Simulation of ultrasound backscattering by red cell aggregates: effect of shear rate and anisotropy

Tissue characterization using ultrasound (US) scattering allows extraction of relevant cellular biophysical information noninvasively. Characterization of the level of red blood cell (RBC) aggregation is one of the proposed application. In the current paper, it is hypothesized that the microstructure of the RBCs is a main determinant of the US backscattered power. A simulation model was developed to study the effect of various RBC configurations on the backscattered power. It is an iterative dynamical model that considers the effect of the adhesive and repulsive forces between RBCs, and the effect of the flow. The method is shown to be efficient to model polydispersity in size, shape, and orientation of the aggregates due to the flow, and to relate these variations to the US backscattering properties. Three levels of aggregability at shear rates varying between 0.05 and 10 s(-1) were modeled at 40% hematocrit. The simulated backscattered power increased with a decrease in the shear rate or an increase in the RBC aggregability. Angular dependence of the backscattered power was observed. It is the first attempt to model the US power backscattered by RBC aggregates polydisperse in size and shape due to the shearing of the flow.     

Aggregation of red blood cells studied by ultrasound backscattering

The erythrocyte aggregation phenomenon is an important factor in capillary circulation. This phenomenon can be evaluated by a number of methods (microscopic observations, viscometry, light measurements) which cannot be applied simply to in vivo measurements. In contrast, ultrasound which propagates through soft tissues allows measurement of the mechanical properties of red blood cell (RBC) suspensions which depend on the aggregation phenomenon. We devised an apparatus in order to measure in vitro the ultrasonic backscattering intensity of RBC suspensions. First, with latex particles of different sizes, the ultrasonic backscattering coefficient has been measured in order to evaluate the apparatus response. Then, the ultrasonic backscattering coefficient of different aggregated erythrocyte suspensions has been measured and correlated with the erythrocyte sedimentation rate. Finally, the size of RBC aggregates of different suspensions has been evaluated.     

Assessment of red blood cell aggregation with dextran by ultrasonic interferometry.

Aggregation of human red blood cells (RBCs) induced by dextrans of various molecular weight has been studied by using a new ultrasonic interferometry method. This method, based on A-mode echography, allowed for the measurement of the accumulation rate of particles on a solid plate which is related to their sedimentation rate (i.e., to their mean size). The initial aggregation process, the mean and the maximum sedimentation rate of aggregates and the packing of the sedimented RBCs have been investigated. Effects of hematocrit, molecular weight of dextrans and inhibition by dextran 40 on the RBC aggregation induced by dextran of higher molecular weight have been determined by analysing variations of the aggregate size. Results obtained confirm the aggregation effect of dextrans of molecular weights equal or higher than 70,000 dalton and disaggregation effect of dextran 40,000 dalton on aggregation by dextrans of higher molecular weight.     

Viscoelastic properties of whole blood. Influence of fast sedimenting red blood cell aggregates

Red blood cell (RBC) aggregation is known to be of deciding influence on erythrocyte sedimentation-rate (ESR) and on whole blood viscoelastic properties. The rheological behaviour of blood collected from a control-group with normal ESR is compared to the viscoelastic behaviour of blood collected from two groups with high to very high ESR, whose individuals are suffering from chronical polyarthritis and Morbus Bechterew, respectively. The rheological properties are evaluated by means of an oscillating-flow capillary-rheometer where the viscous (eta') and elastic (eta") component of the complex viscosity (eta) is measured at a constant frequency of 2 Hz. Correcting for the varying hematocrit of the different blood samples according to an exponential equation, the viscoelastic data are found to be elevated in the groups with high ESR. For the viscous properties this is only due to the increase of the plasma viscosity. A correction for the plasma viscosity, however, shows that the viscous properties at low shear- rates (2s-1) are significantly reduced, whereas elastic properties in a range of medium shear-rates (10s-1 to 50s-1) are significantly increased (P less than 0.001, t-test of Student). This result is discussed to be due to the high packing density of the RBC in fast sedimenting aggregates. High packing density reduces the effective volume of the RBC but increases the stiffness of the aggregates.     

