Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model

Actin instability alters red blood cell mechanics and Piezo1 channel activity

The organization and dynamics of the spectrin-actin membrane cytoskeleton play a crucial role in determining the mechanical properties of red blood cells (RBC). RBC are subjected to various forces that induce deformation during blood microcirculation. Such forces also regulate membrane tension, leading to Piezo1 channel activation, which is functionally linked to RBC dehydration through calcium influx and subsequent activation of Gardos channels, ultimately resulting in variations in RBC volume. In this study, we investigated how actin instability affects Piezo1 channel gating, in relation to RBC deformation and mechanical properties, using micropipette aspiration and optical tweezers. Actin instability, induced by 0.5 μM Cytochalasin-D (Cyt-D), led to a 22% reduction in the activation pressure. Additionally, we observed a decreasing trend in Young's modulus, membrane tension, and viscosity. By measuring the time required for cell shape recovery after deformation in an optical trap, we found that Cyt-D-treated RBC took approximately 14% longer to recover compared to untreated cells. The bimodal imaging feature of our experimental approach allowed us to simultaneously measure and correlate activation pressure with mechanical properties at the single-cell level. A significant correlation was found between these parameters in both treated and untreated RBC. Our findings demonstrate the influence of actin instability on both Piezo1 activation and RBC mechanics. These results offer new insights into the interplay between F-actin and Piezo1 in RBC mechanobiology.

Viscoelasticity of diverse biological samples quantified by Acoustic Force Microrheology (AFMR)

In the context of soft matter and cellular mechanics, microrheology - the use of micron-sized particles to probe the frequency-dependent viscoelastic response of materials - is widely used to shed light onto the mechanics and dynamics of molecular structures. Here we present the implementation of active microrheology in an Acoustic Force Spectroscopy setup (AFMR), which combines multiplexing with the possibility of probing a wide range of forces ( ~ pN to ~nN) and frequencies (0.01-100 Hz). To demonstrate the potential of this approach, we perform active microrheology on biological samples of increasing complexity and stiffness: collagen gels, red blood cells (RBCs), and human fibroblasts, spanning a viscoelastic modulus range of five orders of magnitude. We show that AFMR can successfully quantify viscoelastic properties by probing many beads with high single-particle precision and reproducibility. Finally, we demonstrate that AFMR to map local sample heterogeneities as well as detect cellular responses to drugs.

Shape Transitions of Red Blood Cell under Oscillatory Flows in Microchannels

This paper aims to examine the ability to control Red Blood Cell (RBCs) dynamics and the associated extracellular flow patterns in microfluidic channels via oscillatory flows. Our computational approach employs a hybrid continuum-particle coupling, in which the cell membrane and cytosol fluid are modeled using the Dissipative Particle Dynamics (DPD) method. The blood plasma is modeled as an incompressible fluid via the Immersed Boundary Method (IBM). This coupling is novel because it provides an accurate description of RBC dynamics while the extracellular flow patterns around the RBCs are also captured in detail. Our coupling methodology is validated with available experimental and computational data in the literature and shows excellent agreement. We explore the controlling regimes by varying the shape of the oscillatory flow waveform at the channel inlet. Our simulation results show that a host of RBC morphological dynamics emerges depending on the channel geometry, the incoming flow waveform, and the RBC initial location. Complex dynamics of RBC are induced by the flow waveform. Our results show that the RBC shape is strongly dependent on its initial location. Our results suggest that the controlling of oscillatory flows can be used to induce specific morphological shapes of RBCs and the surrounding fluid patterns in bio-engineering applications.

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.

