Accurate coarse-grained modeling of red blood cells

Interplay of size, deformability, and device layout on cell transport in microfluidics

Microfluidics have been widely used for cell sorting and capture. In this work, numerical simulations of cell transport in microfluidic devices were studied considering cell sizes, deformability, and five different device designs. Among these five designs, deterministic lateral displacement device (DLD) and hyperuniform device (HU) performed better in promoting cell-micropost collision due to the continuously shifted micropost positions as compared with regular grid, staggered, and hexagonal layout designs. However, the grid and the hexagonal layouts showed best in differentiating cells by their size dependent velocity due to the size exclusion effect for cell transport in clear and straight paths in the flow direction. A systematic study of the velocity differentiation under different dimensionless groups was performed showing that the velocity difference is dominated by the micropost separation distance perpendicular to the direction of flow. Microfluidic experiments also confirmed the velocity differentiation results. The study can provide guiding principles for microfluidic design.

Two-component macrophage model for active phagocytosis with pseudopod formation

Macrophage phagocytosis is critical for the immune response, homeostasis regulation, and tissue repair. This intricate process involves complex changes in cell morphology, cytoskeletal reorganization, and various receptor-ligand interactions controlled by mechanical constraints. However, there is a lack of comprehensive theoretical and computational models that investigate the mechanical process of phagocytosis in the context of cytoskeletal rearrangement. To address this issue, we propose a novel coarse-grained mesoscopic model that integrates a fluid-like cell membrane and a cytoskeletal network to study the dynamic phagocytosis process. The growth of actin filaments results in the formation of long and thin pseudopods, and the initial cytoskeleton can be disassembled upon target entry and reconstructed after phagocytosis. Through dynamic changes in the cytoskeleton, our macrophage model achieves active phagocytosis by forming a phagocytic cup utilizing pseudopods in two distinct ways. We have developed a new algorithm for modifying membrane area to prevent membrane rupture and ensure sufficient surface area during phagocytosis. In addition, the bending modulus, shear stiffness, and cortical tension of the macrophage model are investigated through computation of the axial force for the tubular structure and micropipette aspiration. With this model, we simulate active phagocytosis at the cytoskeletal level and investigate the mechanical process during the dynamic interplay between macrophage and target particles.

A Simulation of the Mechanical Testing of the Cell Membrane and Cytoskeleton

Cell models play a crucial role in analyzing the mechanical response of cells and quantifying cellular damage incurred during micromanipulation. While traditional models can capture the overall mechanical behavior of cells, they often lack the ability to discern among distinct cellular components. Consequently, by employing dissipative particle dynamics, this study constructed a triangular network-like representation of the cell membrane along with cross-linked cytoskeletal chains. The mechanical properties of both the membrane and cytoskeleton were then analyzed through a series of simulated mechanical tests, validated against real-world experiments. The investigation utilized particle-tracking rheology to monitor changes in the mean square displacements of membrane particles over time, facilitating the analysis of the membrane's storage and loss moduli. Additionally, the cytoskeletal network's storage and loss moduli were examined via a double-plate oscillatory shear experiment. The simulation results revealed that both the membrane and cytoskeleton exhibit viscoelastic behavior, as evidenced by the power-law dependency of their storage and loss moduli on frequency. Furthermore, indentation and microinjection simulations were conducted to examine the overall mechanical properties of cells. In the indentation experiments, an increase in the shear modulus of the membrane's WLCs correlated with a higher Young's modulus for the entire cell. Regarding the microinjection experiment, augmenting the microinjection speed resulted in reduced deformation of the cell at the point of membrane rupture and a lower percentage of high strain.

Signaling-biophysical modeling unravels mechanistic control of red blood cell phagocytosis by macrophages in sickle cell disease

Red blood cell (RBC) aging manifests through progressive changes in cell morphology, rigidity, and expression of membrane proteins. To maintain the quality of circulating blood, splenic macrophages detect the biochemical signals and biophysical changes of RBCs and selectively clear them through erythrophagocytosis. In sickle cell disease (SCD), RBCs display alterations affecting their interaction with macrophages, leading to aberrant phagocytosis that may cause life-threatening spleen sequestration crises. To illuminate the mechanistic control of RBC engulfment by macrophages in SCD, we integrate a system biology model of RBC-macrophage signaling interactions with a biophysical model of macrophage engulfment, as well as in vitro phagocytosis experiments using the spleen-on-a-chip technology. Our modeling framework accurately predicts the phagocytosis dynamics of RBCs under different disease conditions, reveals patterns distinguishing normal and sickle RBCs, and identifies molecular targets including Src homology 2 domain-containing protein tyrosine phosphatase-1 (SHP1) and cluster of differentiation 47 (CD47)/signal regulatory protein α (SIRPα) as therapeutic targets to facilitate the controlled clearance of sickle RBCs in the spleen.

Experimental measurement and numerical modeling of deformation behavior of breast cancer cells passing through constricted microfluidic channels

During the multistep process of metastasis, cancer cells encounter various mechanical forces which make them deform drastically. Developing accurate in-silico models, capable of simulating the interactions between the mechanical forces and highly deformable cancer cells, can pave the way for the development of novel diagnostic and predictive methods for metastatic progression. Spring-network models of cancer cell, empowered by our recently proposed identification approach, promises a versatile numerical tool for developing experimentally validated models that can simulate complex interactions at cellular scale. Using this numerical tool, we presented spring-network models of breast cancer cells that can accurately replicate the experimental data of deformation behavior of the cells flowing in a fluidic domain and passing narrow constrictions comparable to microcapillary. First, using high-speed imaging, we experimentally studied the deformability of breast cancer cell lines with varying metastatic potential (MCF-7 (less invasive), SKBR-3 (medium-high invasive), and MDA-MB-231 (highly invasive)) in terms of their entry time to a constricted microfluidic channel. We observed that MDA-MB-231, that has the highest metastatic potential, is the most deformable cell among the three. Then, by focusing on this cell line, experimental measurements were expanded to two more constricted microchannel dimensions. The experimental deformability data in three constricted microchannel sizes for various cell sizes, enabled accurate identification of the unknown parameters of the spring-network model of the breast cancer cell line (MDA-MB-231). Our results show that the identified parameters depend on the cell size, suggesting the need for a systematic procedure for identifying the size-dependent parameters of spring-network models of cells. As the numerical results show, the presented cell models can simulate the entry process of the cell into constricted channels with very good agreements with the measured experimental data.

