Biconcave Red Blood Cells Research Articles

Red Blood Cell Flow in the Cardiovascular System: A Fluid Dynamics Perspective

The dynamics of red blood cells (RBCs) is one of the major aspects of the cardiovascular system that has been studied intensively in the past few decades. The dynamics of biconcave RBCs are thought to have major influences in cardiovascular diseases, the problems associated with cardiovascular assistive devices, and the determination of blood rheology and properties. This article provides an overview of the works that have been accomplished in the past few decades and aim to study the dynamics of RBCs under different flow conditions. While significant progress has been made in both experimental and numerical studies, a detailed understanding of the behavior of RBCs is still faced with many challenges. Experimentally, the size of RBCs is considered to be a major limitation that allows measurements to be performed under conditions similar to physiological conditions. In numerical computations, researchers still are working to develop a model that can cover the details of the RBC mechanics as it deforms and moves in the bloodstream. Moreover, most of reported computational models have been confined to the behavior of a single RBC in 2-dimensional domains. Advanced models are yet to be developed for accurate description of RBC dynamics under physiological flow conditions in 3-dimensional regimes.

Predicting dynamics and rheology of blood flow: A comparative study of multiscale and low-dimensional models of red blood cells

We compare the predictive capability of two mathematical models for red blood cells (RBCs) focusing on blood flow in capillaries and arterioles. Both RBC models as well as their corresponding blood flows are based on the dissipative particle dynamics (DPD) method, a coarse-grained molecular dynamics approach. The first model employs a multiscale description of the RBC (MS-RBC), with its membrane represented by hundreds or even thousands of DPD-particles connected by springs into a triangular network in combination with out-of-plane elastic bending resistance. Extra dissipation within the network accounts for membrane viscosity, while the characteristic biconcave RBC shape is achieved by imposition of constraints for constant membrane area and constant cell volume. The second model is based on a low-dimensional description (LD-RBC) constructed as a closed torus-like ring of only 10 large DPD colloidal particles. They are connected into a ring by worm-like chain (WLC) springs combined with bending resistance. The LD-RBC model can be fitted to represent the entire range of nonlinear elastic deformations as measured by optical-tweezers for healthy and for infected RBCs in malaria. MS-RBCs suspensions model the dynamics and rheology of blood flow accurately for any vessel size but this approach is computationally expensive for vessel diameters above 100 μm. Surprisingly, the much more economical suspensions of LD-RBCs also capture the blood flow dynamics and rheology accurately except for small-size vessels comparable to RBC diameter. In particular, the LD-RBC suspensions are shown to properly capture the experimental data for the apparent viscosity of blood and its cell-free layer (CFL) in tube flow. Taken together, these findings suggest a hierarchical approach in modeling blood flow in the arterial tree, whereby the MS-RBC model should be employed for capillaries and arterioles below 100 μm, the LD-RBC model for arterioles, and the continuum description for arteries.

Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell

A two-dimensional computer simulation model was proposed for tank-treading and tumbling motions of an elastic biconcave red blood cell (RBC) under steady shear flow. The RBC model consisted of an outer cellular membrane and an inner fluid; the membrane's elastic properties were modeled by springs for stretch/compression and bending to consider the membrane's natural state in a practical manner. Membrane deformation was coupled with incompressible viscous flow of the inner and outer fluids of the RBC using a particle method. The proposed simulation model was capable of reproducing tank-treading and tumbling motions of an RBC along with rotational oscillation, which is the transition between the two motions. In simulations using the same initial RBC shape with different natural states of the RBC membrane, only tank-treading motion was exhibited in the case of a uniform natural state of the membrane, and a nonuniform natural state was necessary to generate the rotational oscillation and tumbling motion. Simulation results corresponded to published data from experimental and computational studies. In the range of simulation parameters considered, the relative membrane elastic force versus fluid viscous force was approximately 1 at the transition when the natural state nonuniformity was taken into account in estimating the membrane elastic force. A combination of natural state nonuniformity and elastic spring constant determined that change in the RBC deformation at the transition is that from a large compressive deformation to no deformation, such as rigid body.