Effects of dextran molecular weight on red blood cell aggregation

The reversible aggregation of human red blood cells (RBC) by proteins or polymers continues to be of biologic and biophysical interest, yet the mechanistic details governing the process are still being explored. Although a depletion model with osmotic attractive forces due to polymer depletion near the RBC surface has been proposed for aggregation by the neutral polyglucose dextran, its applicability at high molecular mass has not been established. In this study, RBC aggregation was measured over a wide range of dextran molecular mass (70 kDa to 28 MDa) at concentrations ≤2 g/dL. Our results indicate that aggregation does not monotonically increase with polymer size; instead, it demonstrates an optimum dextran molecular mass around 200-500 kDa. We used a model for depletion-mediated RBC aggregation to calculate the expected depletion energies. This model was found to be consistent with the experimental results and thus provides new insight into polymer-RBC interactions.     

Thromboxane induced red blood cell lysis

The two thromboxane A2 mimetics, carbocyclic thromboxane A2 (CTA2) and U-46619 (9,11-methanoepoxy PGH2) at concentrations of 400 ng/ml significantly enhanced the release of hemoglobin from both feline and human erythrocyte suspensions. This effect was significantly attenuated by the thromboxane receptor antagonist BM-13,505 indicating that the membrane leakiness is in some way receptor mediated. The effects also appear to be concentration-dependent over the range of 100-400 ng/ml. The membrane labilizing effect of thromboxane analogs is not due to a non-specific eicosanoid effect since iloprost, the stable prostacyclin analog, actually stabilized erythrocyte membranes. Moreover, synthetic thromboxane A2 exerted similar effects to that of the two TxA2-mimetics. This membrane labilizing action of thromboxanes may be important in propagating the other pathophysiologic effects of thromboxane A2 in cardiovascular disease states.     

Thromboxane induced red blood cell lysis

The two thromboxane A₂ mimetics, carbocyclic thromboxane A₂ (CTA₂) and U-46619 (9,11-methanoepoxy PGH₂) at concentrations of 400 ng/ml significantly enhanced the release of hemoglobin from both feline and human erythrocyte suspensions. This effect was significantly attenuated by the thromboxane receptor antagonist BM-13,505 indicating that the membrane leakiness is in some way receptor mediated. The effects also appear to be concentration-dependent over the range of 100–400 ng/ml. The membrane labilizing effect of thromboxane analogs is not due to a non-specific eicosanoid effect since iloprost, the stable prostacyclin analog, actually stabilized erythrocyte membranes. Moreover, synthetic thromboxane A₂ exerted similar effects to that of the two TxA₂-mimetics. This membrane labilizing action of thromboxanes may be important in propagating the other pathophysiologic effects of thromboxane A₂ in cardiovascular disease states.     

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.     

Visible chemiluminescence induced by t-butyl hydroperoxide in red blood cell suspensions

Red blood cells from Wistar rats were exposed to milimolar concentrations of t-butyl hydroperoxide. Extensive hemoglobin oxidation (methemoglobin formation), t-butyl hydroperoxide cleavage (t-butanol formation) and peroxidation (measured by oxygen consumption and thiobarbituric acid reactive substances) was observed. Significant chemiluminescence was emitted by the system. Hemoglobin oxidation and t-butanol production were independent of oxygen pressure and free radical scavengers, however, luminescence was enhanced as oxygen pressure increased and it was reduced by addition of free radical scavengers. The spectral distribution of the light emitted suggests that the luminescence detected is not due to singlet oxygen dimol emission. The results are in agreement with a lipid peroxidative mechanism initiated by t-butoxy radicals produced in the interaction of hemoglobin and t-butyl hydroperoxide.     