Unraveling the motion and deformation characteristics of red blood cells in a deterministic lateral displacement device

Deterministic Lateral Displacement (DLD) device has gained widespread recognition and trusted for filtering blood cells. However, there remains a crucial need to explore the complex interplay between deformable cells and flow within the DLD device to improve its design. This paper presents an approach utilizing a mesoscopic cell-level numerical model based on dissipative particle dynamics to effectively capture this complex phenomenon. To establish the model's credibility, a series of numerical simulations were conducted and the numerical results were validated with nominal experimental data from the literature. These include single cell stretching experiment, comparisons of the morphological characteristics of cells in DLD, and comparison the specific row-shift fraction of DLD required to initiate the zigzag mode. Additionally, we investigate the effect of cell rigidity, which serves as an indicator of cell health, on average flow velocity, trajectory, and asphericity. Moreover, we extend the existing theory of predicting zigzag mode for solid spherical particles to encompass the behavior of red blood cells. To achieve this, we introduce a new concept of effective diameter and demonstrate its applicability in providing highly accurate predictions across a wide range of conditions.

A cell-and-plasma numerical model reveals hemodynamic stress and flow adaptation in zebrafish microvessels after morphological alteration

The development of a functional cardiovascular system ensures a sustainable oxygen, nutrient and hormone delivery system for successful embryonic development and homeostasis in adulthood. While early vessels are formed by biochemical signaling and genetic programming, the onset of blood flow provides mechanical cues that participate in vascular remodeling of the embryonic vascular system. The zebrafish is a prolific animal model for studying the quantitative relationship between blood flow and vascular morphogenesis due to a combination of favorable factors including blood flow visualization in optically transparent larvae. In this study, we have developed a cell-and-plasma blood transport model using computational fluid dynamics (CFD) to understand how red blood cell (RBC) partitioning affect lumen wall shear stress (WSS) and blood pressure in zebrafish trunk blood vascular networks with altered rheology and morphology. By performing live imaging of embryos with reduced hematocrit, we discovered that cardiac output and caudal artery flow rates were maintained. These adaptation trends were recapitulated in our CFD models, which showed reduction in network WSS via viscosity reduction in the caudal artery/vein and via pressure gradient weakening in the intersegmental vessels (ISVs). Embryos with experimentally reduced lumen diameter showed reduced cardiac output and caudal artery flow rate. Factoring in this trend into our CFD models, simulations highlighted that lumen diameter reduction increased vessel WSS but this increase was mitigated by flow reduction due to the adaptive network pressure gradient weakening. Additionally, hypothetical network CFD models with different vessel lumen diameter distribution characteristics indicated the significance of axial variation in lumen diameter and cross-sectional shape for establishing physiological WSS gradients along ISVs. In summary, our work demonstrates how both experiment-driven and hypothetical CFD modeling can be employed for the study of blood flow physiology during vascular remodeling.

Anisotropic short-range attractions precisely model branched erythrocyte aggregates

Homogeneous suspensions of red blood cells (RBCs or erythrocytes) in blood plasma are unstable in the absence of driving forces and form elongated stacks, called rouleaux. These erythrocyte aggregates are often branched porous networks - a feature that existing red blood cell aggregation models and simulations fail to predict exactly. Here we establish that alignment-dependent attractive forces in a system of dimers can precisely generate branched structures similar to RBC aggregates observed under a microscope. Our simulations consistently predict that the growth rate of typical mean rouleau size remains sub-linear - a hallmark from past studies - which we also confirm by deriving a reaction kernel taking into account appropriate collision cross-section, approach velocities, and an area-dependent sticking probability. The system exhibits unique features such as the existence of percolated and/or single giant cluster states, multiple coexisting mass-size scalings, and transition to a branched phase upon fine-tuning of model parameters. Upon decreasing the depletion thickness we find that the percolation threshold increases but the morphology of the structures opens up towards an increased degree of branching. Remarkably the system self-organizes to produce a universal power-law size distribution scaling irrespective of the model parameters.

Probing interactions of red blood cells and contracting fibrin platelet clots

Contraction of blood clots plays an important role in blood clotting, a natural process that restores hemostasis and regulates thrombosis in the body. Upon injury, a chain of events culminate in the formation of a soft plug of cells and fibrin fibers attaching to wound edges. Platelets become activated and apply contractile forces to shrink the overall clot size, modify clot structure, and mechanically stabilize the clot. Impaired blood clot contraction results in unhealthy volumetric, mechanical, and structural properties of blood clots associated with a range of severe medical conditions for patients with bleeding and thrombotic disorders. Due to the inherent mechanical complexity of blood clots and a confluence of multiple interdependent factors governing clot contraction, the mechanics and dynamics of clot contraction and the interactions with red blood cells (RBCs) remain elusive. Using an experimentally informed, physics-based mesoscale computational model, we probe the dynamic interactions among platelets, fibrin polymers, and RBCs, and examine the properties of contracted blood clots. Our simulations confirm that RBCs strongly affect clot contraction. We find that RBC retention and compaction in thrombi can be solely a result of mechanistic contraction of fibrin mesh due to platelet activity. Retention of RBCs hinders clot contraction and reduces clot contractility. Expulsion of RBCs located closer to clot outer surface results in the development of a dense fibrin shell in thrombus clots commonly observed in experiments. Our simulations identify the essential parameters and interactions that control blood clot contraction process, highlighting its dependence on platelet concentration and the initial clot size. Furthermore, our computational model can serve as a useful tool in clinically relevant studies of hemostasis and thrombosis disorders, and post thrombotic clot lysis, deformation, and breaking.

