL-12 production (P=0.024) compared to D1-PLT-SN. This response was again LPS-dependent. Conclusions These data demonstrate a novel two-event mechanism of monocyte inflammatory response that was dependent upon both the presence of date-of-expiry blood product SN and LPS. Further, these results demonstrate different cytokines responses induced by date-of-expiry PLT-SN and PRBC-SN. These data are consistent with the evidence from the ovine TRALI model, and enhancing its relevance to transfusion related changes in humans.

A comprehensive ovine model of blood transfusion

Background The growing awareness of transfusion-associated morbidity and mortality necessitates investigations into the underlying mechanisms. Small animals have been the dominant transfusion model but have associated limitations. This study aimed to develop a comprehensive large animal (ovine) model of transfusion encompassing: blood collection, processing and storage, compatibility testing right through to post-transfusion outcomes. Materials and methods Two units of blood were collected from each of 12 adult male Merino sheep and processed into 24 ovine-packed red blood cell (PRBC) units. Baseline haematological parameters of ovine blood and PRBC cells were analysed. Biochemical changes in ovine PRBCs were characterized during the 42-day storage period. Immunological compatibility of the blood was confirmed with sera from potential recipient sheep, using a saline and albumin agglutination cross-match. Following confirmation of compatibility, each recipient sheep (n = 12) was transfused with two units of ovine PRBC. Results Procedures for collecting, processing, cross-matching and transfusing ovine blood were established. Although ovine red blood cells are smaller and higher in number, their mean cell haemoglobin concentration is similar to human red blood cells. Ovine PRBC showed improved storage properties in saline–adenine–glucose–mannitol (SAG-M) compared with previous human PRBC studies. Seventy-six compatibility tests were performed and 17·1% were incompatible. Only cross-match compatible ovine PRBC were transfused and no adverse reactions were observed. Conclusion These findings demonstrate the utility of the ovine model for future blood transfusion studies and highlight the importance of compatibility testing in animal models involving homologous transfusions.

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.