Effects of sedimentation of small red blood cell aggregates on blood flow in narrow horizontal tubes

The flow properties of aggregating red cell suspensions flowing at low flow rates through horizontal tubes are analyzed using a theoretical model. The effects of sedimentation of small aggregates, which will be formed at comparatively high flow rates, on the relative apparent viscosity are considered. In the case in which a large number of small aggregates are formed in a suspension flowing through a horizontal tube, it seems that red cells are transported as a concentrated suspension through the bottom part of the tube because of sedimentation of aggregates. A two-layer flow model is used for the distribution of red cells. It consists of plasma in the upper part and a concentrated red cell suspension in the bottom part of the tube divided by a smooth and horizontal interface. It is assumed that the suspension is a Newtonian fluid whose viscosity increases exponentially with hematocrit. The velocity distribution, the relative apparent viscosity and the flux of red cells are calculated as functions of width of plasma layer for a different discharge hematocrit. The theoretical results are compared with the results obtained from experimental data. The relative apparent viscosity increases rapidly with an increasing degree of sedimentation over a wide range of plasma layer widths.     

Amphiphile induced echinocyte-spheroechinocyte transformation of red blood cell shape

A possible physical explanation of the echinocyte-spheroechinocyte red blood cell (RBC) shape transformation induced by the intercalation of amphiphilic molecules into the outer layer of the RBC plasma membrane bilayer is given. The stable RBC shape is determined by the minimization of the membrane elastic energy, consisting of the bilayer bending energy, the bilayer relative stretching energy and the skeleton shear elastic energy. It is shown that for a given relative cell volume the calculated number of echinocyte spicula increases while their size decreases as the number of the intercalated amphiphilic molecules in the outer layer of the cell membrane bilayer is increased, which is in agreement with experimental observations. Further, it is shown that the equilibrium difference between the outer and the inner membrane leaflet areas of the stable RBC shapes increases if the amount of the intercalated amphiphiles is increased, thereby verifying theoretically the original bilayer couple hypothesis of Sheetz and Singer (1974) and Evans (1974). Received: 22 August 1997 / Revised version: 25 November 1997 / Accepted: 11 February 1998     

Optical evaluation of red blood cell geometry using micropipette aspiration.

Although red blood cell (RBC) geometry has been extensively studied by micropipette aspiration, the small size of RBC and pipettes vs. the optical resolution of light microscopy suggests the need to consider potential errors. The present study addressed such difficulties and investigated four specific problems: (1) use of exact equations to calculate RBC membrane area and volume; (2) calibration of the pipette internal diameter (PID); (3) correction for a noncylindrical pipette barrel; (4) diffraction distortion of the RBC image. The observed PID represents a cylinder lens enlargement that can be theoretically derived from the glass/buffer refractive index ratio (1.49/1.33 = 1.12). This enlargement was experimentally confirmed by: (1) studying pipettes bent to allow measurement through the barrel (horizontal) and at the orifice (vertical), with a resulting diameter ratio of 1.12 +/- 0.01; (2) and by replacing the surrounding buffer with immersion oil and hence abolishing the lens phenomenon (ratio = 1.12 +/- 0.02). In addition, use of aspirated oil droplets demonstrated a 3.2 +/- 0.2% error when the PID is focused at a sharp, maximum diameter. The average pipette cone angle was 1.49 +/- 0.09 degrees and varied considerably with pipette pulling procedures; calculated tongue geometry inside the pipette was affected by the noncylindrical pipette barrel. The RBC diffraction error, demonstrated by touching two aspirated cells held by opposing pipettes, was 0.091 +/- 0.002 microns. The PID, cone angle, and diffraction artifacts significantly (p < 0.001) affected calculated RBC geometry (average errors up to 5.4% for area and 9.6% for volume). Two new methods to calculate, rather than directly measure, the PID from images of a single RBC, during either osmotic or pressure manipulation, were evaluated; the osmotic method closely predicted the PID, whereas the pressure method markedly underestimated the PID. Our results thus confirm the need to consider the above-mentioned phenomena when determining RBC geometric parameters via micropipette aspiration.     