Dynamic response of red blood cells in health and disease

The viscoelastic response of the red blood cells (RBCs) affected by hematological disorders become severely impaired by the altered biophysical and morphological properties. These include traits like reduced deformability, increased membrane viscosity, and change in cell shape, causing substantial changes in the overall hemodynamics. RBCs, by virtue of their highly elastic membrane and low bending rigidity, exhibit complex dynamics when exposed to cyclic, transient forces in the microcirculation. Here, we employ mesoscopic numerical simulations based on the dissipative particle dynamics (DPD) framework to explore the dynamics of healthy, schizont stage malaria-infected and type 2 diabetes mellitus affected RBCs subjected to external time-dependent loads. The paper focuses on the imposition and cessation of external forcing on the cells of two different typologies, saw-tooth cyclic wave loading and sudden loads in the form of creep and relaxation phenomena. The effects of varying the rate of stress and the applied stress magnitude were investigated. Our simulations disclosed unique shape transitions of the hysteresis curves at varied loading rates. A careful analysis reveals a critical threshold of half cycle time of the from wherein the deformation of all cells observed, healthy or otherwise, falls under the nearly reversible deformation regime displaying minimal energy dissipation. Finally, we also examined the individual effects of the different constitutive and geometric characteristics attributed to the pathological cells and observed interesting recovery dynamics of spherocytes and cells having high shear moduli. The distinguished deformation behaviour of healthy and diseased cells could establish external force as a valuable initial biomarker.

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.

Microfluidic technologies for cell deformability cytometry

Microfluidic detection methods for cell deformability cytometry have been regarded as powerful tools for single-cell analysis of cellular mechanical phenotypes, thus having been widely applied in the fields of cell preparation, separation, clinical diagnostics and so on. Featured with traits like easy operations, low cost and high throughput, such methods have shown great potentials on investigating physiological state and pathological changes during cellular deformation. Herein, a review on the advancements of microfluidic-based cell deformation cytometry is presented. We discuss several representative microfluidic-based cell deformability cytometry methods with their frontiers in practical applications. Finally, we analyze the current status and propose the remaining challenges with future perspectives and development directions.

The Cell Physiome: What Do We Need in a Computational Physiology Framework for Predicting Single-Cell Biology?

Modern biology and biomedicine are undergoing a big data explosion, needing advanced computational algorithms to extract mechanistic insights on the physiological state of living cells. We present the motivation for the Cell Physiome project: a framework and approach for creating, sharing, and using biophysics-based computational models of single-cell physiology. Using examples in calcium signaling, bioenergetics, and endosomal trafficking, we highlight the need for spatially detailed, biophysics-based computational models to uncover new mechanisms underlying cell biology. We review progress and challenges to date toward creating cell physiome models. We then introduce bond graphs as an efficient way to create cell physiome models that integrate chemical, mechanical, electromagnetic, and thermal processes while maintaining mass and energy balance. Bond graphs enhance modularization and reusability of computational models of cells at scale. We conclude with a look forward at steps that will help fully realize this exciting new field of mechanistic biomedical data science. Expected final online publication date for the Annual Review of Biomedical Data Science, Volume 5 is August 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Scale-invariance in miniature coarse-grained red blood cells by fluctuation analysis

To accurately represent the morphological and elastic properties of a human red blood cell, Fu et al. [Fu et al., Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, 2017, 210, 193-203] recently developed a coarse-grained molecular dynamics model with particular detail in the membrane. However, such a model accrues an extremely high computational cost for whole-cell simulation when assuming an appropriate length scaling - that of the bilayer thickness. To date, the model has only simulated "miniature" cells in order to circumvent this, with the a priori assumption that these miniaturised cells correctly represent their full-sized counterparts. The present work assesses the validity of this approach, by testing the scale invariance of the model through simulating cells of various diameters; first qualitatively in their shape evolution, then quantitatively by measuring their bending rigidity through fluctuation analysis. Cells of diameter of at least 0.5 μm were able to form the characteristic biconcave shape of human red blood cells, though smaller cells instead equilibrated to bowl-shaped stomatocytes. Thermal fluctuation analysis showed the bending rigidity to be constant over all cell sizes tested, and consistent between measurements on the whole-cell and on a planar section of bilayer. This is as expected from the theory on both counts. Therefore, we confirm that the evaluated model is a good representation of a full-size RBC when the model diameter is ≥0.5 μm, in terms of the morphological and mechanical properties investigated.

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.