Single-cell characterization of deformation and dynamics of mesenchymal stem cells in microfluidic systems: A computational study

Understanding the homing dynamics of individual mesenchymal stem cells (MSCs) in physiologically relevant microenvironments is crucial for improving the efficacy of MSC-based therapies for therapeutic and targeting purposes. This study investigates the passive homing behavior of individual MSCs in micropores that mimic interendothelial clefts through predictive computational simulations informed by previous microfluidic experiments. Initially, we quantified the size-dependent behavior of MSCs in micropores and elucidated the underlying mechanisms. Subsequently, we analyzed the shape deformation and traversal dynamics of each MSC. In addition, we conducted a systematic investigation to understand how the mechanical properties of MSCs impact their traversal process. We considered geometric and mechanical parameters, such as reduced cell volume, cell-to-nucleus diameter ratio, and cytoskeletal prestress states. Furthermore, we quantified the changes in the MSC traversal process and identified the quantitative limits in their response to variations in micropore length. Taken together, the computational results indicate the complex dynamic behavior of individual MSCs in the confined microflow. This finding offers an objective way to evaluate the homing ability of MSCs in an interendothelial-slit-like microenvironment.

Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots

While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

In silico and in vitro study of the adhesion dynamics of erythrophagocytosis in sickle cell disease

Erythrophagocytosis occurring in the spleen is a critical process for removing senescent and diseased red blood cells (RBCs) from the microcirculation. Although some progress has been made in understanding how the biological signaling pathways mediate the phagocytic processes, the role of the biophysical interaction between RBCs and macrophages, particularly under pathological conditions such as sickle cell disease, has not been adequately studied. Here, we combine computational simulations with microfluidic experiments to quantify RBC-macrophage adhesion dynamics under flow conditions comparable to those in the red pulp of the spleen. We also investigate the RBC-macrophage interaction under normoxic and hypoxic conditions. First, we calibrate key model parameters in the adhesion model using microfluidic experiments for normal and sickle RBCs under normoxia and hypoxia. We then study the adhesion dynamics between the RBC and the macrophage. Our simulation illustrates three typical adhesion states, each characterized by a distinct dynamic motion of the RBCs, namely firm adhesion, flipping adhesion, and no adhesion (either due to no contact with macrophages or detachment from the macrophages). We also track the number of bonds formed when RBCs and macrophages are in contact, as well as the contact area between the two interacting cells, providing mechanistic explanations for the three adhesion states observed in the simulations and microfluidic experiments. Furthermore, we quantify, for the first time to our knowledge, the adhesive forces between RBCs (normal and sickle) and macrophages under different oxygenated conditions. Our results show that the adhesive forces between normal cells and macrophages under normoxia are in the range of 33-58 pN and 53-92 pN for sickle cells under normoxia and 155-170 pN for sickle cells under hypoxia. Taken together, our microfluidic and simulation results improve our understanding of the biophysical interaction between RBCs and macrophages in sickle cell disease and provide a solid foundation for investigating the filtration function of the splenic macrophages under physiological and pathological conditions.

A combined computational and experimental investigation of the filtration function of splenic macrophages in sickle cell disease

Being the largest lymphatic organ in the body, the spleen also constantly controls the quality of red blood cells (RBCs) in circulation through its two major filtration components, namely interendothelial slits (IES) and red pulp macrophages. In contrast to the extensive studies in understanding the filtration function of IES, there are relatively fewer works on investigating how the splenic macrophages retain the aged and diseased RBCs, i.e., RBCs in sickle cell disease (SCD). Herein, we perform a computational study informed by companion experiments to quantify the dynamics of RBCs captured and retained by the macrophages. We first calibrate the parameters in the computational model based on microfluidic experimental measurements for sickle RBCs under normoxia and hypoxia, as those parameters are not available in the literature. Next, we quantify the impact of a set of key factors that are expected to dictate the RBC retention by the macrophages in the spleen, namely, blood flow conditions, RBC aggregation, hematocrit, RBC morphology, and oxygen levels. Our simulation results show that hypoxic conditions could enhance the adhesion between the sickle RBCs and macrophages. This, in turn, increases the retention of RBCs by as much as five-fold, which could be a possible cause of RBC congestion in the spleen of patients with SCD. Our study on the impact of RBC aggregation illustrates a 'clustering effect', where multiple RBCs in one aggregate can make contact and adhere to the macrophages, leading to a higher retention rate than that resulting from RBC-macrophage pair interactions. Our simulations of sickle RBCs flowing past macrophages for a range of blood flow velocities indicate that the increased blood velocity could quickly attenuate the function of the red pulp macrophages on detaining aged or diseased RBCs, thereby providing a possible rationale for the slow blood flow in the open circulation of the spleen. Furthermore, we quantify the impact of RBC morphology on their tendency to be retained by the macrophages. We find that the sickle and granular-shaped RBCs are more likely to be filtered by macrophages in the spleen. This finding is consistent with the observation of low percentages of these two forms of sickle RBCs in the blood smear of SCD patients. Taken together, our experimental and simulation results aid in our quantitative understanding of the function of splenic macrophages in retaining the diseased RBCs and provide an opportunity to combine such knowledge with the current knowledge of the interaction between IES and traversing RBCs to apprehend the complete filtration function of the spleen in SCD.

In silico modeling of patient-specific blood rheology in type 2 diabetes mellitus

Increased blood viscosity in type 2 diabetes mellitus (T2DM) is a risk factor for the development of insulin resistance and diabetes-related vascular complications; however, individuals with T2DM exhibit heterogeneous hemorheological properties, including cell deformation and aggregation. Using a multiscale red blood cell (RBC) model with key parameters derived from patient-specific data, we present a computational study of the rheological properties of blood from individual patients with T2DM. Specifically, one key model parameter, which determines the shear stiffness of the RBC membrane (μ) is informed by the high-shear-rate blood viscosity of patients with T2DM. At the same time, the other, which contributes to the strength of the RBC aggregation interaction (D0), is derived from the low-shear-rate blood viscosity of patients with T2DM. The T2DM RBC suspensions are simulated at different shear rates, and the predicted blood viscosity is compared with clinical laboratory-measured data. The results show that the blood viscosity obtained from clinical laboratories and computational simulations are in agreement at both low and high shear rates. These quantitative simulation results demonstrate that the patient-specific model has truly learned the rheological behavior of T2DM blood by unifying the mechanical and aggregation factors of the RBCs, which provides an effective way to extract quantitative predictions of the rheological properties of the blood of individual patients with T2DM.

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.

