Computational Analysis of Dynamic Interaction of Two Red Blood Cells in a Capillary

Colloid Transport in Bicontinuous Nanoporous Media

Colloid transport and retention in porous media are critical processes influencing various Earth science applications, from groundwater remediation to enhanced oil recovery. These phenomena become particularly complex in the confined spaces of nanoporous media, where strong boundary layer effects and nanoconfinement significantly alter colloid behavior. In this work, we use particle dynamics models to simulate colloid transport and retention processes in bicontinuous nanoporous (BNP) media under pressure gradients. By utilizing particle-based models, we track the movement of each colloid and elucidate the underlying colloid retention mechanisms. Under unfavorable attachment conditions, the results reveal two colloid retention mechanisms: physical straining and trapping in low-flow zone. Furthermore, we investigate the effects of critical factors including colloid volume fraction, d, pressure difference, ΔP, interaction between colloids and BNP media, Ec-p, and among colloids, Ec-c, on colloid transport. Analysis of breakthrough curves and colloid displacements demonstrates that higher values of d, lower values of ΔP, and strong Ec-p attractions significantly increase colloid retention, which further lead to colloid clogging and jamming. In contrast, Ec-c has minimal impact on colloid transport due to the limited colloid-colloid interaction in nanoporous channels. This work provides critical insights into the fundamental factors governing colloid transport and retention within stochastic nanoporous materials.

Analysis of the Suitability of an Effective Viscosity to Represent Interactions Between Red Blood Cells in Shear Flow

Many methods to computationally predict red blood cell damage have been introduced, and among these are Lagrangian methods that track the cells along their pathlines. Such methods typically do not explicitly include cell-cell interactions. Due to the high volume fraction of red blood cells (RBCs) in blood, these interactions could impact cell mechanics and thus the amount of damage caused by the flow. To investigate this question, cell-resolved simulations of red blood cells in shear flow were performed for multiple interacting cells, as well as for single cells in unbounded flow at an effective viscosity. Simulations run without adjusting the bulk viscosity produced larger errors unilaterally and were not considered further for comparison. We show that a periodic box containing at least 8 cells and a spherical harmonic of degree larger than 10 are necessary to produce converged higher-order statistics. The maximum difference between the single-cell and multiple-cell cases in terms of peak strain was 3.7%. To achieve this, one must use the whole blood viscosity and average over multiple cell orientations when adopting a single-cell simulation approach. The differences between the models in terms of average strain were slightly larger (maximum difference of 6.9%). However, given the accuracy of the single-cell approach in predicting the maximum strain, which is useful in hemolysis prediction, and its computational cost that is orders of magnitude less than the multiple-cell approach, one may use it as an affordable cell-resolved approach for hemolysis prediction.

A mechanistic model of cross-bridge migration in RBC aggregation and disaggregation

Red blood cells (RBCs) clump together under low flow conditions in a process called RBC aggregation, which can alter RBC perfusion in a microvascular network. As elevated RBC aggregation is commonly associated with cardiovascular and inflammatory diseases, a better understanding of aggregation is essential. Unlike RBC aggregation in polymer solutions which can be well explained by polymer depletion theory, plasma-mediated RBC aggregation has features that best match explanations with cross-bridging mechanisms. Previous studies have demonstrated the dominant role of fibrinogen (Fg) in promoting aggregate formation and recent cell-force spectroscopy (CFS) experiments on interacting RBC doublets in plasma have reported an inverse relationship between disaggregation force and the adhesive contact area between RBCs. This has led investigators to revisit the hypothesis of inter-RBC cross-bridging which involves cross-bridge migration under interfacial tension during the forced disaggregation of RBC aggregates. In this study, we developed the cross-bridge migration model (CBMM) in plasma that mechanistically represents the migrating cross-bridge hypothesis. Transport of mobile Fg cross-bridges (mFg) was calculated using a convection-diffusion transport equation with our novel introduction of convective cross-bridge drift that arises due to intercellular friction. By parametrically transforming the diffusivity of mFg in the CBMM, we were able to match experimental observations of both RBC doublet formation kinematics and RBC doublet disaggregation forces under optical tweezers tension. We found that non-specific cross-bridging promotes spontaneous growth of adhesion area between RBC doublets whereas specific cross-bridging tends to prevent adhesion area growth. Our CBMM was also able to correlate Fg concentration shifts from healthy population blood plasma to SLE (lupus) condition blood plasma with the observed increase in doublet disaggregation forces for the RBC doublets in SLE plasma.