Impact of gap size and groove design of hydrodynamic bearing on plasma skimming effect for use in rotary blood pump

Plasma skimming can exclude red blood cells from high shear regions in the gaps formed by hydrodynamic bearings in rotary blood pumps. We investigated the effect of the gap size and groove design on the plasma skimming efficiency. Spiral groove bearings (SGBs) were installed into a specially designed test rig for in vitro experiments performed using human blood. The measured gap between the ridges of the bearing and the rotor surface was 17-26 µm at a flow rate of 150 ml/min and a rotor speed of 2400 rpm. Three different patterns of SGBs were designed (SGB-0, SGB-30, and SGB-60) with various degrees of the circumferential component. The hematocrit measured by a high-speed camera was compared with the hematocrit in the circuit, and the plasma skimming efficiency for the three bearing patterns was evaluated at hematocrits of 20%, 25%, and 30%. SGB-60, which had the strongest circumferential component, provided the best plasma skimming efficiency. When the gap size was less than 20 µm, the red blood cells in the gaps between the ridges of the bearing and rotor surface reduced significantly and the efficiency became higher than 90%. The gap size had the strongest effect on producing a significant plasma skimming. The plasma skimming efficiency can be significantly improved by optimizing the bearing gap size and groove design, which facilitates the further development of SGBs for use in applications such as rotary blood pumps.

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.

Research on Human Erythrocyte's Threshold Free Energy for Hemolysis and Damage from Coupling Effect of Shear and Impact Based on Immersed Boundary-Lattice Boltzmann Method

Researches on the principle of human red blood cell's (RBC) injuring and judgment basis play an important role in decreasing the hemolysis in a blood pump. In the current study, the judgment of hemolysis in a blood pump study was through some experiment data and empirical formula. The paper forms a criterion of RBC's mechanical injury in the aspect of RBC's free energy. First, the paper introduces the nonlinear spring network model of RBC in the frame of immersed boundary-lattice Boltzmann method (IB-LBM). Then, the shape, free energy, and time needed for erythrocyte to be shorn in different shear flow and impacted in different impact flow are simulated. Combining existing research on RBC's threshold limit for hemolysis in shear and impact flow with this paper's, the RBC's free energy of the threshold limit for hemolysis is found to be 3.46 × 10⁻¹⁵ J. The threshold impact velocity of RBC for hemolysis is 8.68 m/s. The threshold value of RBC can be used for judgment of RBC's damage when the RBC is having a complicated flow of blood pumps such as coupling effect of shear and impact flow. According to the change law of RBC's free energy in the process of being shorn and impacted, this paper proposed a judging criterion for hemolysis when the RBC is under the coupling effect of shear and impact based on the increased free energy of RBC.

Definitions of local density in density-dependent potentials for mixtures

Density-dependent potentials are frequently used in materials simulations because of their approximate description of many-body effects at minimal computational cost. However, in order to apply such models to multicomponent systems, an appropriate definition of total local particle density is required. Here, we discuss two definitions of local density in the context of many-body dissipative particle dynamics. We show that only a potential which combines local densities from all particle types in its argument gives physically meaningful results for all composition ratios. Drawing on the ideas from metal potentials, we redefine local density such that it can accommodate different intertype interactions despite the constraint to keep the main interaction parameter constant, known as Warren's no-go theorem, and generalize the many-body potential to heterogeneous systems. We then show via simulation how liquid-liquid and liquid-solid coexistence can arise just by tuning the interaction parameters.

Identifying the start of a platelet aggregate by the shear rate and the cell-depleted layer

Computer simulations were performed to study the transport of red blood cells and platelets in high shear flows, mimicking earlier published in vitro experiments in microfluidic devices with high affinity for platelet aggregate formation. The goal is to understand and predict where thrombus formation starts. Additionally, the need of cell-based modelling in these microfluidic devices is demonstrated by comparing our results with macroscopic models, wherein blood is modelled as a continuous fluid. Hemocell, a cell-based blood flow simulation framework is used to investigate the transport physics in the microfluidic devices. The simulations show an enlarged cell-depleted layer at the site where a platelet aggregate forms in the experiments. In this enlarged cell-depleted layer, the probability to find a platelet is higher than in the rest of the microfluidic device. In addition, the shear rates are sufficiently high to allow for the von Willebrand factor to elongate in this region. We hypothesize that the enlarged cell-depleted layer combined with a sufficiently large platelet flux and sufficiently high shear rates result in an haemodynamic environment that is a preferred location for initial platelet aggregation.