Simulation of a tumor cell flowing through a symmetric bifurcated microvessel

Microvessel bifurcations serve as the major sites of tumor cell adhesion and further extravasation. In this study, the movement, deformation, and adhesion of a circulating tumor cell flowing in a symmetric microvessel with diverging and converging bifurcations were simulated by dissipative particle dynamics combined with a spring-based network model. Effects of the initial position of the CTC, externally-applied acceleration and the presence of RBCs on the motion of the CTC were investigated. The results demonstrated that the CTC released at the centerline of the parent vessel would attach to the vessel wall when arriving at the apex of diverging bifurcation and slide into the daughter branch determined by its centroid deflection and finally form firm adhesion at relatively lower flow rates. As the external acceleration increases, the increasing shear force enlarges the contact area for the adherent CTC on the one hand and reduces the residence time on the other hand. With the presence of RBCs in the bloodstream, the collision between the adherent tumor cell at the diverging bifurcation and flowing RBCs promotes the firm adhesion of CTC at lower flow rates.

The full model of micropipette aspiration of cells: A mesoscopic simulation

Studies on the interaction between cells and micromanipulation tools are necessary to optimize the procedures and improve the developmental potential of cells. The molecular dynamics simulation is not possible for such a large-scale simulation, and the spring-damped viscoelastic models and the constitutive equations of the continuum are usually adopted to model the cells as a whole without consideration of the different properties presented by the heterogeneous subcellular components. In this study, we utilized coarse-grained modeling to develop a subcellular model of suspension cell dynamics and a model of a holding micropipette for the fixation of a suspension cell, and designed a large-scale, accurate mesoscopic simulation environment for specific cell micromanipulation. We established a triangular mesh cell membrane and a uniformly distributed, non-intersecting cytoskeleton network and added polymerization/depolymerization processes to connect the cytoskeleton chains with the membrane and cross-linking proteins. In the cell aspiration model, we adopted the profile of the reversed Poiseuille flow to calibrate the viscosity of the fluid and set the bounce-back condition and the appropriate solid-fluid force coefficient to realize non-slip flow at the boundary. The rheological properties of the cells during micropipette aspiration were further analyzed in the simulation by varying parameters such as the inner diameter of the micropipette, negative pressure, and maximum bond length. The model well reproduced the experimentally observed cell deformation phenomenon at low and high pressures. The dynamic response of the cell elongation observed from the simulation was consistent with that obtained from the analysis of the experimental data collected from a custom-designed micromanipulation system. STATEMENT OF SIGNIFICANCE: In this study, we extended the coarse-grained modeling of cells by developing a relatively large-scale micromanipulation environment consisting of a subcellular cell dynamics model and a fluid flow model for cell aspiration. We simulated cytoskeleton filaments that were uniformly distributed in space via applying Harmonic energy to model cytoskeleton with a high level of fidelity. The shortcoming of the soft repulsion in the solid-fluid interaction in the current simulation technique was solved by implementing the bounce-back boundary and the condition that the total force imposed by the wall particles on the fluid particles was equal to the pressure of the fluid. This work paved the way for understanding the mechanical properties of cells and improving the biological efficacy of micromanipulation.

Quantifying Shear-induced Margination and Adhesion of Platelets in Microvascular Blood Flow

Platelet margination and adhesion are two critical and closely related steps in thrombus formation. Using dissipative particle dynamics (DPD) method that seamlessly models blood cells, blood plasma, and vessel walls with functionalized surfaces, we quantify the shear-induced margination and adhesion of platelets in microvascular blood flow. The results show that the occurrence of shear-induced RBC-platelet collisions has a remarkable influence on the degree of platelet margination. We characterize the lateral motion of individual platelets by a mean square displacement analysis of platelet trajectories, and find that the wall-induced lift force and the shear-induced displacement in wall-bounded flow cause the variation in near-wall platelet distribution. We then investigate the platelet adhesive dynamics under different flow conditions, by conducting DPD simulations of blood flow in a microtube with fibrinogen-coated wall surfaces. We find that the platelet adhesion is enhanced with the increase of fibrinogen concentration level but decreased with the increase of shear rate. These results are consistent with available experimental results. In addition, we demonstrate that the adherent platelets have a negative impact on the margination dynamics of the circulating platelets, which is mainly due to the climbing effect induced by the adherent ones. Taken together, these findings provide useful insights into the platelet margination and adhesion dynamics, which may facilitate the understanding of the predominant processes governing the initial stage of thrombus formation.

Probing the Interaction Between Supercarrier RBC Membrane and Nanoparticles for Optimal Drug Delivery

Red blood cell (RBC) membrane-hitchhiking nanoparticles (NPs) have been an increasingly popular supercarrier for targeted drug delivery. However, the kinetic details of the shear-induced NP detachment process from RBC in blood flow remain unclear. Here, we perform detailed computational simulations of the traversal dynamics of an RBC-NP composite supercarrier with tunable properties. We show that the detachment of NPs from RBC occurs in a shear-dependent manner which is consistent with previous experiment results. We quantify the NP detachment rate in the microcapillary flow, and our simulation results suggest that there may be an optimal adhesion strength span of 25-40 μJ/m² for rigid spherical NPs to improve the supercarrier performance and targeting efficiency. In addition, we find that the stiffness and the shape of NPs alter the detachment efficiency by changing the RBC-NP contact areas. Together, these findings provide unique insights into the shear-dependent NP release from the RBC surface, facilitating the clinical utility of RBC-NP composite supercarriers in targeted and localized drug delivery with high precision and efficiency.

Biomechanical activation of blood platelets via adhesion to von Willebrand factor studied with mesoscopic simulations

Platelet adhesion and activation are essential initial processes of arterial and microvascular hemostasis, where high hydrodynamic forces from the bloodflow impede coagulation. The process relies on von Willebrand factor (VWF)-a linear multimeric protein of blood plasma plays a pivotal role in mechanochemical regulation of shear-induced platelet aggregation (SIPA). Adhesive interactions between VWF and glycoprotein receptors GPIb are crucial for platelet recruitment under high shear stress in fluid. Recent advances in experimental studies revealed that mechanical tension on the extracellular part of GPIb may trigger a cascade of biochemical reactions in platelets leading to activation of integrins [Formula: see text] (also known as GPIIb/IIIa) and strengthening of the adhesion. The present paper is aimed at investigation of this process by three-dimensional computer simulations of platelet adhesion to surface-grafted VWF multimers in pressure-driven flow of platelet-rich plasma. The simulations demonstrate that GPIb-mediated mechanotransduction is a feasible way of platelet activation and stabilization of platelet aggregates under high shear stress. Quantitative understanding of mechanochemical processes involved in SIPA would potentially promote the discovery of new anti-platelet medication and the development of multiscale numerical models of platelet thrombosis and hemostasis.