Photon-cell interactive Monte Carlo model based on the geometric optics theory for photon migration in blood by incorporating both extra- and intracellular pathways

A photon-cell interactive Monte Carlo (pciMC) that tracks photon migration in both the extra- and intracellular spaces is developed without using macroscopic scattering phase functions and anisotropy factors, as required for the conventional Monte Carlos (MCs). The interaction of photons at the plasma-cell boundary of randomly oriented 3-D biconcave red blood cells (RBCs) is modeled using the geometric optics. The pciMC incorporates different photon velocities from the extra- to intracellular space, whereas the conventional MC treats RBCs as points in the space with a constant velocity. In comparison to the experiments, the pciMC yielded the mean errors in photon migration time of 9.8±6.8 and 11.2±8.5% for suspensions of small and large RBCs (RBC(small), RBC(large)) averaged over the optically diffusing region from 2000 to 4000 μm, while the conventional random walk Monte Carlo simulation gave statistically higher mean errors of 19.0±5.8 ( p < 0.047) and 21.7±19.1% (p < 0.055), respectively. The gradients of optical density in the diffusing region yielded statistically insignificant differences between the pciMC and experiments with the mean errors between them being 1.4 and 0.9% in RBC(small) and RBC(larger), respectively. The pciMC based on the geometric optics can be used to accurately predict photon migration in the optically diffusing, turbid medium.

Deformation and Motion of a Red Blood Cell in a Shear Flow Simulated by a Lattice Boltzmann Model

A lattice Boltzmann model is presented to simulate the deformation and motions of a red blood cell (RBC) in a shear flow. The curvatures of the membrane of a static RBC with different chemical potential drops calculated by our model agree with those computed by a shooting method very well. Our simulation results show that in a shear flow, a biconcave RBC becomes highly flattened and undergoes tank-treading motion. With intrinsically parallel dynamics, this lattice Boltzmann method is expected to find wide applications to both single and multi-vesicles suspension as well as complex open membranes in various fluid flows for a wide range of Reynolds numbers.

Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method

A novel method is developed to simulate suspensions of deformable particles by coupling the lattice-Boltzmann method (LBM) for the fluid phase to a linear finite-element analysis (FEA) describing particle deformation. The methodology addresses the need for an efficient method to simulate large numbers of three-dimensional and deformable particles at high volume fraction in order to capture suspension rheology, microstructure, and self-diffusion in a variety of applications. The robustness and accuracy of the LBM–FEA method is demonstrated by simulating an inflating thin-walled sphere, a deformable spherical capsule in shear flow, a settling sphere in a confined channel, two approaching spheres, spheres in shear flow, and red blood cell deformation in flow chambers. Additionally, simulations of suspensions of hundreds of biconcave red blood cells at 40% volume fraction produce continuum-scale physics and accurately predict suspension viscosity and the shear-thinning behaviour of blood. Simulations of fluid-filled spherical capsules which have red-blood-cell membrane properties also display deformation-induced shear-thinning behaviour at 40% volume fraction, although the suspension viscosity is significantly lower than blood.

One-dimensional jumping optical tweezers for optical stretching of bi-concave human red blood cells

We report the experimental demonstration of optical stretching of individual bio-concave human red blood cells (RBCs) with one-dimensional jumping optical tweezers. We trapped a RBC in isotonic buffer solution in a conventional stationary single-beam gradient-force optical trap and discretely scanned the trapping beam with an acousto-optic modulator such that the focal point of the trapping beam jumped back-and-forth between two fixed points. At the jumping frequency on the order of a 100 Hz and higher, and the jumping distance in the range of a few microns, the bi-concave RBC was stably trapped and stretched. The elongation of the stretched RBC was measured as a function of the beam-scanning amplitude, and the experimental results were explained qualitatively by a theoretical model.