Effects of red blood cell aggregation on the blood flow in a symmetrical stenosed microvessel

In order to figure out whether red blood cell (RBC) aggregation is beneficial or deleterious for the blood flow through a stenosis, fluid mechanics of a microvascular stenosis was examined through simulating the dynamics of deformable red blood cells suspended in plasma using dissipative particle dynamics. The spatial variation in time-averaged cell-free layer (CFL) thickness and velocity profiles indicated that the blood flow exhibits asymmetry along the flow direction. The RBC accumulation occurs upstream the stenosis, leading to a thinner CFL and reduced flow velocity. Therefore, the emergence of stenosis produces an increased blood flow resistance. In addition, an enhanced Fahraeus-Lindqvist effect was observed in the presence of the stenosis. Finally, the effect of RBC aggregation combined with decreased stenosis on the blood flow was investigated. The findings showed that when the RBC clusters pass through the stenosis with a throat comparable to the RBC core in diameter, the blood flow resistance decreases with increasing intercellular interaction strength. But if the RBC core is larger and even several times than the throat, the blood flow resistance increases largely under strong RBC aggregation, which may contribute to the mechanism of the microthrombus formation.

Modeling Cell Adhesion and Extravasation in Microvascular System

The blood flow behaviors in the microvessels determine the transport modes and further affect the metastasis of circulating tumor cells (CTCs). Much biochemical and biological efforts have been made on CTC metastasis; however, precise experimental measurement and accurate theoretical prediction on its mechanical mechanism are limited. To complement these, numerical modeling of a CTC extravasation from the blood circulation, including the steps of adhesion and transmigration, is discussed in this chapter. The results demonstrate that CTCs prefer to adhere at the positive curvature of curved microvessels, which is attributed to the positive wall shear stress/gradient. Then, the effects of particulate nature of blood on CTC adhesion are investigated and are found to be significant in the microvessels. Furthermore, the presence of red blood cell (RBC) aggregates is also found to promote the CTC adhesion by providing an additional wall-directed force. Finally, a single cell passing through a narrow slit, mimicking CTC transmigration, was examined under the effects of cell deformability. It showed that the cell shape and surface area increase play a more important role than the cell elasticity in cell transit across the narrow slit.

Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?

Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.

Getting in shape and swimming: the role of cortical forces and membrane heterogeneity in eukaryotic cells

Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves-crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highly-simplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes. Such gradients can lead to a number of different characteristic cell shapes, and our first objective is to understand how different distributions of membrane tension influence the shape of cells in an inviscid quiescent fluid. We then analyze the effects of spatial variation in other membrane properties, and how they interact with tension gradients to determine the shape. We also study the effect of fluid-cell interactions and show how tension leads to cell movement, how the balance between tension gradients and a variable bending modulus determine the shape and direction of movement, and how the efficiency of movement depends on the properties of the fluid and the distribution of tension and bending modulus in the membrane.

Modeling of Biomechanics and Biorheology of Red Blood Cells in Type 2 Diabetes Mellitus

Erythrocytes in patients with type-2 diabetes mellitus (T2DM) are associated with reduced cell deformability and elevated blood viscosity, which contribute to impaired blood flow and other pathophysiological aspects of diabetes-related vascular complications. In this study, by using a two-component red blood cell (RBC) model and systematic parameter variation, we perform detailed computational simulations to probe the alteration of the biomechanical, rheological, and dynamic behavior of T2DM RBCs in response to morphological change and membrane stiffening. First, we examine the elastic response of T2DM RBCs subject to static tensile forcing and their viscoelastic relaxation response upon release of the stretching force. Second, we investigate the membrane fluctuations of T2DM RBCs and explore the effect of cell shape on the fluctuation amplitudes. Third, we subject the T2DM RBCs to shear flow and probe the effects of cell shape and effective membrane viscosity on their tank-treading movement. In addition, we model the cell dynamic behavior in a microfluidic channel with constriction and quantify the biorheological properties of individual T2DM RBCs. Finally, we simulate T2DM RBC suspensions under shear and compare the predicted viscosity with experimental measurements. Taken together, these simulation results and their comparison with currently available experimental data are helpful in identifying a specific parametric model-the first of its kind, to our knowledge-that best describes the main hallmarks of T2DM RBCs, which can be used in future simulation studies of hematologic complications of T2DM patients.

