Similar but Distinct Roles of Membrane and Interior Fluid Viscosities in Capsule Dynamics in Shear Flows

Comment on "Dynamics and rheology of vesicles under confined Poiseuille flow" by Z. Gou, H. Zhang, A. Nait-Ouhra, M. Abbasi, A. Farutin and C. Misbah, Soft Matter, 2023, , 9101

In a recent paper, [Gou et al., Soft Matter, 2023, 19, 9101-9114] studied numerically the viscosity of a confined suspension of vesicles flowing in a channel as a function of vesicle concentration. In order to discuss the genericity of the observed behaviour, namely a nearly constant effective viscosity at low concentrations, we complement their study by a comparison with the few existing ones in the literature. In particular, we highlight that they fail to reproduce well established results for blood viscosity in microcirculation, thereby suggesting that the conclusions regarding the optimization of cell transport and oxygenation may not apply. We conclude with a quick discussion on potential improvements regarding numerical modeling, as long as physiological relevance is sought.

Droplet dynamics in homogeneous isotropic turbulence with the immersed boundary-lattice Boltzmann method

We develop a numerical method for simulating the dynamics of a droplet immersed in a generic time-dependent velocity gradient field. This approach is grounded on the hybrid coupling between the lattice Boltzmann (LB) method, employed for the flow simulation, and the immersed boundary (IB) method, utilized to couple the droplet with the surrounding fluid. We show how to enrich the numerical scheme with a mesh regularization technique, allowing droplets to sustain large deformations. The resulting methodology is adapted to simulate the dynamics of droplets in homogeneous and isotropic turbulence, with the characteristic size of the droplet being smaller than the characteristic Kolmogorov scale of the outer turbulent flow. We report statistical results for droplet deformation and orientation collected from an ensemble of turbulent trajectories, as well as comparisons with theoretical models in the limit of small deformation.

A computational study of cell membrane damage and intracellular delivery in a cross-slot microchannel

We propose a three-dimensional computational framework to simulate the flow-induced cell membrane damage and the resulting enhanced intracellular mass transport in a cross-slot microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane and solve the cell deformation using a well-tested immersed-boundary lattice-Boltzmann method. The cell membrane damage, which is directly related to the membrane permeability, is considered using continuum damage mechanics. The transport of the diffusive solute into the cell is solved by a lattice-Boltzmann model. After validating the computational framework against several benchmark cases, we consider a cell flowing through a cross-slot microchannel, focusing on the effects of the flow strength, channel fluid viscosity and cell membrane viscosity on the membrane damage and enhanced intracellular transport. Interestingly, we find that under a comparable pressure drop across the device, for cells with low membrane viscosity, the inertial flow regime, which can be achieved by driving a low-viscosity liquid at a high speed, often leads to much larger membrane damage, compared with the high-viscosity low-speed viscous flow regime. However, the enhancement can be significantly reduced or even reversed by an increase of the cell membrane viscosity, which limits cell deformation, particularly in the inertial flow regime. Our computational framework and simulation results may guide the design and optimisation of microfluidic devices, which use cross-slot geometry to disrupt cell membranes to enhance intracellular delivery of solutes.

Effect of constitutive law on the erythrocyte membrane response to large strains

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

Effects of membrane viscoelasticity on the red blood cell dynamics in a microcapillary

The mechanical properties of red blood cells (RBCs) play key roles in their biological functions in microcirculation. In particular, RBCs must deform significantly to travel through microcapillaries with sizes comparable with or even smaller than their own. Although the dynamics of RBCs in microcapillaries have received considerable attention, the effect of membrane viscoelasticity has been largely overlooked. In this work, we present a computational study based on the boundary integral method and thin-shell mechanics to examine how membrane viscoelasticity influences the dynamics of RBCs flowing through straight and constricted microcapillaries. Our results reveal that the cell with a viscoelastic membrane undergoes substantially different motion and deformation compared with results based on a purely elastic membrane model. Comparisons with experimental data also suggest the importance of accounting for membrane viscoelasticity to properly capture the transient dynamics of an RBC flowing through a microcapillary. Taken together, these findings demonstrate the significant effects of membrane viscoelasticity on RBC dynamics in different microcapillary environments. The computational framework also lays the groundwork for more accurate quantitative modeling of the mechanical response of RBCs in their mechanotransduction process in subsequent investigations.

