Numerical Simulations of Red-Blood Cells in Fluid Flow: A Discrete Multiphysics Study

In this paper, we present a methodological study of modelling red blood cells (RBCs) in shear-induced flows based on the discrete multiphysics (DMP) approach. The DMP is an alternative approach from traditional multiphysics based on meshless particle-based methods. The proposed technique has been successful in modelling multiphysics and multi-phase problems with large interfacial deformations such as those in biological systems. In this study, we present the proposed method and introduce an accurate geometrical representation of the RBC. The results were validated against available data in the literature. We further illustrate that the proposed method is capable of modelling the rupture of the RBC membrane with minimum computational difficulty.

Influence of numerical resolution on the dynamics of finite-size particles with the lattice Boltzmann method

We investigate and compare the accuracy and efficiency of different numerical approaches to model the dynamics of finite-size particles using the lattice Boltzmann method (LBM). This includes the standard bounce-back (BB) and the equilibrium interpolation (EI) schemes. To accurately compare the different implementations, we first introduce a boundary condition to approximate the flow properties of an unbounded fluid in a finite simulation domain, taking into account the perturbation induced by a moving particle. We show that this boundary treatment is efficient in suppressing detrimental effects on the dynamics of spherical and ellipsoidal particles arising from the finite size of the simulation domain. We then investigate the performances of the BB and EI schemes in modeling the dynamics of a spherical particle settling under Stokes conditions, which can now be reproduced with great accuracy thanks to the treatment of the exterior boundary. We find that the EI scheme outperforms the BB scheme in providing a better accuracy scaling with respect to the resolution of the settling particle, while suppressing finite-size effects due to the particle discretization on the lattice grid. Additionally, in order to further increase the capability of the algorithm in modeling particles of sizes comparable to the lattice spacing, we propose an improvement to the EI scheme, the complete equilibrium interpolation (CEI). This approach allows us to accurately capture the boundaries of the particle also when located between two fluid nodes. We evaluate the CEI performance in solving the dynamics of an under-resolved particle under analogous Stokes conditions and also for the case of a rotating ellipsoid in a shear flow. Finally, we show that EI and CEI are able to recover the correct flow solutions also at small, but finite, Reynolds number. Adopting the CEI scheme it is not only possible to detect particles with zero lattice occupation, but also to increase up to one order of magnitude the accuracy of the dynamics of particles with a size comparable to the lattice spacing with respect to the BB and the EI schemes.

Vascular journey and adhesion mechanics of micro-sized carriers in narrow capillaries

In this work a Lattice Boltzmann-Immersed Boundary method is used for predicting the dynamics of rigid and deformable adhesive micro-carriers (1 μm) navigating a capillary by the size of 10 μm with 20% hematocrit. Red cells and particles are modeled as a collection of mass-spring elements responding to a bending potential, an elastic potential and total enclosed area conservation constraint. Furthermore, particle surfaces are uniformly decorated with adhesive molecules (ligands) interacting with receptors disposed on the walls. Particle adhesion is modeled as a short-range ligad-receptor interaction and in term of formation and destruction probability functions that discriminate whether a chemical bond can be formed or destroyed. If a bond is established an attractive elastic force is activated. Particle transport and adhesion are characterized in terms of their ability to reach the capillary peripheries (margination rate) and firmly adhere the vasculature. This analysis is carried out systematically by varying particles' and cells' releasing positions and stiffness (Ca = 0 and 10^-2). Moreover, three rigid and soft representative particles are transported on a finer mesh (Δx = 15 nm) and the chemical strength of their adhesive coating is varied (σ = 0.5, 1.0, and 2.0) to precisely analyze the resulting adhesion mechanics. Stiffness is found to weakly influence the margination rate while significantly affect the ability of such constructs to efficiently interact with the endothelium by forming stable chemical bonds.