GPU-accelerated Red Blood Cells Simulations with Transport Dissipative Particle Dynamics

Mesoscopic numerical simulations provide a unique approach for the quantification of the chemical influences on red blood cell functionalities. The transport Dissipative Particles Dynamics (tDPD) method can lead to such effective multiscale simulations due to its ability to simultaneously capture mesoscopic advection, diffusion, and reaction. In this paper, we present a GPU-accelerated red blood cell simulation package based on a tDPD adaptation of our red blood cell model, which can correctly recover the cell membrane viscosity, elasticity, bending stiffness, and cross-membrane chemical transport. The package essentially processes all computational workloads in parallel by GPU, and it incorporates multi-stream scheduling and non-blocking MPI communications to improve inter-node scalability. Our code is validated for accuracy and compared against the CPU counterpart for speed. Strong scaling and weak scaling are also presented to characterizes scalability. We observe a speedup of 10.1 on one GPU over all 16 cores within a single node, and a weak scaling efficiency of 91% across 256 nodes. The program enables quick-turnaround and high-throughput numerical simulations for investigating chemical-driven red blood cell phenomena and disorders.

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.

Probing the Twisted Structure of Sickle Hemoglobin Fibers via Particle Simulations

Polymerization of sickle hemoglobin (HbS) is the primary pathogenic event of sickle cell disease. For insight into the nature of the HbS polymer fiber formation, we develop a particle model-resembling a coarse-grained molecular model-constructed to match the intermolecular contacts between HbS molecules. We demonstrate that the particle model predicts the formation of HbS polymer fibers by attachment of monomers to rough fiber ends and the growth rate increases linearly with HbS concentration. We show that the characteristic 14-molecule fiber cross section is preserved during growth. We also correlate the asymmetry of the contact sites on the HbS molecular surface with the structure of the polymer fiber composed of seven helically twisted double strands. Finally, we show that the same asymmetry mediates the mechanical and structural properties of the HbS polymer fiber.

A comparative study of coarse-graining methods for polymeric fluids: Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization

We construct effective coarse-grained (CG) models for polymeric fluids by employing two coarse-graining strategies. The first one is a forward-coarse-graining procedure by the Mori-Zwanzig (MZ) projection while the other one applies a reverse-coarse-graining procedure, such as the iterative Boltzmann inversion (IBI) and the stochastic parametric optimization (SPO). More specifically, we perform molecular dynamics (MD) simulations of star polymer melts to provide the atomistic fields to be coarse-grained. Each molecule of a star polymer with internal degrees of freedom is coarsened into a single CG particle and the effective interactions between CG particles can be either evaluated directly from microscopic dynamics based on the MZ formalism, or obtained by the reverse methods, i.e., IBI and SPO. The forward procedure has no free parameters to tune and recovers the MD system faithfully. For the reverse procedure, we find that the parameters in CG models cannot be selected arbitrarily. If the free parameters are properly defined, the reverse CG procedure also yields an accurate effective potential. Moreover, we explain how an aggressive coarse-graining procedure introduces the many-body effect, which makes the pairwise potential invalid for the same system at densities away from the training point. From this work, general guidelines for coarse-graining of polymeric fluids can be drawn.

Numerical simulation of a compound capsule in a constricted microchannel

Simulations of the passage of eukaryotic cells through a constricted channel aid in studying the properties of cancer cells and their transport in the bloodstream. Compound capsules, which explicitly model the outer cell membrane and nuclear lamina, have the potential to improve computational model fidelity. However, general simulations of compound capsules transiting a constricted microchannel have not been conducted and the influence of the compound capsule model on computational performance is not well known. In this study, we extend a parallel hemodynamics application to simulate the fluid-structure interaction between compound capsules and fluid. With this framework, we compare the deformation of simple and compound capsules in constricted microchannels, and explore how deformation depends on the capillary number and on the volume fraction of the inner membrane. The computational framework's parallel performance in this setting is evaluated and future development lessons are discussed.

Biomechanics and biorheology of red blood cells in sickle cell anemia

Sickle cell anemia (SCA) is an inherited blood disorder that causes painful crises due to vaso-occlusion of small blood vessels. The primary cause of the clinical phenotype of SCA is the intracellular polymerization of sickle hemoglobin resulting in sickling of red blood cells (RBCs) in deoxygenated conditions. In this review, we discuss the biomechanical and biorheological characteristics of sickle RBCs and sickle blood as well as their implications toward a better understanding of the pathophysiology and pathogenesis of SCA. Additionally, we highlight the adhesive heterogeneity of RBCs in SCA and their specific contribution to vaso-occlusive crisis.

MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease

Healthy red blood cells (RBCs) have remarkable deformability, squeezing through narrow capillaries as small as 3 microns in diameter without any damage. However, in many hematological disorders the spectrin network and lipid bilayer of diseased RBCs may be significantly altered, leading to impaired functionality including loss of deformability. We employ a two-component whole-cell multiscale model to quantify the biomechanical characteristics of the healthy and diseased RBCs, including Plasmodium falciparum-infected RBCs (Pf-RBCs) and defective RBCs in hereditary disorders, such as spherocytosis and elliptocytosis. In particular, we develop a two-step multiscale framework based on coarse-grained molecular dynamics (CGMD) and dissipative particle dynamics (DPD) to predict the static and dynamic responses of RBCs subject to tensile forcing, using experimental information only on the structural defects in the lipid bilayer, cytoskeleton, and their interaction. We first employ CGMD on a small RBC patch to compute the shear modulus, bending stiffness, and network parameters, which are subsequently used as input to a whole-cell DPD model to predict the RBC shape and corresponding stress field. For Pf-RBCs at trophozoite and schizont stages, the presence of cytoadherent knobs elevates the shear response in the lipid bilayer and stiffens the RBC membrane. For RBCs in spherocytosis and elliptocytosis, the bilayer-cytoskeleton interaction is weakened, resulting in substantial increase of the tensile stress in the lipid bilayer. Furthermore, we investigate the transient behavior of stretching deformation and shape relaxation of the normal and defective RBCs. Different from the normal RBCs possessing high elasticity, our simulations reveal that the defective RBCs respond irreversibly, i.e., they lose their ability to recover the normal biconcave shape in successive loading cycles of stretching and relaxation. Our findings provide fundamental insights into the microstructure and biomechanics of RBCs, and demonstrate that the two-step multiscale framework presented here can be used effectively for in silico studies of hematological disorders based on first principles and patient-specific experimental input at the protein level.

MD Study of Solution Concentrations on Ion Distribution in a Nanopore-Based Device Inspired from Red Blood Cells

A molecular dynamics model of a nanopore-based device, which is similar to the nanopores in a cell membrane, was used to determine the influence of solution concentration on radial ion distribution, screening effects, and the radial potential profile in the nanopore. Results from these simulations indicate that as the solution concentration increases, the density peaks for both the counterion and coion near the charged wall increase at different speeds as screening effects appeared. Consequently, the potential near the charged wall of the nanopore changed from negative to positive during the simulation. The detailed understanding of ion distribution in nanopores is important for controlling the ion permeability and improving the cell transfection and also the design and application of nanofluidic devices.

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.

Numerical simulation of a single cell passing through a narrow slit

The narrow slit between endothelial cells that line the microvessel wall is the principal pathway for tumor cell extravasation to the surrounding tissue. To understand this crucial step for tumor hematogenous metastasis, we used dissipative particle dynamics method to investigate an individual cell passing through a narrow slit numerically. The cell membrane was simulated by a spring-based network model which can separate the internal cytoplasm and surrounding fluid. The effects of the cell elasticity, cell shape, nucleus and slit size on the cell transmigration through the slit were investigated. Under a fixed driving force, the cell with higher elasticity can be elongated more and pass faster through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area by merely 9.3 % can enable the cell to pass through the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell passing through the narrow slit. In addition, the simulation results indicate that the cell migration velocity decreases during entrance but increases during exit of the slit, which is qualitatively in agreement with the experimental observation.

Multifractal characterization of morphology of human red blood cells membrane skeleton

The purpose of this paper is to show applicability of multifractal analysis in investigations of the morphological changes of ultra-structures of red blood cells (RBCs) membrane skeleton measured using atomic force microscopy (AFM). Human RBCs obtained from healthy and hypertensive donors as well as healthy erythrocytes irradiated with neutrons (45 μGy) were studied. The membrane skeleton of the cells was imaged using AFM in a contact mode. Morphological characterization of the three-dimensional RBC surfaces was realized by a multifractal method. The nanometre scale study of human RBCs surface morphology revealed a multifractal geometry. The generalized dimensions Dq and the singularity spectrum f(α) provided quantitative values that characterize the local scale properties of their membrane skeleton organization. Surface characterization was made using areal ISO 25178-2: 2012 topography parameters in combination with AFM topography measurement. The surface structure of human RBCs is complex with hierarchical substructures resulting from the organization of the erythrocyte membrane skeleton. The analysed AFM images confirm a multifractal nature of the surface that could be useful in histology to quantify human RBC architectural changes associated with different disease states. In case of very precise measurements when the red cell surface is not wrinkled even very fine differences can be uncovered as was shown for the erythrocytes treated with a very low dose of ionizing radiation.

Patient-specific blood rheology in sickle-cell anaemia

Sickle-cell anaemia (SCA) is an inherited blood disorder exhibiting heterogeneous cell morphology and abnormal rheology, especially under hypoxic conditions. By using a multiscale red blood cell (RBC) model with parameters derived from patient-specific data, we present a mesoscopic computational study of the haemodynamic and rheological characteristics of blood from SCA patients with hydroxyurea (HU) treatment (on-HU) and those without HU treatment (off-HU). We determine the shear viscosity of blood in health as well as in different states of disease. Our results suggest that treatment with HU improves or worsens the rheological characteristics of blood in SCA depending on the degree of hypoxia. However, on-HU groups always have higher levels of haematocrit-to-viscosity ratio (HVR) than off-HU groups, indicating that HU can indeed improve the oxygen transport potential of blood. Our patient-specific computational simulations suggest that the HVR level, rather than the shear viscosity of sickle RBC suspensions, may be a more reliable indicator in assessing the response to HU treatment.

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.

Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the “all-or-nothing” phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.

Blood tests, which provide a wealth of information on the state of human health, are often performed on cell-free samples. Therefore, blood-plasma separation needs to be achieved. A simple but effective solution for isolating plasma from blood utilizes capillary bifurcations. In a particle-based simulation study of plasma skimming in capillary bifurcations, the blood flow properties such as velocity and pressure fields differ drastically at the inlet and outlet regions. Therefore, a new open (non-periodic) boundary is required. In this paper, we have developed and validated a general parallel framework for open boundary conditions. This is a non-trivial enabling technology that could be used in all open boundary systems and all particle-based Lagrangian simulations. We performed systematic 3D simulations of blood flow in arteriolar bifurcations and elucidated the biophysical mechanism of blood-plasma separation as well as quantified the effects of branch size and bifurcation angle on cell separation efficiency, which have not been addressed before. We also demonstrated the applicability of the methodology in arterial trees with multiple inlets and outlets.

Erythrocyte stiffness during morphological remodeling induced by carbon ion radiation

The adverse effect induced by carbon ion radiation (CIR) is still an unavoidable hazard to the treatment object. Thus, evaluation of its adverse effects on the body is a critical problem with respect to radiation therapy. We aimed to investigate the change between the configuration and mechanical properties of erythrocytes induced by radiation and found differences in both the configuration and the mechanical properties with involving in morphological remodeling process. Syrian hamsters were subjected to whole-body irradiation with carbon ion beams (1, 2, 4, and 6 Gy) or X-rays (2, 4, 6, and 12 Gy) for 3, 14 and 28 days. Erythrocytes in peripheral blood and bone marrow were collected for cytomorphological analysis. The mechanical properties of the erythrocytes were determined using atomic force microscopy, and the expression of the cytoskeletal protein spectrin-α1 was analyzed via western blotting. The results showed that dynamic changes were evident in erythrocytes exposed to different doses of carbon ion beams compared with X-rays and the control (0 Gy). The magnitude of impairment of the cell number and cellular morphology manifested the subtle variation according to the irradiation dose. In particular, the differences in the size, shape and mechanical properties of the erythrocytes were well exhibited. Furthermore, immunoblot data showed that the expression of the cytoskeletal protein spectrin-α1 was changed after irradiation, and there was a common pattern among its substantive characteristics in the irradiated group. Based on these findings, the present study concluded that CIR could induce a change in mechanical properties during morphological remodeling of erythrocytes. According to the unique characteristics of the biomechanical categories, we deduce that changes in cytomorphology and mechanical properties can be measured to evaluate the adverse effects generated by tumor radiotherapy. Additionally, for the first time, the current study provides a new strategy for enhancing the assessment of the curative effects and safety of clinical radiotherapy, as well as reducing adverse effects.