Theoretical and experimental study of the time dependent flow of red blood cell suspension through narrow pores

The Hemorheometer has been adapted to allow the recording of the flow rate during the filtration process. For newtonian fluids, the flow rate variation versus time through the pores is well approximated by Poiseuille's law. For dilute red blood cell suspensions, the same analysis can be applied by introducing the concept of "apparent filtration viscosity" which is higher than the usual viscosity measured by Couette viscometry. The apparent filtration viscosity parameter is related to the deformations undergone by red blood cells as they pass through the narrow pores. Apparent filtration viscosity can be used to obtain a precise determination of the erythrocyte deformability. Measurements performed, for a given blood sample, with pores of different diameters (5 microns, 8 microns and 12 microns) show that the error on the value of apparent filtration viscosity is less than 3%. As a result, the sensitivity of the filtration method allows to discriminate among normal blood samples. High concentrations of erythrocytes or leucocytes are found to modify the apparent filtration viscosity. These factors are apparent in the recorded filtration curves. Their effects on filtration measurements can be easily estimated.     

Treatment of whole blood (WB) and red blood cells (RBC) with S-303 inactivates pathogens and retains in vitro quality of stored RBC

A pathogen inactivation (PI) process has been developed using the frangible anchor linker effector (FRALE) compound S-303. A series of experiments were performed in whole blood (WB) to measure the level of viral and bacterial inactivation. The results showed that 0.2 mM S-303 and 2 mM glutathione (GSH) inactivated >6.5 logs of HIV, >5.7 logs of Bluetongue virus, >7.0 logs of Yersinia enterocolitica, 4.2 logs of Serratia marcescens, and 7.5 logs of Staphylococcus epidermidis. Recent development for S-303 is focused on optimization of the PI process for red blood cell concentrates (RBC). A series of studies in RBC showed that 0.2 mM S-303 and 20 mM GSH inactivated approximately 5 logs or greater of Y. enterocolitica, E. coli, S. marcescens, S. aureus, HIV, bovine viral diarrhoea virus, bluetongue virus and human adenovirus 5. In both applications of the S-303 process, in vitro parameters of RBC function and physiology were retained compared to conventional RBC. Results from these studies indicate that S-303 can be applicable for PI of RBC and WB.     

Theoretical and experimental analysis of the sedimentation kinetics of concentrated red cell suspensions in a centrifugal field: determination of the aggregation and deformation of RBC by flux density and viscosity functions

The flow properties of blood are mostly determined using various viscometric approaches, and described in terms of a shear rate or shear stress dependent apparent viscosity. The interpretation of results are rather difficult, especially at low shear rates when particle sedimentation and migration within the viscometer gap are significant. By contrast, analysing the separation process in concentrated RBC suspensions in a centrifugal field also yields information about the viscosity function, including particle-particle interaction and deformation parameters. In this paper, the sedimentation process is approached by means of the theory of kinematic waves and theoretically described by solving the corresponding one-dimensional quasi-linear partial differential equation based on viscosity/flow function as a function of volume concentration. The sedimentation kinetics of rigid spherical RBC suspended in saline and normal RBC suspended in Dx-saline solutions were investigated by means of a separation analyser (LUMiFuge 114). The instrument detects the light transmission over the total length of the cell containing the suspension. During centrifugation the analyser automatically determines the position of the particle free fluid/suspension interface or the sediment by means of a special algorithm. The data obtained with sedimentation of rigid spherical RBC at different volume concentrations demonstrate that, in the case of suspensions rotated in containers of constant cross section, there is good agreement between the theory of kinematic waves developed by Anestis and Schneider (1983) and the results of the experiments. Such good agreement was obtained even though a restrictive one-dimensional model was used to obtain the theoretically derived sedimentation time course. In addition, we describe an algorithm enabling the experimental determination of the viscosity and related flux density function to be made for any suspension. Through this approach, we investigated in detail the rheological behavior of suspended rigid spheres at low Reynolds numbers ranging from 10(-6) to 10(-3). The method here introduced also enabled us to investigate RBC suspensions with respect to the deformability and interactions of the cells by means of the separation analysis. Normal, rigid as well as aggregating RBC exhibited marked differences in the sedimentation kinetics, which were quantified by means of the flux and viscosity functions based on the theory of kinematic waves.     