The cooperative role of membrane skeleton and bilayer in the mechanical behaviour of red blood cells

Red blood cell (RBC) shape, behaviour and deformability can be consistently accounted for by a model for the elastic properties of the RBC membrane that includes the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending. The role of the corresponding energy terms in different RBC shape and deformation situations is analyzed. RBC shape transformations are compared to the shape transformations of phospholipid vesicles that are driven by the difference between the equilibrium areas of the bilayer leaflets (Δ A 0). It is deduced that the skeleton energy contributions play a crucial role in the formation of an echinocyte. The effect of a transformation of the natural biconcave RBC shape into an echinocyte on its resistance to entry into capillary-sized cylindrical tubes is analyzed. It is shown that, during the aspiration of an echinocyte into a pipette, there are two competing skeleton deformation effects, which arise due to skeleton density changes, one due to spicule formation and the other due to deformation induced by micropipette aspiration. Furthermore, the shift of the observed dependence of the projection length on the aspiration pressure of more crenated cells towards higher aspiration pressures can be accounted for by an increase of the equilibrium area difference Δ A 0 and consequent modification of the nonlocal contribution to the cell elastic energy.

Relaxation enhancement of the transverse magnetization of water protons in paramagnetic suspensions of red blood cells.

The enhancement of the water proton transverse relaxation, delta R2, brought about by a difference between intra and extracellular paramagnetic susceptibilities in a suspension of red blood cells (RBC) has been evaluated both experimentally and theoretically in terms of (i) the refocusing interval, delta 180, of a CPMG pulse sequence, (ii) the difference in paramagnetic susceptibility, and (iii) the shape of the cell surface. At a hematocrit of 45, the increase in the relaxation enhancement, delta R2, with increasing delta 180, was a factor of two greater for the naturally biconcave RBC, than for the quasi-spherical RBC in hypotonic suspensions. This difference could be modeled in terms of a transmembrane correlation time, tau = 5.5 ms, across an RBC surface characterized by a demagnetizing factor which differs by 0.13 from that of a sphere. The increase in delta R2 with increasing magnetization difference between the RBC and its surroundings was found to be marginally less than quadratic, both experimentally and from the model.

The Effect of Low-Osmolar Ionic and Nonionic Contrast Media on Human Blood Viscosity, Erythrocyte Morphology, and Aggregation Behavior

The effects of three low-osmolar radiographic contrast media (CM)--two nonionic (iohexol, iopamidol) and one ionic (ioxaglate)--on red blood cell (RBC) morphology and aggregation behavior, as well as on blood and plasma viscosity, have been studied. Blood taken from normal, healthy individuals and from patients with uremia was investigated. The authors controlled for the effects of dilution, ionic and nonionic hyperosomolality, and specific chemotoxicity. With ioxaglate, the normal biconcave RBC morphology was fairly well maintained. Iohexol produced a mixture of more-or-less normal cells and echinocytes, while iopamidol yielded only echinocytes. Irregular RBC aggregates have been frequently associated with the presence of echinocyte morphology. In the case of ioxaglate, the capacity of normal blood for rouleaux formation was preserved. This appeared to be compatible with an only moderate decrease in low shear viscosity values. In comparison to the normal control group, RBCs from patients with uremia were clearly more sensitive for hyperosmolar stress. It can be concluded that, in contrast to the nonionic CM, the ionic dimeric compound ioxaglate seems to protect human RBCs against hyperosmolar stress by a mechanism unknown at the present.

Surface tension and deformations of membrane structures : relation to two-dimensional phase transitions

We analyse the thermal fluctuations of two types of flexible membranes : 1) Closed systems (such as the membrane of a biconcave red blood cell) where the chemical constituents of the membrane are fixed in number, but the membrane surface S is adjustable. 2) Open systems (such as bilayer films) where constituent molecules can be exchanged with a reservoir (at the outer surface of the rim). For the first case, the surface tension is zero; fluctuations are then very large, and limited only by certain anharmonic terms. We show that these terms can be analysed exactly - the problem being related to the spherical model of phase transitions. Although the anharmonic terms are strong, they do not modify the laws derived for the light scattering in the simpler harmonic model constructed earlier by one of us [1]. For the second case, there is a finite surface tension, and the fluctuations are much less pathological. This seems to agree with recent measurements by inelastic light scattering on black films by Grabowski and Cowen.