SIMULATION OF CELL MOTION IN THE MICROCHANNEL WITH A SQUARE CAVITY

Isolating circulating tumor cells (CTCs) from the blood plays an important role in the specific treatment of tumor diseases. In this study, a dissipative particle dynamics method combined with a spring-based cell model was employed to simulate the motion of a single or two cells in the microchannel with a square cavity. For a single cell with a small diameter, it will be captured by the square cavity at an appropriate flow rate. For cells whose diameter is not small enough compared to the opening size of the square cavity, they will not be captured at any flow rate. Based on this, cells of different sizes could be successfully separated when passing through this microchannel. Through the analysis of the flow behavior of uncaptured cells, the movement of cells in microchannels is divided into four stages: “guiding,” “rapid,” “slow”, and “ascending” according to the lateral movement speed and centroid position of cells. When the CTC moves together with a red blood cell, as the flow rate decreases, it would be trapped by the microcavity, whereas the RBC is not captured. Thus, CTC can be isolated from blood samples of cancer patients. The method of predicting cell movement behavior through simulation can also provide some reference for the design of microfluidic channels.

Shape transformations of red blood cells in the capillary and their possible connections to oxygen transportation

In this work, a series of numerical simulations have been performed to obtain the steady shapes of red blood cells under a shear force field in the capillary. Two possible classes of steady shapes, the axisymmetric parachute and the non-axisymmetric parachute, are found. If we assume that oxygen diffusion across the red cell membrane is mediated by membrane curvature, it is found that the non-axisymmetric parachute will be more favorable due to its special shape which enables it to have a larger portion of membrane patch capable of releasing oxygen to tissues.

Morphometry and Stiffness of Red Blood Cells—Signatures of Neurodegenerative Diseases and Aging

Human red blood cells (RBCs) are unique cells with the remarkable ability to deform, which is crucial for their oxygen transport function, and which can be significantly altered under pathophysiological conditions. Here we performed ultrastructural analysis of RBCs as a peripheral cell model, looking for specific signatures of the neurodegenerative pathologies (NDDs)—Parkinson’s disease (PD), amyotrophic lateral sclerosis (ALS) and Alzheimer’s disease (AD), utilizing atomic force (AFM) and conventional optical (OM) microscopy. We found significant differences in the morphology and stiffness of RBCs isolated from patients with the selected NDDs and those from healthy individuals. Neurodegenerative pathologies’ RBCs are characterized by a reduced abundance of biconcave discoid shape, lower surface roughness and a higher Young’s modulus, compared to healthy cells. Although reduced, the biconcave is still the predominant shape in ALS and AD cells, while the morphology of PD is dominated by crenate cells. The features of RBCs underwent a marked aging-induced transformation, which followed different aging pathways for NDDs and normal healthy states. It was found that the diameter, height and volume of the different cell shape types have different values for NDDs and healthy cells. Common and specific morphological signatures of the NDDs were identified.

Flow-driven competition between two capsules passing through a narrow pore

By incorporating a distance function into the finite element simulation, we investigate the flow-driven competition between two soft capsules passing through a narrow pore, employing the arbitrary Lagrangian-Eulerian formulation to satisfy the boundary conditions for fluid flow and capsule deformation. In our simulations, the motion and deformation of the capsules can be described in an intuitive manner, and the order in which capsules of different sizes pass through a pore can be clearly determined. Meanwhile, when the capsules are near the narrow pore, the change of the flow field is also very interesting and can be expressed intuitively. It is shown that, driven by the Poiseuille flow, the larger capsule has a stronger tendency to pass through the pore than the small one, which can be attributed to the greater resistance and the volume advantage of the larger capsule. In addition, we demonstrate that this tendency can be reversed by changing the inlet velocity and setting the initial position of the smaller capsule closer to the axis of the pore. And as long as the large one passes through first, the small one will offset the axis to the same orientation as the initial, while the large one always moves along the axis.

The Relationship Between Aggregation and Deformability of Red Blood Cells in Health and Disease

The molecular organization of the membrane of the red blood cell controls cell morphology and function and is thereby a main determinant of red blood cell homeostasis in the circulation. The role of membrane organization is prominently reflected in red blood cell deformation and aggregation. However, there is little knowledge on whether they are controlled by the same membrane property and if so, to what extent. To address the potential interdependence of these two parameters, we measured deformation and aggregation in a variety of physiological as well as pathological conditions. As a first step, we correlated a number of deformability and aggregation parameters in red blood cells from healthy donors, which we obtained in the course of our studies on red blood cell homeostasis in health and disease. This analysis yielded some statistically significant correlations. Also, we found that most of these correlations were absent in misshapen red blood cells that have an inborn defect in the interaction between the membrane and the cytoskeleton. The observations suggest that deformability and aggregation share at least one common, membrane-related molecular mechanism. Together with data obtained after treatment with various agents known to affect membrane organization in vitro, our findings suggest that a phosphorylation-controlled interaction between the cytoskeleton and the integral membrane protein band 3 is part of the membrane-centered mechanism that plays a role in deformability as well as aggregation.

Multiple Particle Manipulation under Dielectrophoresis Effect: Modeling and Experiments

The dissipative particle dynamics (DPD) technique was employed to design multiple microfluidic devices for investigating the motion of bioparticles at low Reynolds numbers. A DPD in-house FORTRAN code was developed to simulate the trajectories of two microparticles in the presence of hydrodynamic and transverse deflecting force fields via considering interparticle interaction forces. The particle-particle interactions were described by using a simplified version of the Morse potential. The transverse deflecting force considered in this microfluidic application was the dielectrophoresis (DEP) force. Multiple microfluidic devices with different configurations of microelectrodes were numerically designed to investigate the dielectrophoretic behavior of bioparticles for their trajectories and the focusing of bioparticles into a single stream in the middle of the microchannel. The DPD simulation results were verified and validated against previously reported numerical and experimental works in the literature. The computationally designed microdevices were fabricated by employing standard lithographic techniques, and experiments were conducted via taking red blood cells as the representative bioparticles. The experimental results for the trajectories and focusing showed good agreement with the numerical results.

Red blood cell motion and deformation in a curved microvessel

The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.

Hybrid smoothed dissipative particle dynamics and immersed boundary method for simulation of red blood cells in flows

In biofluid flow systems, often the flow problems of fluids of complex structures, such as the flow of red blood cells (RBCs) through complex capillary vessels, need to be considered. The smoothed dissipative particle dynamics (SDPD), a particle-based method, is one of the easy and flexible methods to model such complex structure fluids. It couples the best features of the smoothed particle hydrodynamics (SPH) and dissipative particle dynamics (DPD), with parameters having specific physical meaning (coming from SPH discretization of the Navier-Stokes equations), combined with thermal fluctuations in a mesoscale simulation, in a similar manner to the DPD. On the other hand, the immersed boundary method (IBM), a preferred method for handling fluid-structure interaction problems, has also been widely used to handle the fluid-RBC interaction in RBC simulations. In this paper, we aim to couple SDPD and IBM together to carry out the simulations of RBCs in complex flow problems. First, we develop the SDPD-IBM model in details, including the SDPD model for the evolving fluid flow, the RBC model for calculating RBC deformation force, the IBM for treating fluid-RBC interaction, and the solid boundary treatment model as well. We then conduct the verification and validation of the combined SDPD-IBM method. Finally, we demonstrate the capability of the SDPD-IBM method by simulating the flows of RBCs in rectangular, cylinder, curved, bifurcated, and constricted tubes, respectively.

A Two-Dimensional Numerical Investigation of Transport of Malaria-Infected Red Blood Cells in Stenotic Microchannels

The malaria-infected red blood cells experience a significant decrease in cell deformability and increase in cell membrane adhesion. Blood hemodynamics in microvessels is significantly affected by the alteration of the mechanical property as well as the aggregation of parasitized red blood cells. In this study, we aim to numerically study the connection between cell-level mechanobiological properties of human red blood cells and related malaria disease state by investigating the transport of multiple red blood cell aggregates passing through microchannels with symmetric stenosis. Effects of stenosis magnitude, aggregation strength, and cell deformability on cell rheology and flow characteristics were studied by a two-dimensional model using the fictitious domain-immersed boundary method. The results indicated that the motion and dissociation of red blood cell aggregates were influenced by these factors and the flow resistance increases with the increase of aggregating strength and cell stiffness. Further, the roughness of the velocity profile was enhanced by cell aggregation, which considerably affected the blood flow characteristics. The study may assist us in understanding cellular-level mechanisms in disease development.