Oxygen transport across tank-treading red blood cell: Individual and joint roles of flow convection and oxygen-hemoglobin reaction

Gas, especially oxygen, transport in the microcirculation is a complex phenomenon, however, of critical importance for maintaining normal biological functions, and the cytoplasm fluid in red blood cells (RBCs) is the major vehicle for transporting oxygen from lungs to tissues via the circulatory system. Existing theoretical and numerical studies have neglected the cytoplasm convection effect by treating RBCs as rigid particles undergoing a constant translation velocity. As a consequence, the influence and mechanism of the cytoplasm flow on oxygen transport are still not clear in microcirculation research. In this study, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions: the top plate of a higher oxygen pressure (P_O2) representing the RBC core in the central region of a microvessel and the bottom plate of a lower P_O2 representing the microvessel wall. Numerical simulations are conducted to investigate the individual and combined effects of cytoplasm convection and oxygen-hemoglobin (O₂-Hb) reaction on the oxygen transport efficiency across the tank-treading capsule, and different P_O2 situations and shear rates are also tested. Due to the lower oxygen diffusivity in cytoplasm, the presence of the capsule reduces the oxygen transfer flux across the gap by 7.34 % in the pure diffusion system where the flow convection and O₂-Hb reaction are both neglected. Including the flow convection or the O₂-Hb reaction has little influence on the oxygen flux; however, when they act together as in real microcirculation situations, the enhancement in oxygen transport could be significant, especially in the low P_O2 and high shear rate situations. In particular, with the respective P_O2 at 60 and 30 mmHg on the top and bottom plates and a 400 s^-1 shear rate, the oxygen flux reduction is only 0.02 %, suggesting that the cytoplasm convection can improve the oxygen transport across RBCs considerably. The simulation results are scrutinized to explore the underlying mechanism for the enhancement, and a new nondimensional parameter is introduced to characterize the importance of cytoplasm convection in oxygen transport. These simulation results, discussion and analysis could be helpful for a better understanding of the complex oxygen transport process and therefor valuable for relevant studies.

Tank-treading dynamics of red blood cells in shear flow: On the membrane viscosity rheology

In this article, extensive three-dimensional simulations are conducted for tank-treading (TT) red blood cells (RBCs) in shear flow with different cell viscous properties and flow conditions. Apart from recent numerical studies on TT RBCs, this research considers the uncertainty in cytoplasm viscosity, covers a more complete range of shear flow situations of available experiments, and examines the TT behaviors in more details. Key TT characteristics, including the rotation frequency, deformation index, and inclination angle, are compared with available experimental results of similar shear flow conditions. Fairly good simulation-experiment agreements for these parameters can be obtained by adjusting the membrane viscosity values; however, different rheological relationships between the membrane viscosity and the flow shear rate are noted for these comparisons: shear thinning from the TT frequency, Newtonian from the inclination angle, and shear thickening from the cell deformation. Previous studies claimed a shear-thinning membrane viscosity model based on the TT frequency results; however, such a conclusion seems premature from our results and more carefully designed and better controlled investigations are required for the RBC membrane rheology. In addition, our simulation results reveal complicate RBC TT features and such information could be helpful for a better understanding of in vivo and in vitro RBC dynamics.

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, nonsymmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes in RBC properties.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC. However, the membrane viscosity [Formula: see text] plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity [Formula: see text] on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios [Formula: see text], larger values of [Formula: see text] lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing [Formula: see text] or increasing [Formula: see text] results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Loading and relaxation dynamics of a red blood cell

We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the loading (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the relaxation (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., t_L and t_R. When the intensity of the mechanical load is small enough, the two kinds of dynamics are symmetrical (t_L≈t_R) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an asymmetry is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times t_L and t_R. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.