Characterization of monoclonal antibodies against human red blood group cells antigens by laser backscattering

A problem in immunohematology is to define the antibody quality which is related to its affinity expressed by the equilibrium constant. The activity of an antibody can be measured by the strength of its interaction, related to the adhesive energy exchanged during RBC agglutination which depends on the antigen-antibody liaison strength. To estimate this adhesive energy, two methods are used in this paper. Firstly, the dissociation behaviour of suspended RBC agglutinates was analysed by laser backscattering intensity (r) in a Couette flow. Backscattered intensity issued from shear-induced mechanical dissociation is recorded and submitted to a numerical process to obtain the energy parameter (ED). Secondly, a modification of this technique is proposed for measuring specific binding energy. Samples were exposed to increasing shear stress, and backscattered intensity was recorded. A constant increase of this intensity with raising shear stress was observed, pointed to a progressive dissociation of RBC agglutinates into smaller ones. Considering that complete dissociation of agglutinates is only approached asymptotically it is assumed that the final break-up of doublets (two-cell agglutinates) is produced at a critical shear stress (tauC) reflecting the work done to breaking-up the molecular bridges between both adjacent cells. This shear stress is defined by the extrapolation of the linear part of the curves [r-log tau] to the backscattered signal (r0) corresponding to the complete dispersion of RBCs. These approaches permit to define the specific surface adhesive energy (Gamma) by using the Derjaguin relation and to assess the functional characterization of specific immunoglobulins. In conclusion, two parameters characterizing monoclonal antibody agglutination properties, ED and Gamma, were estimated by laser backscattering methods, which could be very useful for antibodies quality control.     

Polyamines--sickling red blood cell interaction.

The binding of polyamine as a function of concentration to normal and sickling rcc'. blood cells is analyzed by Langmuir type binding isotherms, based on the Gouy-Chapman model for an electrical double Iayer, where the zeta potential is a function of only the normal distance coordinate. For normal erythrocytes, the apparent exotropic binding constants are found to be 103, 110, and 130 dl/g at normal distance coordinates of 4, 5, and 6 Å, iezpectively. The esotropic binding constant is determined to be 420 dl/g at a distance of 7 Å. For sickling red blood cells, the apparent exotropic binding constants are 3.3, 3.8, 4.6, and 6-7 dl/g at a distance of 4 to 7 Å. The esotropic binding constant at a distance of 8 Å is found to be 12-9 dl/g. The apparent binding affinity of polyamines to the normal red blood cell. therefore, is approximately 30 times greater than to the sickling erythrocyte.The Praxis pulse nuclear magnetic resonance spectrometer is used to determine the spin-lattice relaxation time (T₁) for water in the presence of normal and sickling red blood cells. The spin-lattice relaxation time is found to be 540 ms for normal erythrocytes and 445 ms for sickling red blood cells in the oxy state. Differences in the spin-spin relaxation time (T₂) for the two types of erythrocyte are negligible, being within the range of normal experimental error.     

Interrelation between HeLa-S3 cell transfection and hemolysis in red blood cell suspension using pulsed ultrasound of various duty cycles

We have studied the in vitro transfection of a plasmid DNA with the lacZ gene to HeLa-S3 cells and hemolysis in a red blood cell (RBC) suspension under pulsed ultrasound with duty cycles of 10, 20 and 30% using a digital sonifier at a frequency of 20 kHz and an intensity of 6.2 W/cm² on the surface of a horn tip. Cultured HeLa-S3 cells in suspension were exposed to pulsed ultrasound for an apparent exposure time t from 0 to 60 s. HeLa-S3 viability decreased as a single exponential function of the total exposure time t=t with a common time constant =3.8 s for three duty cycles. Transfection was evaluated by counting the number of -galactosidase(-Gal)-positive cells relative to the total number of cells. Pulsed ultrasound provided an enhanced transfer of the -Gal plasmid to HeLa-S3 cells, 3.4-fold as compared with that in the case of the control. The optimal transfection efficiencies were 0.75, 0.80 and 0.74% near t= with =10, 20 and 30%, respectively. The number ratio of -Gal-positive cells to the surviving cells after exposure increased with t according to a modified logistic equation. The degree of hemolysis also increased exponentially with t at a time constant =₀/ for the RBC suspension in physiological saline at a hematocrit concentration of 0.5% with ₀=0.9 s. Thus the total exposure time for the optimal transfection efficiency was , that is, nearly four times of ₀. Hemolysis in the RBC suspension may be a useful model for determining optimal transfection by pulsed ultrasound of various duty cycles.     

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...     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.