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.

Circulating cell clusters aggravate the hemorheological abnormalities in COVID-19

Microthrombi and circulating cell clusters (CCCs) are common microscopic findings in patients with COVID-19 at different stages in the disease course, implying that they may function as the primary drivers in disease progression. Inspired by a recent flow imaging cytometry study of the blood samples from patients with COVID-19, we perform computational simulations to investigate the dynamics of different types of CCCs, namely white blood cell (WBC) clusters, platelet clusters and red blood cell (RBC) clusters, over a range of shear flows and quantify their impact on the viscosity of the blood. Our simulation results indicate that the increased level of fibrinogen in patients with COVID-19 can promote the formation of RBC clusters at relatively low shear rates, thereby elevating the blood viscosity, a mechanism that also leads to an increase in viscosity in other blood diseases, such as sickle cell disease and type 2 diabetes mellitus. We further discover that the presence of WBC clusters could also aggravate the abnormalities of local blood rheology. In particular, the extent of elevation of the local blood viscosity is enlarged as the size of the WBC clusters grows. On the other hand, the impact of platelet clusters on the local rheology is found to be negligible, which is likely due to the smaller size of the platelets. The difference in the impact of WBC and platelet clusters on local hemorheology provides a compelling explanation for the clinical finding that the number of WBC clusters is significantly correlated with thrombotic events in COVID-19 whereas platelet clusters do not. Overall, our study demonstrates that our computational models based on dissipative particle dynamics can serve as a powerful tool to conduct quantitative investigation of the mechanism causing the pathological alterations of hemorheology and explore their connections to the clinical manifestations in COVID-19.

Stability preserving data-driven models with latent dynamics

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a given data set. We present a model framework where the stability of the coupled dynamics can be easily enforced. The model is implemented by recurrent cells and trained using backpropagation through time. Numerical examples using benchmark tests from order reduction problems demonstrate the stability of the model and the efficiency of the recurrent cell implementation. As applications, two fluid-structure interaction problems are considered to illustrate the accuracy and predictive capability of the model.

Molecular Modeling in Anion Exchange Membrane Research: A Brief Review of Recent Applications

Anion Exchange Membrane (AEM) fuel cells have attracted growing interest, due to their encouraging advantages, including high power density and relatively low cost. AEM is a polymer matrix, which conducts hydroxide (OH−) ions, prevents physical contact of electrodes, and has positively charged head groups (mainly quaternary ammonium (QA) groups), covalently bound to the polymer backbone. The chemical instability of the quaternary ammonium (QA)-based head groups, at alkaline pH and elevated temperature, is a significant threshold in AEMFC technology. This review work aims to introduce recent studies on the chemical stability of various QA-based head groups and transportation of OH− ions in AEMFC, via modeling and simulation techniques, at different scales. It starts by introducing the fundamental theories behind AEM-based fuel-cell technology. In the main body of this review, we present selected computational studies that deal with the effects of various parameters on AEMs, via a variety of multi-length and multi-time-scale modeling and simulation methods. Such methods include electronic structure calculations via the quantum Density Functional Theory (DFT), ab initio, classical all-atom Molecular Dynamics (MD) simulations, and coarse-grained MD simulations. The explored processing and structural parameters include temperature, hydration levels, several QA-based head groups, various types of QA-based head groups and backbones, etc. Nowadays, many methods and software packages for molecular and materials modeling are available. Applications of such methods may help to understand the transportation mechanisms of OH− ions, the chemical stability of functional head groups, and many other relevant properties, leading to a performance-based molecular and structure design as well as, ultimately, improved AEM-based fuel cell performances. This contribution aims to introduce those molecular modeling methods and their recent applications to the AEM-based fuel cells research community.

A new membrane formulation for modelling the flow of stomatocyte, discocyte, and echinocyte red blood cells

In this work, a numerical model that enables simulation of the deformation and flow behaviour of differently aged Red Blood Cells (RBCs) is developed. Such cells change shape and decrease in deformability as they age, thus impacting their ability to pass through the narrow capillaries in the body. While the body filters unviable cells from the blood naturally, cell aging poses key challenges for blood stored for transfusions. Therefore, understanding the influence RBC morphology and deformability have on their flow is vital. While several existing models represent young Discocyte RBC shapes well, a limited number of numerical models are developed to model aged RBC morphologies like Stomatocytes and Echinocytes. The existing models are also limited to shear and stretching simulations. Flow characteristics of these morphologies are yet to be investigated. This paper aims to develop a new membrane formulation for the numerical modelling of Stomatocyte, Discocytes and Echinocyte RBC morphologies to investigate their deformation and flow behaviour. The model used represents blood plasma using the Lattice Boltzmann Method (LBM) and the RBC membrane using the discrete element method (DEM). The membrane and the plasma are coupled by the Immersed Boundary Method (IBM). Previous LBM-IBM-DEM formulations represent RBC membrane response based on forces generated from changes in the local area, local length, local bending, and cell volume. In this new model, two new force terms are added: the local area difference force and the local curvature force, which are specially incorporated to model the flow and deformation behaviour of Stomatocytes and Echinocytes. To verify the developed model, the deformation behaviour of the three types of RBC morphologies are compared to well-characterised stretching and shear experiments. The flow modelling capabilities of the method are then demonstrated by modelling the flow of each cell through a narrow capillary. The developed model is found to be as accurate as benchmark Smoothed Particle Hydrodynamics (SPH) approaches while being significantly more computationally efficient.

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.

Multiphysics and multiscale modeling of microthrombosis in COVID-19

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients’ fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis.

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. We employ a novel multiphysics and multiscale computational framework to investigate the underlying mechanism of the pathological formation of microthrombi and circulating cell clusters in COVID-19. We quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19, through which we identify the potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19.

Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Projection-based model reduction for the immersed boundary method

Fluid-structure interactions are central to many biomolecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to alleviate the computational cost, we apply reduced-order techniques to eliminate the degrees of freedom associated with the large number of fluid variables. We show how reduced models can be derived using Petrov-Galerkin projection and subspaces that maintain the incompressibility condition. More importantly, the reduced-order model (ROM) is shown to preserve the Lyapunov stability. We also address the practical issue of computing coefficient matrices in the ROM using an interpolation technique. The efficiency and robustness of the proposed formulation are examined with test examples from various applications.

The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.

Recent Advances in Computational Modeling of Biomechanics and Biorheology of Red Blood Cells in Diabetes

Diabetes mellitus, a metabolic disease characterized by chronically elevated blood glucose levels, affects about 29 million Americans and more than 422 million adults all over the world. Particularly, type 2 diabetes mellitus (T2DM) accounts for 90-95% of the cases of vascular disease and its prevalence is increasing due to the rising obesity rates in modern societies. Although multiple factors associated with diabetes, such as reduced red blood cell (RBC) deformability, enhanced RBC aggregation and adhesion to the endothelium, as well as elevated blood viscosity are thought to contribute to the hemodynamic impairment and vascular occlusion, clinical or experimental studies cannot directly quantify the contributions of these factors to the abnormal hematology in T2DM. Recently, computational modeling has been employed to dissect the impacts of the aberrant biomechanics of diabetic RBCs and their adverse effects on microcirculation. In this review, we summarize the recent advances in the developments and applications of computational models in investigating the abnormal properties of diabetic blood from the cellular level to the vascular level. We expect that this review will motivate and steer the development of new models in this area and shift the attention of the community from conventional laboratory studies to combined experimental and computational investigations, aiming to provide new inspirations for the development of advanced tools to improve our understanding of the pathogenesis and pathology of T2DM.

Computational investigation of blood cell transport in retinal microaneurysms

Microaneurysms (MAs) are one of the earliest clinically visible signs of diabetic retinopathy (DR). MA leakage or rupture may precipitate local pathology in the surrounding neural retina that impacts visual function. Thrombosis in MAs may affect their turnover time, an indicator associated with visual and anatomic outcomes in the diabetic eyes. In this work, we perform computational modeling of blood flow in microchannels containing various MAs to investigate the pathologies of MAs in DR. The particle-based model employed in this study can explicitly represent red blood cells (RBCs) and platelets as well as their interaction in the blood flow, a process that is very difficult to observe in vivo. Our simulations illustrate that while the main blood flow from the parent vessels can perfuse the entire lumen of MAs with small body-to-neck ratio (BNR), it can only perfuse part of the lumen in MAs with large BNR, particularly at a low hematocrit level, leading to possible hypoxic conditions inside MAs. We also quantify the impacts of the size of MAs, blood flow velocity, hematocrit and RBC stiffness and adhesion on the likelihood of platelets entering MAs as well as their residence time inside, two factors that are thought to be associated with thrombus formation in MAs. Our results show that enlarged MA size, increased blood velocity and hematocrit in the parent vessel of MAs as well as the RBC-RBC adhesion promote the migration of platelets into MAs and also prolong their residence time, thereby increasing the propensity of thrombosis within MAs. Overall, our work suggests that computational simulations using particle-based models can help to understand the microvascular pathology pertaining to MAs in DR and provide insights to stimulate and steer new experimental and computational studies in this area.

Curvature-Mediated Pair Interactions of Soft Nanoparticles Adhered to a Cell Membrane

The curvature-mediated interactions by cell membranes are crucial in many biological processes. We systematically studied the curvature-mediated wrapping of soft nanoparticles (NPs) by a tensionless membrane and the underlying pair interactions between NPs in determining it. We found that there are three types of wrapping pathways, namely, independence, cooperation, and tubulation. The particle size, adhesion strength, and softness are found to be strongly related with the wrapping mechanism. Reducing the adhesion strength transforms the wrapping pathway from cooperation to independence, while enhancing the NP softness requires a stronger adhesion to achieve the cooperative wrapping. This transformation of the wrapping pathway is controlled by the curvature-mediated interactions between NPs. For either soft or rigid NPs, the pair interactions are repulsive at short-ranged distances between NPs, while at long-ranged distances, a larger adhesion between NPs and a membrane is needed to generate attraction between NPs. Moreover, an enhancement of NP softness weakens the repulsion between NPs. These distinct behaviors of soft NPs are ascribed to the gentler deformation of the membrane at the face-to-face region between NPs due to the flattening and spreading of soft NPs along the membrane, requiring a reduced energy cost for soft NPs to approach each other. Our results provide a mechanistic understanding in detail about the membrane-mediated interactions between NPs and their interactions with cell membranes, which is helpful to understand the curvature-mediated assemblies of adhesive proteins or NPs on membranes, and offer novel possibilities for designing an effective NP-based vehicle for controlled drug delivery.

A systematic approach for developing mechanistic models for realistic simulation of cancer cell motion and deformation

Understanding and predicting metastatic progression and developing novel diagnostic methods can highly benefit from accurate models of the deformability of cancer cells. Spring-based network models of cells can provide a versatile way of integrating deforming cancer cells with other physical and biochemical phenomena, but these models have parameters that need to be accurately identified. In this study we established a systematic method for identifying parameters of spring-network models of cancer cells. We developed a genetic algorithm and coupled it to the fluid-solid interaction model of the cell, immersed in blood plasma or other fluids, to minimize the difference between numerical and experimental data of cell motion and deformation. We used the method to create a validated model for the human lung cancer cell line (H1975), employing existing experimental data of its deformation in a narrow microchannel constriction considering cell-wall friction. Furthermore, using this validated model with accurately identified parameters, we studied the details of motion and deformation of the cancer cell in the microchannel constriction and the effects of flow rates on them. We found that ignoring the viscosity of the cell membrane and the friction between the cell and wall can introduce remarkable errors.