Curvature dynamics and long-range effects on fluid-fluid interfaces with colloids

We investigate the dynamics of a phase-separating binary fluid, containing colloidal dumbbells anchored to the fluid-fluid interface. Extensive lattice Boltzmann-immersed boundary method simulations reveal that the presence of soft dumbbells can significantly affect the curvature dynamics of the interface between phase-separating fluids, even though the coarsening dynamics is left nearly unchanged. In addition, our results show that the curvature dynamics exhibits distinct non-local effects, which might be exploited for the design of new soft mesoscale materials. We point out that the inspection of the statistical dynamics of the curvature can disclose new insights into local inhomogeneities of the binary fluid configuration, as a function of the volume fraction and aspect ratio of the dumbbells.

A micro-scale simulation of red blood cell passage through symmetric and asymmetric bifurcated vessels

Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper presents a simulation study performed on the two-dimensional motions and deformation of multiple red blood cells in microvessels with diverging and converging bifurcations. Fluid dynamics and membrane mechanics were incorporated. Effects of cell shape, hematocrit, and deformability of the cell membrane on rheological behavior of the red blood cells and the hemodynamics have been investigated. It was shown that the blood entering the daughter branch with a higher flow rate tended to receive disproportionally more cells. The results also demonstrate that red blood cells in microvessels experienced lateral migration in the parent channel and blunted velocity profiles in both straight section and daughter branches, and this effect was influenced by the shape and the initial position of the cells, the hematocrit, and the membrane deformability. In addition, a cell free region around the tip of the confluence was observed. The simulation results are qualitatively consistent with existing experimental findings. This study may provide fundamental knowledge for a better understanding of hemodynamic behavior of micro-scale blood flow.

Computational biorheology of human blood flow in health and disease

Hematologic disorders arising from infectious diseases, hereditary factors and environmental influences can lead to, and can be influenced by, significant changes in the shape, mechanical and physical properties of red blood cells (RBCs), and the biorheology of blood flow. Hence, modeling of hematologic disorders should take into account the multiphase nature of blood flow, especially in arterioles and capillaries. We present here an overview of a general computational framework based on dissipative particle dynamics (DPD) which has broad applicability in cell biophysics with implications for diagnostics, therapeutics and drug efficacy assessments for a wide variety of human diseases. This computational approach, validated by independent experimental results, is capable of modeling the biorheology of whole blood and its individual components during blood flow so as to investigate cell mechanistic processes in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to arterioles and can also be used to model RBCs down to the spectrin level. We start from experimental measurements of a single RBC to extract the relevant biophysical parameters, using single-cell measurements involving such methods as optical tweezers, atomic force microscopy and micropipette aspiration, and cell-population experiments involving microfluidic devices. We then use these validated RBC models to predict the biorheological behavior of whole blood in healthy or pathological states, and compare the simulations with experimental results involving apparent viscosity and other relevant parameters. While the approach discussed here is sufficiently general to address a broad spectrum of hematologic disorders including certain types of cancer, this paper specifically deals with results obtained using this computational framework for blood flow in malaria and sickle cell anemia.

Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells

Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of transition, but rather follows a simple scaling law independent of volume fraction.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

A review of numerical methods for red blood cell flow simulation

In this review, we provide an overview of the simulation techniques employed for modelling the flow of red blood cells (RBCs) in blood plasma. The scope of this review omits the fluid modelling aspect while focusing on other key components in the RBC-plasma model such as (1) describing the RBC deformation with shell-based and spring-based RBC models, (2) constitutive models for RBC aggregation based on bridging theory and depletion theory and (3) additional strategies required for completing the RBC-plasma flow model. These include topics such as modelling fluid-structure interaction with the immersed boundary method and boundary integral method, and updating the variations in multiphase fluid property through the employment of index field methods. Lastly, we summarily discuss the current state and aims of RBC modelling and suggest some research directions for the further development of this field of modelling.

Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease

We review recent advances in multiscale modeling of the mechanics of healthy and diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the traditional continuum-based methods but also particle-based methods used to model both the RBCs and the blood plasma. We highlight examples of successful simulations of blood flow including malaria and sickle cell anemia.