Theory of non-Newtonian viscosity of red blood cell suspension: effect of red cell deformation

The effects of the deformation of red blood cells on non-Newtonian viscosity of a concentrated red cell suspension are investigated theoretically. To simplify the problem an elastic spherical shell filled with an incompressible Newtonian fluid is considered as a model of a normal red cell. The equation of the surface of the shell suspended in a steady simple shear flow is calculated on the assumption that the deformation from a spherical shape is very small. The relative viscosity of a concentrated suspension of such particles is obtained based on the "free surface cell" method proposed by Happel. It is shown that the relative viscosity decreases as the shear rate increases.     

Influence of microflow on hepatic sinusoid blood flow and red blood cell deformation

Hepatic sinusoids present complex anatomical structures such as the endothelial sieve pores and the Disse space, which govern the microscopic blood flow in the sinusoids and are associated with structural variations in liver fibrosis and cirrhosis. However, the contributions of the permeability of endothelial and collagen layers and the roughness of hepatocyte microvilli to the features of this microflow remain largely unknown. Here, an immersed boundary method coupled with a lattice Boltzmann method was adopted in an in vitro hepatic sinusoidal model, and flow field and erythrocyte deformation analyses were conducted by introducing three new source terms including permeability of the endothelial layer, resistance of hepatocyte microvilli and collagen layers, and deformation of red blood cells (RBCs). Numerical calculations indicated that alterations in endothelial permeability could significantly affect the flow velocity and flow rate distributions in hepatic sinusoids. Interestingly, a biphasic regulating pattern of shear stress occurred simultaneously on the surface of hepatocytes and the lower side of endothelium, i.e., the shear stress increased with increased thickness of hepatocyte microvilli and collagen layer when the endothelial permeability was high but decreased with the increase of the thickness at low endothelial permeability. Additionally, this specified microflow manipulates typical RBC deformation inside the sinusoid, yielding one-third of the variation of deformable index with varied endothelial permeability. These simulations not only are consistent with experimental measurements using in vitro liver sinusoidal chip but also elaborate the contributions of endothelial and collagen layer permeability and wall roughness. Thus, our results provide a basis for further characterizing this microflow and understanding its effects on cellular migration and deformation in the hepatic sinusoids.     

Osmotic deformation of red blood cell ghosts induced by carbohydrates

The osmotic response of bovine red blood cell ghosts to a series of sugars is studied by light scattering. The sealed and right-side-out ghosts are prepared by the procedure of Steck and Kant (Steck, T.L. and Kant, J.A. (1974) Methods Enzymol. 31, 172–180), swollen in a hypotonic phosphate-buffered saline solution and their size and shape determined by elastic and quasielastic light scattering. Different carbohydrates are then added to the suspending medium in order to examine the osmotic responses, and the osmotic deformation of ghosts is shown to be spherically symmetric. Having thus established the deformation behavior, we then rank the osmotic activity of a carbohydrate relative to a standard, i.e., raffinose. It is found that the osmotic response of the ghosts to sucrose is about the same as that to raffinose, and the response to the smaller carbohydrates simply follows the number of carbons in various sugars; glucose and fractose are about 1.7 times less effective than raffinose, and pentaerythritol and meso-erythritol are 2.3 times less effective. Glyceraldehyde, which is 3.6 times less effective than raffinose, is the least effective sugar analog among those that we have tested.     

Optical incoherent technique for noninvasive assessment of blood flow in tissues: Theoretical model and experimental study

Laser noninvasive methods for assessment of a tissue blood flow (BF), for example, the Laser Doppler Flowmetry (LDF), are well-known today. However, in such methods, low-frequency fluctuations (LFFs) in the registered optical signal caused by blood volume changes inside a tissue have not been studied in details until now. The aim of this study is to investigate the LFFs formation and to justify the LFFs-based diagnostic technique for cutaneous BF assessment. LFFs are theoretically described and experimentally shown in the input LDF signal inside the frequency range 0 to 10 Hz. They are substantiated as the basis of the new diagnostic method, in which BF is defined as the magnitude of blood volume changes in a tissue per unit time. The hand-made prototype of the promising diagnostic tool with light emitted diodes is used to validate the technique in experiments in vivo on 16 healthy volunteers in comparison with the LDF method. Experimental results show a good similarity of the recorded BF for both coherent and incoherent method. The proposed technique makes it possible the creation of inexpensive diagnostic equipment for assessment of cutaneous BF without using lasers and coherent light, completely and functionally comparable to LDF devices.     

A multiscale model for red blood cell mechanics

The objective of this article is the derivation of a continuum model for mechanics of red blood cells via multiscale analysis. On the microscopic level, we consider realistic discrete models in terms of energy functionals defined on networks/lattices. Using concepts of Γ-convergence, convergence results as well as explicit homogenisation formulae are derived. Based on a characterisation via energy functionals, appropriate macroscopic stress–strain relationships (constitutive equations) can be determined. Further, mechanical moduli of the derived macroscopic continuum model are directly related to microscopic moduli. As a test case we consider optical tweezers experiments, one of the most common experiments to study mechanical properties of cells. Our simulations of the derived continuum model are based on finite element methods and account explicitly for membrane mechanics and its coupling with bulk mechanics. Since the discretisation of the continuum model can be chosen freely, rather than it is given by the topology of the microscopic cytoskeletal network, the approach allows a significant reduction of computational efforts. Our approach is highly flexible and can be generalised to many other cell models, also including biochemical control.     

A statistical model for red blood cell survival

A statistical model for the survival time of red blood cells (RBCs) with a continuous distribution of cell lifespans is presented. The underlying distribution of RBC lifespans is derived from a probability density function with a bathtub-shaped hazard curve, and accounts for death of RBCs due to senescence (age-dependent increasing hazard rate) and random destruction (constant hazard), as well as for death due to initial or delayed failures and neocytolysis (equivalent to early red cell mortality). The model yields survival times similar to those of previously published studies of RBC survival and is easily amenable to inclusion of drug effects and haemolytic disorders.     

Static equilibrium configurations of a model red blood cell

Summary The membrane of the red blood cell is modeled as a fluid shell which resists bending and changes in area. The differential equations governing the mechanical equilibrium of such a membrane are derived and axisymmetric solutions are obtained numerically.     

Stress-free state of the red blood cell membrane and the deformation of its skeleton

The response of a red blood cell (RBC) to deformation depends on its membrane, a composite of a lipid bilayer and a skeleton, which is a closed, twodimensional network of spectrin tetramers as its bonds. The deformation of the skeleton and its lateral redistribution are studied in terms of the RBC resting state for a fixed geometry of the RBC, partially aspirated into a micropipette. The geometry of the RBC skeleton in its initial state is taken to be either two concentric circles, a references biconcave shape or a sphere. It is assumed that in its initial state the skeleton is distributed laterally in a homogeneous manner with its bonds either unstressed, presenting its stress-free state, or prestressed. The lateral distribution was calculated using a variational calculation. It was assumed that the spectrin tetramer bonds exhibit a linear elasticity. The results showed a significant effect of the initial skeleton geometry on its lateral distribution in the deformed state. The proposed model is used to analyze the measurements of skeleton extension ratios by the method of applying two modes of RBC micropipette aspiration.     

A three-dimensional viscoelastic model for cell deformation with experimental verification

A three-dimensional viscoelastic finite element model is developed for cell micromanipulation by magnetocytometry. The model provides a robust tool for analysis of detailed strain/stress fields induced in the cell monolayer produced by forcing one microbead attached atop a single cell or cell monolayer on a basal substrate. Both the membrane/cortex and the cytoskeleton are modeled as Maxwell viscoelastic materials, but the structural effect of the membrane/cortex was found to be negligible on the timescales corresponding to magnetocytometry. Numerical predictions are validated against experiments performed on NIH 3T3 fibroblasts and previous experimental work. The system proved to be linear with respect to cytoskeleton mechanical properties and bead forcing. Stress and strain patterns were highly localized, suggesting that the effects of magnetocytometry are confined to a region extending <10 microm from the bead. Modulation of cell height has little effect on the results, provided the monolayer is >5 micro m thick. NIH 3T3 fibroblasts exhibited a viscoelastic timescale of approximately 1 s and a shear modulus of approximately 1000 Pa.     

Nonlinear large deformation of a spherical red blood cell induced by ultrasonic standing wave

Biomechanics and Modeling in Mechanobiology - A computational model is developed to investigate the nonlinear static deformation of a spherical (osmotically swollen) red blood cell (RBC) induced by...     

Conductometric study of shear-dependent processes in red cell suspensions. I. Effect of red blood cell aggregate morphology on blood conductance

The conductance and capacitance of flowing and quiescent red blood cell (RBC) suspensions were measured at a frequency of 0.2 MHz. The results demonstrate that the time-dependent changes in the conductance recorded during the aggregation process differ in nature for suspensions of short linear rouleaux, branched aggregates and RBC networks. It is shown that the conductance of RBC suspensions measured during the aggregation and disaggregation processes follows the morphological transformations of the RBC aggregates. Thus, this method enables characterization of the morphology of RBC aggregates formed in whole blood and in suspensions with physiological hematocrits both under flow conditions and in stasis. These results in combination with previous ones suggest that this technique can be used for studies of dynamic RBC aggregation and probably for diagnostic use.     

Permselectivity changes in malaria (Plasmodium falciparum) infected human red blood cell membranes

The development of the malaria parasite Plasmodium falciparum in human red blood cells induces parasite-dependent perturbations in the permselectivity properties of the host cell membrane. The changes appear as parasites develop from ring to the trophozoite stage and persist during schizogony. In the present work we assessed the permeability changes of the infected cells to anionic substances by the use of radioactive and fluorescent probes. Our data show that i) covalent binding probes, such as diisothiocyano ditritiostilbene disulfonic acid [3H]H2DIDS, which are virtually impermeant to normal red blood cells, became markedly permeant to trophozoites and schizonts, as evidenced by high labeling of intracellular hemoglobin; ii) permeation of the fluorescent anion transport substrate NBD-taurine, measured in the efflux mode, was very rapid and substantially enhanced in parasitized erythrocytes, as compared with noninfected cells; iii) this efflux could not be blocked by H2DIDS, which is a specific inhibitor of anion transport in normal red blood cells; iv) permeation of anionic probes was temperature dependent (Ea:11 +/- 1 kcal/mole); and v) could be blocked by nonspecific transport inhibitors that are known to interact with membrane lipids. The appearance of a new permeation pathway in the host cell membrane of trophozoites is associated with structural modification of the host cell membrane matrix.     

Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses

A proposed mechanism for metabolic flow regulation involves the saturation-dependent release of ATP by red blood cells, which triggers an upstream conducted response signal and arteriolar vasodilation. To analyze this mechanism, a theoretical model is used to simulate the variation of oxygen and ATP levels along a flow pathway of seven representative segments, including two vasoactive arteriolar segments. The conducted response signal is defined by integrating the ATP concentration along the vascular pathway, assuming exponential decay of the signal in the upstream direction with a length constant of approximately 1 cm. Arteriolar tone depends on the conducted metabolic signal and on local wall shear stress and wall tension. Arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model predicts that conducted responses stimulated by ATP release in venules and propagated to arterioles can account for increases in perfusion in response to increased oxygen demand that are consistent with experimental findings at low to moderate oxygen consumption rates. Myogenic and shear-dependent responses are found to act in opposition to this mechanism of metabolic flow regulation.