How the spleen reshapes and retains young and old red blood cells: A computational investigation

The spleen, the largest secondary lymphoid organ in humans, not only fulfils a broad range of immune functions, but also plays an important role in red blood cell’s (RBC) life cycle. Although much progress has been made to elucidate the critical biological processes involved in the maturation of young RBCs (reticulocytes) as well as removal of senescent RBCs in the spleen, the underlying mechanisms driving these processes are still obscure. Herein, we perform a computational study to simulate the passage of RBCs through interendothelial slits (IES) in the spleen at different stages of their lifespan and investigate the role of the spleen in facilitating the maturation of reticulocytes and in clearing the senescent RBCs. Our simulations reveal that at the beginning of the RBC life cycle, intracellular non-deformable particles in reticulocytes can be biomechanically expelled from the cell upon passage through IES, an insightful explanation of why this peculiar “pitting” process is spleen-specific. Our results also show that immature RBCs shed surface area by releasing vesicles after crossing IES and progressively acquire the biconcave shape of mature RBCs. These findings likely explain why RBCs from splenectomized patients are significantly larger than those from nonsplenectomized subjects. Finally, we show that at the end of their life span, senescent RBCs are not only retained by IES due to reduced deformability but also become susceptible to mechanical lysis under shear stress. This finding supports the recent hypothesis that transformation into a hemolyzed ghost is a prerequisite for phagocytosis of senescent RBCs. Altogether, our computational investigation illustrates critical biological processes in the spleen that cannot be observed in vivo or in vitro and offer insights into the role of the spleen in the RBC physiology.

The spleen, the largest secondary lymphoid organ in humans, not only fulfils a broad range of immune functions, but also plays an important role in red blood cell (RBC) life cycle. In this study, we perform a computational study to simulate the passage of RBCs through interendothelial slits (IES) in the spleen at different stages of their lifespan, a critical biological process that cannot be observed in humans. Our simulation results illustrate a specific role of spleen in shaping young RBCs, which points to a probable missing step in current in vitro RBC culture protocols that fail to generate a majority of typical biconcave RBCs. Our results also reveal that intra-splenic mechanical constraints likely contribute to the final clearance and elimination of aged RBCs. Altogether, we demonstrate that our computational model can provide mechanistic rationales for experimental studies, offer insights into the role of the spleen in the RBC physiology and help the optimization of in vitro RBC culture techniques.

Computational modeling of biomechanics and biorheology of heated red blood cells

Because of their compromised deformability, heat denatured erythrocytes have been used as labeled probes to visualize spleen tissue or to assess the ability of the spleen to retain stiff red blood cells (RBCs) for over three decades, e.g., see Looareesuwan et al. N. Engl. J. Med. (1987). Despite their good accessibility, it is still an open question how heated RBCs compare to certain diseased RBCs in terms of their biomechanical and biorheological responses, which may undermine their effective usage and even lead to misleading experimental observations. To help answering this question, we perform a systematic computational study of the hemorheological properties of heated RBCs with several physiologically relevant static and hemodynamic settings, including optical-tweezers test, relaxation of prestretched RBCs, RBC traversal through a capillary-like channel and a spleen-like slit, and a viscometric rheology test. We show that our in silico RBC models agree well with existing experiments. Moreover, under static tests, heated RBCs exhibit deformability deterioration comparable to certain disease-impaired RBCs such as those in malaria. For RBC traversal under confinement (through microchannel or slit), heated RBCs show prolonged transit time or retention depending on the level of confinement and heating procedure, suggesting that carefully heat-treated RBCs may be useful for studying splenic- or vaso-occlusion in vascular pathologies. For the rheology test, we expand the existing bulk viscosity data of heated RBCs to a wider range of shear rates (1-1000 s^-1) to represent most pathophysiological conditions in macro- or microcirculation. Although heated RBC suspension shows elevated viscosity comparable to certain diseased RBC suspensions under relatively high shear rates (100-1000 s^-1), they underestimate the elevated viscosity (e.g., in sickle cell anemia) at low shear rates (<10 s^-1). Our work provides mechanistic rationale for selective usage of heated RBC as a potentially useful model for studying the abnormal traversal dynamics and hemorheology in certain blood disorders.

In-Flow dynamics of an area-difference-energy spring-particle red blood cell model on non-uniform grids

In this paper the area-difference-energy spring-particle (ADE-SP) red blood cell (RBC) structural model developed by Chen and Boyle is coupled with a lattice Boltzmann flux solver to simulate RBC dynamics. The novel ADE-SP model accounts for bending resistance due to the membrane area difference of RBCs while the lattice Boltzmann flux solver offers reduced computational runtimes through GPU parallelisation and enabling the employment of non-uniform meshes. This coupled model is used to simulate RBC dynamics and predictions are compared with existing experimental measurements. The simulations successfully predict tumbling, tank-treading, swinging and intermittent behaviour of an RBC in shear flow, and demonstrate the capability of the model in capturing in-flow RBC behaviours.

Margination and adhesion dynamics of tumor cells in a real microvascular network

In tumor metastasis, the margination and adhesion of tumor cells are two critical and closely related steps, which may determine the destination where the tumor cells extravasate to. We performed a direct three-dimensional simulation on the behaviors of the tumor cells in a real microvascular network, by a hybrid method of the smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). The tumor cells are found to adhere at the microvascular bifurcations more frequently, and there is a positive correlation between the adhesion of the tumor cells and the wall-directed force from the surrounding red blood cells (RBCs). The larger the wall-directed force is, the closer the tumor cells are marginated towards the wall, and the higher the probability of adhesion behavior happen is. A relatively low or high hematocrit can help to prevent the adhesion of tumor cells, and similarly, increasing the shear rate of blood flow can serve the same purpose. These results suggest that the tumor cells may be more likely to extravasate at the microvascular bifurcations if the blood flow is slow and the hematocrit is moderate.

Integrating blood cell mechanics, platelet adhesive dynamics and coagulation cascade for modelling thrombus formation in normal and diabetic blood

Normal haemostasis is an important physiological mechanism that prevents excessive bleeding during trauma, whereas the pathological thrombosis especially in diabetics leads to increased incidence of heart attacks and strokes as well as peripheral vascular events. In this work, we propose a new multiscale framework that integrates seamlessly four key components of blood clotting, namely transport of coagulation factors, coagulation kinetics, blood cell mechanics and platelet adhesive dynamics, to model the development of thrombi under physiological and pathological conditions. We implement this framework to simulate platelet adhesion due to the exposure of tissue factor in a three-dimensional microchannel. Our results show that our model can simulate thrombin-mediated platelet activation in the flowing blood, resulting in platelet adhesion to the injury site of the channel wall. Furthermore, we simulate platelet adhesion in diabetic blood, and our results show that both the pathological alterations in the biomechanics of blood cells and changes in the amount of coagulation factors contribute to the excessive platelet adhesion and aggregation in diabetic blood. Taken together, this new framework can be used to probe synergistic mechanisms of thrombus formation under physiological and pathological conditions, and open new directions in modelling complex biological problems that involve several multiscale processes.

PyOIF: Computational tool for modelling of multi-cell flows in complex geometries

A user ready, well documented software package PyOIF contains an implementation of a robust validated computational model for cell flow modelling. The software is capable of simulating processes involving biological cells immersed in a fluid. The examples of such processes are flows in microfluidic channels with numerous applications such as cell sorting, rare cell isolation or flow fractionation. Besides the typical usage of such computational model in the design process of microfluidic devices, PyOIF has been used in the computer-aided discovery involving mechanical properties of cell membranes. With this software, single cell, many cell, as well as dense cell suspensions can be simulated. Many cell simulations include cell-cell interactions and analyse their effect on the cells. PyOIF can be used to test the influence of mechanical properties of the membrane in flows and in membrane-membrane interactions. Dense suspensions may be used to study the effect of cell volume fraction on macroscopic phenomena such as cell-free layer, apparent suspension viscosity or cell degradation. The PyOIF module is based on the official ESPResSo distribution with few modifications and is available under the terms of the GNU General Public Licence. PyOIF is based on Python objects representing the cells and on the C++ computational core for fluid and interaction dynamics. The source code is freely available at GitHub repository, runs natively under Linux and MacOS and can be used in Windows Subsystem for Linux. The communication among PyOIF users and developers is maintained using active mailing lists. This work provides a basic background to the underlying computational models and to the implementation of interactions within this framework. We provide the prospective PyOIF users with a practical example of simulation script with reference to our publicly available User Guide.

Dynamic and reversible shape response of red blood cells in synthetic liquid crystals

Mammalian cells are soft, and correct functioning requires that cells undergo dynamic shape changes in vivo. Although a range of diseases are associated with stiffening of red blood cells (RBCs; e.g., sickle cell anemia or malaria), the mechanical properties and thus shape responses of cells to complex viscoelastic environments are poorly understood. We use vapor pressure measurements to identify aqueous liquid crystals (LCs) that are in osmotic equilibrium with RBCs and explore mechanical coupling between RBCs and LCs. When transferred from an isotropic aqueous phase into a LC, RBCs exhibit complex yet reversible shape transformations, from initially biconcave disks to elongated and folded geometries with noncircular cross-sections. Importantly, whereas the shapes of RBCs are similar in isotropic fluids, when strained by LC, a large variance in shape response is measured, thus unmasking cell-to-cell variation in mechanical properties. Numerical modeling of LC and cell mechanics reveals that RBC shape responses occur at constant cell membrane area but with membrane shear moduli that vary between cells from 2 to 16 × 10^-6 N/m. Temperature-dependent LC elasticity permits continuous tuning of RBC strains, and chemical cross-linking of RBCs, a model for diseased cells, leads to striking changes in shape responses of the RBCs. Overall, these results provide insight into the coupling of strain between soft mammalian cells and synthetic LCs, and hint at new methods for rapidly characterizing mechanical properties of single mammalian cells in a population and thus cell-to-cell variance.

Quantifying Fibrinogen-Dependent Aggregation of Red Blood Cells in Type 2 Diabetes Mellitus

Fibrinogen is regarded as the main glycoprotein in the aggregation of red blood cells (RBCs), a normally occurring phenomenon that has a major impact on blood rheology and hemodynamics, especially under pathological conditions, including type 2 diabetes mellitus (T2DM). In this study, we investigate the fibrinogen-dependent aggregation dynamics of T2DM RBCs through patient-specific predictive computational simulations that invoke key parameters derived from microfluidic experiments. We first calibrate our model parameters at the doublet (a rouleau consisting of two aggregated RBCs) level for healthy blood samples by matching the detaching force required to fully separate RBC doublets with measurements using atomic force microscopy and optical tweezers. Using results from companion microfluidic experiments that also provide in vitro quantitative information on cell-cell adhesive dynamics, we then quantify the rouleau dissociation dynamics at the doublet and multiplet (a rouleau consisting of three or more aggregated RBCs) levels for obese patients with or without T2DM. Specifically, we examine the rouleau breakup rate when it passes through microgates at doublet level and investigate the effect of rouleau alignment in altering its breakup pattern at multiplet level. This study seamlessly integrates in vitro experiments and simulations and consequently enhances our understanding of the complex cell-cell interaction, highlighting the importance of the aggregation and disaggregation dynamics of RBCs in patients at increased risk of microvascular complications.

A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

Red blood cells (RBCs) can deform substantially, a feature that allows them to pass through capillaries that are narrower than the largest dimension of an undeformed RBC. Clearly, to understand how they transport through our microcirculation, we need a constitutive model able of accurately predicting the deformability of RBCs, which seems currently unavailable. To address this void, we herein propose a new model that accounts for the deformability of RBCs by modeling them as deformed droplets with a constant volume. To make sure the model is by construction thermodynamically admissible we employ non-equilibrium thermodynamics as our tool. Since RBCs are merely droplets with the inner fluid exhibiting a higher viscosity than that of the outer one, RBCs are described by a conformation tensor constrained to have a constant determinant (volume). The model predicts the second normal stress coefficient in steady-state simple shear flow to first shear thicken and then shear thin, which is an unexpected behavior; however, we cannot judge whether such a prediction is aphysical or not due to unavailable experimental rheological data in the literature. We show that the new model is capable of addressing the deformability of isolated (very low hematocrit) RBCs in simple shear and the shear viscosity of non-aggregating blood. As derived the model addresses only non-aggregating blood, but can very easily be generalized to account for aggregating blood.

Heterogeneous partition of cellular blood-borne nanoparticles through microvascular bifurcations

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically.