Molecularly based analysis of deformation of spectrin network and human erythrocyte

Chemo-mechanical model of cell polarization initiated by structural polarity

Cell polarization is crucial in most physiological functions. Living cells at the extracellular matrix (ECM) actively coordinate a polarized morphology to target the preferred signals. In particular, the initial heterogeneity of subcellular components, termed as structural polarity, has been discovered to mediate the early attachment and transmigration of cells in tumour metastasis. However, how heterogeneous cells initiate the early polarization remains incompletely discovered. Here, we establish a multiscale model of a cell to explore the chemo-mechanical mechanisms of cell polarization initiated by structural polarity. The two-dimensional vertex model of the cell is built with the main mechanical components of eukaryotic cells. The initial structural polarity of the modeled cell is introduced by seeding heterogeneous actin filaments at the cell cortex and quantified by the ratio of the filamentous forces at the vertices. Then, the structural polarity is integrated in the reaction-diffusion system of Rho GTPase (Cdc42) at the cell cortex to obtain the traction forces at the leading vertices. Finally, the modeled cell is actuated to spread under the traction forces and discovered to develop into a characteristic polarized morphology. The results indicate that the cell polarization is initiated and dynamically developed by structural polarity through the reaction-diffusion system of Cdc42. In addition, the bistability of Cdc42 activation at the cell cortex is defined and discovered to dominate the polarization status of the cell. Furthermore, biphasic (i.e., positive and negative) durotaxis of the cell is successfully modeled at an ECM with a stiffness gradient, and concluded to be codetermined by the chemo-mechanical coupling of the initial structural polarity and ECM stiffness gradient. The proposed multiscale model provides a quantitative way to probe cell polarization coupled with mechanical stimuli, biochemical reaction and cytoskeletal reorganization, and holds the potential to guide studies of cell polarization under multiple stimuli.

Interplay between endothelial glycocalyx layer and red blood cell in microvascular blood flow: A numerical study

The endothelial glycocalyx layer (EGL) plays a crucial role in regulating blood flow in microvessels. Experimental evidence suggests that there is greater blood flow resistance in vivo compared to in vitro, partially due to the presence of the EGL. However, the complex relationship between EGL deformation and blood cell behavior in shear flow and its quantification remains incompletely understood. To address this gap, we employ a particle-based numerical simulation technique to examine the interaction of the EGL with flowing red blood cells (RBCs) in microtubes. We examine changes in EGL deformation in response to variations in shear rate, EGL graft density, and contour height. Our results indicate that the alterations in EGL height are influenced by the mechanical properties of the EGL, flow conditions, and the RBC-EGL interaction. The flowing RBC compresses the EGL, causing a notable reduction in EGL height near the RBC flow. Additionally, we find that the presence of the EGL in the microtube results in increased RBC deformation and a wider gap between the RBC and tube wall due to spatial occupancy. The significant impact of the EGL on RBC flow is particularly evident in microtubes with diameters ranging from 7 to 10µm, a range consistent with notable differences in vascular flow resistance observed between in vivo and in vitro experiments. The simulation results shed insight on the dynamic interplay between RBC and the EGL in microvascular blood flow.

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.

Dynamic mechanisms for membrane skeleton transitions

The plasma membrane and the underlying skeleton form a protective barrier for eukaryotic cells. The molecules forming this complex composite material constantly rearrange under mechanical stress to confer this protective capacity. One of those molecules, spectrin, is ubiquitous in the membrane skeleton and primarily located proximal to the inner leaflet of the plasma membrane and engages in protein-lipid interactions via a set of membrane-anchoring domains. Spectrin is linked by short actin filaments and its conformation varies in different types of cells. In this work, we developed a generalized network model for the membrane skeleton integrated with myosin contractility and membrane mechanics to investigate the response of the spectrin meshwork to mechanical loading. We observed that the force generated by membrane bending is important to maintain a smooth skeletal structure. This suggests that the membrane is not just supported by the skeleton, but has an active contribution to the stability of the cell structure. We found that spectrin and myosin turnover are necessary for the transition between stress and rest states in the skeleton. Our model reveals that the actin-spectrin meshwork dynamics are balanced by the membrane forces with area constraint and volume restriction promoting the stability of the membrane skeleton. Furthermore, we showed that cell attachment to the substrate promotes shape stabilization. Thus, our proposed model gives insight into the shared mechanisms of the membrane skeleton associated with myosin and membrane that can be tested in different types of cells.

Numerical simulation of cellular blood flow in curved micro-vessels with saccular aneurysms: Effect of curvature degree and hematocrit level

The dynamics of cellular blood flow in curved vessels considerably differ from those in straight vessels. It is reported that clotting development is significantly affected by vessel shape irregularities. Thus, the current study aims to investigate the effect of curvature degree and hematocrit level on cellular blood flow in a curved micro-vessel with a saccular aneurysm. Accordingly, a three-dimensional numerical simulation is performed using a validated code developed for cellular blood flow problems. The obtained results show that the cell-free layer thickness is highly dependent on the curvature degree and hematocrit level, which may have a remarkable impact on the apparent viscosity of blood as well as the dynamics of other particles such as drug particulates. The near-wall region exhibits the highest degree of cell deformation, whereas the red blood cells within the aneurysm zone remain nearly undeformed. Meanwhile, the velocity of the red blood cells decreases with the increase in curvature degree, which can affect the quality of the oxygenation process. Because of the saccular aneurysm, a considerable decrease in plasma velocity is predicted. Moreover, no secondary flows are detected in the curved vessel except in the aneurysm zone. An increase in the curvature degree is expected to reduce the blood flow rate by about 10%. Furthermore, low wall shear stress values are predicted in the straight case compared to the values at the apex of the curved vessel, which may affect the structure and function of the endothelial cells of the vessel wall and, hence, increase the aneurysm rupture possibility.

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.

Energy spectrum analysis on a red blood cell model

It is important to understand the dynamics of red blood cells (RBCs) in blood flow. This requires the formulation of coarse-grained RBC models that reproduce the hydrodynamic properties of blood accurately. One of the models that successfully reproduces the rheology and morphology of blood has been proposed by Fedosov et al. [Comput. Methods Appl. Mech. Eng. 199, 1937-1948 (2010)]. The proposed RBC model contains several parameters whose values are determined by either various experiments or physical requirements. In this study, we developed a new method of determining parameter values precisely from the fluctuations of the RBC membrane. Specifically, we studied the relationship between the spectra of the fluctuations and model parameters. Characteristic peaks were observed in the spectra, whose peak frequencies were dependent on the parameter values. In addition, we investigated the spectra of the radius of gyration. We identified the peaks originating from the spring potential and the volume-conserving potential appearing in the spectra. These results lead to the precise experimental determination of the parameters used in the RBC model.

Effective cell membrane tension protects red blood cells against malaria invasion

A critical step in how malaria parasites invade red blood cells (RBCs) is the wrapping of the membrane around the egg-shaped merozoites. Recent experiments have revealed that RBCs can be protected from malaria invasion by high membrane tension. While cellular and biochemical aspects of parasite actomyosin motor forces during the malaria invasion have been well studied, the important role of the biophysical forces induced by the RBC membrane-cytoskeleton composite has not yet been fully understood. In this study, we use a theoretical model for lipid bilayer mechanics, cytoskeleton deformation, and membrane-merozoite interactions to systematically investigate the influence of effective RBC membrane tension, which includes contributions from the lipid bilayer tension, spontaneous tension, interfacial tension, and the resistance of cytoskeleton against shear deformation on the progression of membrane wrapping during the process of malaria invasion. Our model reveals that this effective membrane tension creates a wrapping energy barrier for a complete merozoite entry. We calculate the tension threshold required to impede the malaria invasion. We find that the tension threshold is a nonmonotonic function of spontaneous tension and undergoes a sharp transition from large to small values as the magnitude of interfacial tension increases. We also predict that the physical properties of the RBC cytoskeleton layer-particularly the resting length of the cytoskeleton-play key roles in specifying the degree of the membrane wrapping. We also found that the shear energy of cytoskeleton deformation diverges at the full wrapping state, suggesting the local disassembly of the cytoskeleton is required to complete the merozoite entry. Additionally, using our theoretical framework, we predict the landscape of myosin-mediated forces and the physical properties of the RBC membrane in regulating successful malaria invasion. Our findings on the crucial role of RBC membrane tension in inhibiting malaria invasion can have implications for developing novel antimalarial therapeutic or vaccine-based strategies.

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.

A mathematical model of fibrinogen-mediated erythrocyte-erythrocyte adhesion

Erythrocytes are deformable cells that undergo progressive biophysical and biochemical changes affecting the normal blood flow. Fibrinogen, one of the most abundant plasma proteins, is a primary determinant for changes in haemorheological properties, and a major independent risk factor for cardiovascular diseases. In this study, the adhesion between human erythrocytes is measured by atomic force microscopy (AFM) and its effect observed by micropipette aspiration technique, in the absence and presence of fibrinogen. These experimental data are then used in the development of a mathematical model to examine the biomedical relevant interaction between two erythrocytes. Our designed mathematical model is able to explore the erythrocyte-erythrocyte adhesion forces and changes in erythrocyte morphology. AFM erythrocyte-erythrocyte adhesion data show that the work and detachment force necessary to overcome the adhesion between two erythrocytes increase in the presence of fibrinogen. The changes in erythrocyte morphology, the strong cell-cell adhesion and the slow separation of the two cells are successfully followed in the mathematical simulation. Erythrocyte-erythrocyte adhesion forces and energies are quantified and matched with experimental data. The changes observed on erythrocyte-erythrocyte interactions may give important insights about the pathophysiological relevance of fibrinogen and erythrocyte aggregation in hindering microcirculatory blood flow.

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.

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.

Contraction of the rigor actomyosin complex drives bulk hemoglobin expulsion from hemolyzing erythrocytes

Erythrocyte ghost formation via hemolysis is a key event in the physiological clearance of senescent red blood cells (RBCs) in the spleen. The turnover rate of millions of RBCs per second necessitates a rapid efflux of hemoglobin (Hb) from RBCs by a not yet identified mechanism. Using high-speed video-microscopy of isolated RBCs, we show that electroporation-induced efflux of cytosolic ATP and other small solutes leads to transient cell shrinkage and echinocytosis, followed by osmotic swelling to the critical hemolytic volume. The onset of hemolysis coincided with a sudden self-propelled cell motion, accompanied by cell contraction and Hb-jet ejection. Our biomechanical model, which relates the Hb-jet-driven cell motion to the cytosolic pressure generation via elastic contraction of the RBC membrane, showed that the contributions of the bilayer and the bilayer-anchored spectrin cytoskeleton to the hemolytic cell motion are negligible. Consistent with the biomechanical analysis, our biochemical experiments, involving extracellular ATP and the myosin inhibitor blebbistatin, identify the low abundant non-muscle myosin 2A (NM2A) as the key contributor to the Hb-jet emission and fast hemolytic cell motion. Thus, our data reveal a rapid myosin-based mechanism of hemolysis, as opposed to a much slower diffusive Hb efflux.

Structural Configuration of Blood Cell Membranes Determines Their Nonlinear Deformation Properties

The ability of neutrophils and red blood cells (RBCs) to undergo significant deformations is a key to their normal functioning. Disruptions of these processes can lead to pathologies. This work studied the influence of structural configuration rearrangements of membranes after exposure to external factors on the ability of native membranes of neutrophils and RBCs to undergo deep deformation. The rearrangement of the structural configuration of neutrophil and RBC membranes under the influence of cytological fixatives caused nonlinear deformation phenomena. There were an increase in Young's modulus, a decrease in the depth of homogeneous bending, and a change in the distance between cytoskeletal junctions. Based on the results of the analysis of experimental data, a mathematical model was proposed that describes the process of deep bending of RBСs and neutrophil membranes.

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.

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.

Development of Mechanical Stability in Late-Stage Embryonic Erythroid Cells: Insights From Fluorescence Imaged Micro-Deformation Studies

The combined use of fluorescence labeling and micro-manipulation of red blood cells has proven to be a powerful tool for understanding and characterizing fundamental mechanisms underlying the mechanical behavior of cells. Here we used this approach to study the development of the membrane-associated cytoskeleton (MAS) in primary embryonic erythroid cells. Erythropoiesis comes in two forms in the mammalian embryo, primitive and definitive, characterized by intra- and extra-vascular maturation, respectively. Primitive erythroid precursors in the murine embryo first begin to circulate at embryonic day (E) 8.25 and mature as a semi-synchronous cohort before enucleating between E12.5 and E16.5. Previously, we determined that the major components of the MAS become localized to the membrane between E10.5 and E12.5, and that this localization is associated with an increase in membrane mechanical stability over this same period. The change in mechanical stability was reflected in the creation of MAS-free regions of the membrane at the tips of the projections formed when cells were aspirated into micropipettes. The tendency to form MAS-free regions decreases as primitive erythroid cells continue to mature through E14.5, at least 2 days after all detectable cytoskeletal components are localized to the membrane, indicating continued strengthening of membrane cohesion after membrane localization of cytoskeletal components. Here we demonstrate that the formation of MAS-free regions is the result of a mechanical failure within the MAS, and not the detachment of membrane bilayer from the MAS. Once a "hole" is formed in the MAS, the skeletal network contracts laterally along the aspirated projection to form the MAS-free region. In protein 4.1-null primitive erythroid cells, the tendency to form MAS-free regions is markedly enhanced. Of note, similar MAS-free regions were observed in maturing erythroid cells from human marrow, indicating that similar processes occur in definitive erythroid cells. We conclude that localization of cytoskeletal components to the cell membrane of mammalian erythroid cells during maturation is insufficient by itself to produce a mature MAS, but that subsequent processes are additionally required to strengthen intraskeletal interactions.

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.

Biomechanical model of cells probing the myosin-II-independent mechanosensing mechanism

Mechanosensing of cells to extracellular matrix (ECM) is highly active and plays a crucial role in various physiological processes. Growing numbers of studies provide evidence that cell sensitivity to ECM stiffness is a complex stress-strain feedback process. However, the mechanisms that rule this process are still not fully known. Here, an alternative mechanosensing scheme of cells, which is different from the previous myosin-II-based mechanisms, is proposed by employing the tension in cortical cytoskeletons (CSKs) as a force module to probe the substrate. The molecular mechanotransduction from cortical CSKs, through actin filaments and focal adhesions, and finally to the substrate, is mechanically modeled to scale the dynamic traction forces of cells. The developed model captures the characteristic spread of cells with respect to ECM stiffness whereby the spread is fully developed on a stiff substrate but not on a soft one. Furthermore, durotactic migration of cells on an elastic-gradient substrate is successfully modeled by the current method. The cells are concluded to migrate, actuated by the polarized traction forces from the stiffness gradient of the substrate and the stiffness matching between cells and substrate. Finally, the cells are proposed to actively target the preferred substrate by following a rule of mechanical matching between cells and substrate. This study provides a theoretical tool to advance our knowledge regarding the passive mechanical properties and the active sensing of cells, and further promotes the discovery of mechanosensing mechanisms as well as the material design for embryonic development and tissue homeostasis.

Organic and inorganic equivalent models for analysis of red blood cell mechanical behaviour

Experimental investigation into the mechanical response of red blood cells is presently impeded with the main impediments being the micro dimensions involved and ethical issues associated with in vivo testing. The widely employed alternative approach of computational modelling suffers from its own inherent limitations being reliant on precise constitutive and boundary information. Moreover, and somewhat critically, numerical computational models themselves are required to be validated by means of experimentation and hence suffer similar impediments. An alternative experimental approach is examined in this paper involving large-scale equivalent models manufactured principally from inorganic, and to lesser extent organic, materials. Although there presently exists no known method providing the means to investigate the mechanical response of red blood cells using scaled models simultaneously having different dimensions and materials, the present paper aims to develop a scaled framework based on the new finite-similitude theory that has appeared in the recent open literature. Computational models are employed to test the effectiveness of the proposed method, which in principle can provide experimental solution methods to a wide range of practical applications including the design of red-blood cell nanorobots and drug delivery systems. By means of experimentally validated numerical experiments under impact loading it is revealed that although exact prediction is not achieved good accuracy can nevertheless be obtained. Furthermore, it is demonstrated how the proposed approach for first time provides a means to relate models at different scales founded on different constitutive equations.

Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension

The inner viscosity of a biological red blood cell is about five times larger than the viscosity of the blood plasma. In this work, we use dissipative particles to enable the proper viscosity contrast in a mesh-based red blood cell model. Each soft particle represents a coarse-grained virtual cluster of hemoglobin proteins contained in the cytosol of the red blood cell. The particle interactions are governed by conservative and dissipative forces. The conservative forces have purely repulsive character, whereas the dissipative forces depend on the relative velocity between the particles. We design two computational experiments that mimic the classical viscometers. With these experiments we study the effects of particle suspension parameters on the inner cell viscosity and provide parameter sets that result in the correct viscosity contrast. The results are validated with both static and dynamic biological experiment, showing an improvement in the accuracy of the original model without major increase in computational complexity.

Electric Factors in Wound Healing

Significance: Electric factors such as electric charges, electrodynamic field, skin battery, and interstitial exclusion permeate wound healing physiology and physiopathology from injury to re-epithelialization. The understanding of how electric factors contribute to wound healing and how treatments may interfere with them is fundamental for the development of better strategies for the management of pathological scarring and chronic wounds. Recent Advances: Angiogenesis, cell migration, macrophage activation hemorheology, and microcirculation can interfere and be interfered with electric factors. New treatments with various types of electric currents, laser, light emitting diode, acupuncture, and weak electric fields applied directly on the wound have been developed to improve wound healing. Critical Issues: Despite the basic and clinical development, pathological scars such as keloids and chronic wounds are still a challenge. Future Directions: New treatments can be developed to improve skin wound healing taking into account the influence of electrical charges. Monitoring electrical activity during skin healing and the influence of treatments on hemorheology and microcirculation are examples of how to use knowledge of electrical factors to increase their effectiveness.

Mechanical behavior of actin and spectrin subjected to high strain rate: A molecular dynamics simulation study

Recent nanoscopy and super-resolution microscopy studies have substantiated the structural contribution of periodic actin-spectrin lattice to the axonal cytoskeleton of neuron. However, sufficient mechanical insight is not present for spectrin and actin-spectrin network, especially in high strain rate scenario. To quantify the mechanical behavior of actin-spectrin cytoskeleton in such conditions, this study determines individual stretching characteristics of actin and spectrin at high strain rate by molecular dynamics (MD) simulation. The actin-spectrin separation criteria are also determined. It is found that both actin and spectrin have high stiffness when susceptible to high strain rate and show strong dependence on applied strain rate. The stretching stiffness of actin and forced unfolding mechanism of spectrin are in harmony with the current literature. Actin-spectrin model provides novel insight into their interaction and separation stretch. It is shown that the region vulnerable to failure is the actin-spectrin interface at lower strain rate, while it is the inter-repeat region of spectrin at higher strain rate.

Computational models of cancer cell transport through the microcirculation

The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.

Red blood cell hitchhiking enhances the accumulation of nano- and micro-particles in the constriction of a stenosed microvessel

We investigate the circulation of nano- and micro-particles, including spherical particles and filamentous nanoworms, with red blood cells (RBCs) suspension in a constricted channel that mimics a stenosed microvessel. Through three-dimensional simulations using the immersed boundary-based Lattice Boltzmann method, the influence of channel geometries, such as the length and ratio of the constriction, on the accumulation of particles is systematically studied. Firstly, we find that the accumulation of spherical particles with 1 μm diameter in the constriction increases with the increases of both the length and ratio of the constriction. This is attributed to the interaction between spheres and RBCs. The RBCs "carry" the spheres and they accumulate inside the constriction together, due to the altered local hydrodynamics induced by the existence of the constriction. Secondly, nanoworms demonstrate higher accumulation than that of spheres inside the constriction, which is associated with the escape of nanoworms from RBC clusters and their accumulation near the wall of main channel. The accumulated near-wall nanoworms will eventually enter the constriction, thus enhancing their concentration inside the constriction. However, an exceptional case occurs in the case of constrictions with large ratio and long length. In such circumstances, the RBCs aggregate together tightly and concentrate at the center of the channel, which makes the nanoworms hardly able to escape from RBC clusters, leading to a similar accumulation of nanoworms and spheres inside the constriction. This study may provide theoretical guidance for the design of nano- and micro-particles for biomedical engineering applications, such as drug delivery systems for patients with stenosed microvessels.

Constitutive Model of Erythrocyte Membranes with Distributions of Spectrin Orientations and Lengths

We present an analytical hyperelastic constitutive model of the red blood cell (erythrocyte) membrane based on recently improved characterizations of density and microscopic structure of its spectrin network from proteomics and cryo-electron tomography. The model includes distributions of both orientations and natural lengths of spectrin and updated copy numbers of proteins. By applying finite deformation to the spectrin network, we obtain the total free energy and stresses in terms of invariants of shear and area deformation. We generalize an expression of the initial shear modulus, which is independent of the number of molecular orientations within the network and also derive a simplified version of the model. We apply the model and its simplified version to analyze micropipette aspiration computationally and analytically and explore the effect of local cytoskeletal density change. We also explore the discrepancies among shear modulus values measured using different experimental techniques reported in the literature. We find that the model exhibits hardening behavior and can explain many of these discrepancies. Moreover, we find that the distribution of natural lengths plays a crucial role in the hardening behavior when the correct copy numbers of proteins are used. The initial shear modulus values we obtain using our current model (5.9-15.6 pN/μm) are close to the early estimates (6-9 pN/μm). This new, to our knowledge, constitutive model establishes a direct connection between the molecular structure of spectrin networks and constitutive laws and also defines a new picture of a much denser spectrin network than assumed in prior studies.

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.

A system for the high-throughput measurement of the shear modulus distribution of human red blood cells

Reduced deformability of red blood cells (RBCs) can affect the hemodynamics of the microcirculation and reduce oxygen transport efficiency. It is also well known that reduced RBC deformability is a signature of various physical disorders, including sepsis, and that the primary determinant of RBC deformability is the membrane shear modulus. To measure the distribution of an individual's RBC shear modulus with high throughput, we a) developed a high-fidelity computational model of RBCs in confined microchannels to inform design decisions; b) created a novel experimental system combining microfluidic flow, imaging, and image analysis; and c) performed automated comparisons between measured quantities and numerical predictions to extract quantitative measures of the RBC shear modulus for each of thousands of cells. We applied our computational simulation platform to construct the appropriate deformability figure(s) of merit to quantify RBC stiffness based on an experimentally measured, steady-state cell shape in flow through a microchannel. In particular, we determined a shape parameter based on the second moment of the cell shape that is sensitive to the changes in the membrane stiffness and cell size. We then conducted microfluidic experiments and developed custom automated image processing codes to identify and track the position and shape of individual RBCs within micro-constrictions. The fabricated microchannels include a square cross-section imaging region (7 by 7 μm) and we applied order 10 kPa pressure differences to induce order 10 mm s^-1 cell velocities. The combination of modeling, microfluidics, and imaging enables, for the first time, quantitative measurement of the shear moduli of thousands of RBCs in human blood samples. We demonstrate the high-throughput features by sensitive quantification of the changes in the distribution of RBC stiffness with aging. This combined measurement and computational platform is ultimately intended to diagnose blood cell disorders in patients.

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.

Modelling of Red Blood Cell Morphological and Deformability Changes during In-Vitro Storage

Storage lesion is a critical issue facing transfusion treatments, and it adversely affects the quality and viability of stored red blood cells (RBCs). RBC deformability is a key indicator of cell health. Deformability measurements of each RBC unit are a key challenge in transfusion medicine research and clinical haematology. In this paper, a numerical study, inspired from the previous research for RBC deformability and morphology predictions, is conducted for the first time, to investigate the deformability and morphology characteristics of RBCs undergoing storage lesion. This study investigates the evolution of the cell shape factor, elongation index and membrane spicule details, where applicable, of discocyte, echinocyte I, echinocyte II, echinocyte III and sphero-echinocyte morphologies during 42 days of in-vitro storage at 4 °C in saline-adenine-glucose-mannitol (SAGM). Computer simulations were performed to investigate the influence of storage lesion-induced membrane structural defects on cell deformability and its recoverability during optical tweezers stretching deformations. The predicted morphology and deformability indicate decreasing quality and viability of stored RBCs undergoing storage lesion. The loss of membrane structural integrity due to the storage lesion further degrades the cell deformability and recoverability during mechanical deformations. This numerical approach provides a potential framework to study the RBC deformation characteristics under varying pathophysiological conditions for better diagnostics and treatments.

Deformation behaviour of stomatocyte, discocyte and echinocyte red blood cell morphologies during optical tweezers stretching

The red blood cell (RBC) deformability is a critical aspect, and assessing the cell deformation characteristics is essential for better diagnostics of healthy and deteriorating RBCs. There is a need to explore the connection between the cell deformation characteristics, cell morphology, disease states, storage lesion and cell shape-transformation conditions for better diagnostics and treatments. A numerical approach inspired from the previous research for RBC morphology predictions and for analysis of RBC deformations is proposed for the first time, to investigate the deformation characteristics of different RBC morphologies. The present study investigates the deformability characteristics of stomatocyte, discocyte and echinocyte morphologies during optical tweezers stretching and provides the opportunity to study the combined contribution of cytoskeletal spectrin network and the lipid-bilayer during RBC deformation. The proposed numerical approach predicts agreeable deformation characteristics of the healthy discocyte with the analogous experimental observations and is extended to further investigate the deformation characteristics of stomatocyte and echinocyte morphologies. In particular, the computer simulations are performed to investigate the influence of direct stretching forces on different equilibrium cell morphologies on cell spectrin link extensions and cell elongation index, along with a parametric analysis on membrane shear modulus, spectrin link extensibility, bending modulus and RBC membrane-bead contact diameter. The results agree with the experimentally observed stiffer nature of stomatocyte and echinocyte with respect to a healthy discocyte at experimentally determined membrane characteristics and suggest the preservation of relevant morphological characteristics, changes in spectrin link densities and the primary contribution of cytoskeletal spectrin network on deformation behaviour of stomatocyte, discocyte and echinocyte morphologies during optical tweezers stretching deformation. The numerical approach presented here forms the foundation for investigations into deformation characteristics and recoverability of RBCs undergoing storage lesion.

Shear-induced non-monotonic viscosity dependence for model red blood cell suspensions in microvessels

The cell-free layer thickness of an aggregating red blood cell (RBC) suspension in a rectangular microchannel is investigated by hybrid fluid-particle numerical modeling. Several factors affect the suspension viscosity, cell-free layer thickness, and the cell aggregate distribution. These include the hematocrit, vessel size, red cell stiffness, aggregation interaction, and shear rate. In particular, the effect of the shear rate on the cell-free layer thickness is controversial. We found that the suspension viscosity increases along with a decrease in the cell-free layer thickness as the shear rate increases for aggregating model RBCs at low shear rates. At moderate to high shear rates, the cell-free layer thickness increases with the increasing shear rate from medium to strong shear flow for both 10% and 20% red blood cell suspensions.

Simulation of circulating tumor cell transport and adhesion in cell suspensions in microfluidic devices

Understanding cell transport and adhesion dynamics under flow is important for many biotransport problems. We investigated the influence of cell size, ligand coating density, micropost size, and intercellular collisions on circulating tumor cell adhesion and transport in microfluidic devices. The cells were modeled as coarse-grained cell membranes and the adhesion was modeled as pairwise interacting potentials, while the fluid was solved using the lattice Boltzmann method. The coupling between the cell and the fluid was achieved through the immersed boundary method. The cell showed transient rolling adhesion in high shear regions and firm adhesion in low shear regions. The adhesive force for rolling cells on a micropost was increasing before the cell reached the crest of the post and then decreasing afterward. The adhesive strength for cells increases with ligand coating density. Cell trajectories in a microfluidic device with a shifted post design were studied as well. At low concentrations, the majority of the cells follow streamlines closely. However, the intercellular collision and collision from red blood cells impacted the cell trajectories. An L 2 norm of | e | was defined to characterize the difference between the cell trajectories and the associated streamlines. It was shown that | e | L 2 increases with micropost sizes and cell concentrations.

Dissipative Coupling of Fluid and Immersed Objects for Modelling of Cells in Flow

Modelling of cell flow for biomedical applications relies in many cases on the correct description of fluid-structure interaction between the cell membrane and the surrounding fluid. We analyse the coupling of the lattice-Boltzmann method for the fluid and the spring network model for the cells. We investigate the bare friction parameter of fluid-structure interaction that is mediated via dissipative coupling. Such coupling mimics the no-slip boundary condition at the interface between the fluid and object. It is an alternative method to the immersed boundary method. Here, the fluid-structure coupling is provided by forces penalising local differences between velocities of the object's boundaries and the surrounding fluid. The method includes a phenomenological friction coefficient that determines the strength of the coupling. This work aims at determination of proper values of such friction coefficient. We derive an explicit formula for computation of this coefficient depending on the mesh density assuming a reference friction is known. We validate this formula on spherical and ellipsoidal objects. We also provide sensitivity analysis of the formula on all parameters entering the model. We conclude that such formula may be used also for objects with irregular shapes provided that the triangular mesh covering the object's surface is in some sense uniform. Our findings are justified by two computational experiments where we simulate motion of a red blood cell in a capillary and in a shear flow. Both experiments confirm our results presented in this work.

Shear rate dependent margination of sphere-like, oblate-like and prolate-like micro-particles within blood flow

This study investigates the shear rate dependent margination of micro-particles (MPs) with different shapes in blood flow through numerical simulations. We develop a multiscale computational model to handle the fluid-structure interactions involved in the blood flow simulations. The lattice Boltzmann method (LBM) is used to solve the plasma dynamics and a coarse-grained model is employed to capture the dynamics of red blood cells (RBCs) and MPs. These two solvers are coupled together by the immersed boundary method (IBM). The shear rate dependent margination of sphere MPs is firstly investigated. We find that margination of sphere MPs dramatically increases with the increment of wall shear rate [small gamma, Greek, dot above]ω under 800 s-1, induced by the breaking of rouleaux in blood flow. However, the margination probability only slowly grows when [small gamma, Greek, dot above]ω > 800 s-1. Furthermore, the shape effect of MPs is examined by comparing the margination behaviors of sphere-like, oblate-like and prolate-like MPs under different wall shear rates. We find that the margination of MPs is governed by the interplay of two factors: hydrodynamic collisions with RBCs including the collision frequency and collision displacement of MPs, and near wall dynamics. MPs that demonstrate poor performance in one process such as collision frequency may stand out in the other process like near wall dynamics. Specifically, the ellipsoidal MPs (oblate and prolate) with small aspect ratio (AR) outperform those with large AR regardless of the wall shear rate, due to their better performance in both the collision with RBCs and near wall dynamics. Additionally, we find there exists a transition shear rate region 700 s-1 < [small gamma, Greek, dot above]ω < 900 s-1 for all of these MPs: the margination probability dramatically increases with the shear rate below this region and slowly grows above this region, similar to sphere MPs. We further use the surface area to volume ratio (SVR) to distinguish different shaped MPs and illustrate their shear rate dependent margination in a contour in the shear rate-SVR plane. It is of significance that we can approximately predict the margination of MPs with a specific SVR. All these simulation results can be potentially applied to guide the design of micro-drug carriers for biomedical applications.

Numerical Investigation of the Effects of Red Blood Cell Cytoplasmic Viscosity Contrasts on Single Cell and Bulk Transport Behaviour

In-silico cellular models of blood are invaluable to gain understanding about the many interesting properties that blood exhibits. However, numerical investigations that focus on the effects of cytoplasmic viscosity in these models are not very prevalent. We present a parallelised method to implement cytoplasmic viscosity for HemoCell, an open-source cellular model based on immersed boundary lattice Boltzmann methods, using an efficient ray-casting algorithm. The effects of the implementation are investigated with single-cell simulations focusing on the deformation in shear flow, the migration due to wall induced lift forces, the characteristic response time in periodic stretching and pair collisions between red blood cells and platelets. Collective transport phenomena are also investigated in many-cell simulations in a pressure driven channel flow. The simulations indicate that the addition of a viscosity contrast between internal and external fluids significantly affects the deformability of a red blood cell, which is most pronounced during very short time-scale events. Therefore, modelling the cytoplasmic viscosity contrast is important in scenarios with high velocity deformation, typically high shear rate flows.

Effect of spectrin network elasticity on the shapes of erythrocyte doublets

Red blood cell (RBC) aggregates play an important role in determining blood rheology. RBCs in plasma or polymer solution interact attractively to form various shapes of RBC doublets, where the attractive interactions can be varied by changing the solution conditions. A systematic numerical study on RBC doublet formation is performed, which takes into account the shear elasticity of the RBC membrane due to the spectrin cytoskeleton, in addition to the membrane bending rigidity. RBC membranes are modeled by two-dimensional triangular networks of linked vertices, which represent three-dimensional cell shapes. The phase space of RBC doublet shapes in a wide range of adhesion strengths, reduced volumes, and shear elasticities is obtained. The shear elasticity of the RBC membrane changes the doublet phases significantly. Experimental images of RBC doublets in different solutions show similar configurations. Furthermore, we show that rouleau formation is affected by the doublet structure.

Morphological and mechanical determinants of cellular uptake of deformable nanoparticles

Understanding the interactions of nanoparticles (NPs) with cell membranes and regulating their cellular uptake processes are of fundamental importance to the design of drug delivery systems with minimum toxicity, high efficiency and long circulation time. Employing the procedure of coarse-graining, we built an elastically deformable NP model with tunable morphological and mechanical properties. We found that the cellular uptake of deformable NPs depends on their shape: an increase in the particle elasticity significantly slows the uptake rate of spherical NPs, slightly retards that of prolate NPs, and promotes the uptake of oblate NPs. The intrinsic mechanisms have been carefully investigated through analysis of the endocytic mechanisms and free energy calculations. These findings provide unique insights into how deformable NPs penetrate across cell membranes and offer novel possibilities for designing effective NP-based carriers for drug delivery.

Label-free sorting of soft microparticles using a bioinspired synthetic cilia array

Isolating cells of interest from a heterogeneous population has been of critical importance in biological studies and clinical applications. In this study, a novel approach is proposed for utilizing an active ciliary system in microfluidic devices to separate particles based on their physical properties. In this approach, the bottom of the microchannel is covered with an equally spaced cilia array of various patterns which is actuated by an external stimuli. 3D simulations are carried out to study cilia-particle interaction and isolation dynamic in a microfluidic channel. It is observed that these elastic hair-like filaments can influence particle's trajectories differently depending on their biophysical properties. This modeling study utilizes immersed boundary method coupled with the lattice Boltzmann method. Soft particles and cilia are implemented through the spring connected network model and point-particle scheme, respectively. It is shown that cilia array with proper stimulation is able to continuously and non-destructively separate cells into subpopulations based on their size, shape, and stiffness. At the end, a design map for fabrication of a programmable microfluidic device capable of isolating various subpopulations of cells is developed. This biocompatible, label-free design can separate cells/soft microparticles with high throughput which can greatly complement existing separation technologies.

A parallel fluid-solid coupling model using LAMMPS and Palabos based on the immersed boundary method

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the Jeffery orbits of an ellipsoid particle in shear flow, red blood cell stretching test, and effective blood viscosity flowing in tubes. It demonstrated essentially linear scaling from 512 to 8192 cores for both strong and weak scaling cases. The computing time for the coupling increased with the solid fraction. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code.

Image-based model of the spectrin cytoskeleton for red blood cell simulation

We simulate deformable red blood cells in the microcirculation using the immersed boundary method with a cytoskeletal model that incorporates structural details revealed by tomographic images. The elasticity of red blood cells is known to be supplied by both their lipid bilayer membranes, which resist bending and local changes in area, and their cytoskeletons, which resist in-plane shear. The cytoskeleton consists of spectrin tetramers that are tethered to the lipid bilayer by ankyrin and by actin-based junctional complexes. We model the cytoskeleton as a random geometric graph, with nodes corresponding to junctional complexes and with edges corresponding to spectrin tetramers such that the edge lengths are given by the end-to-end distances between nodes. The statistical properties of this graph are based on distributions gathered from three-dimensional tomographic images of the cytoskeleton by a segmentation algorithm. We show that the elastic response of our model cytoskeleton, in which the spectrin polymers are treated as entropic springs, is in good agreement with the experimentally measured shear modulus. By simulating red blood cells in flow with the immersed boundary method, we compare this discrete cytoskeletal model to an existing continuum model and predict the extent to which dynamic spectrin network connectivity can protect against failure in the case of a red cell subjected to an applied strain. The methods presented here could form the basis of disease- and patient-specific computational studies of hereditary diseases affecting the red cell cytoskeleton.

Red blood cells are responsible for delivering oxygen to tissues throughout the body. These terminally differentiated cells have developed a fascinating flexibility and resiliency that is critical to navigating the circulatory system. Far from being rigid bodies, red blood cells adopt biconcave disk shapes at equilibrium, parachute-like shapes as they move between large vessels and small capillaries, and more extreme shapes as they traverse the endothelial slits of the spleen. Understanding the remarkable mechanical properties that allow red cells to experience such large deformations while maintaining structural integrity is a fundamental question in physiology that may help advance treatments of genetic disorders such as hereditary spherocytosis and elliptocytosis that affect red cell flexibility and can lead to severe anemia. In this work, we present a model of the red blood cell cytoskeleton based on cryoelectron tomography data. We develop an image processing technique to gather statistics from these data and use these statistics to generate a random entropic network to model the cytoskeleton. We then simulate the behavior of the resulting red blood cells in flow. As we demonstrate through simulations, this method makes it possible to examine the consequences of changes in microstructural properties such as the rate of cytoskeletal remodeling.

An Enhanced Spring-Particle Model for Red Blood Cell Structural Mechanics: Application to the Stomatocyte–Discocyte–Echinocyte Transformation

Red blood cells (RBCs) are the most abundant cellular element suspended in blood. Together with the usual biconcave-shaped RBCs, i.e., discocytes, unusual-shaped RBCs are also observed under physiological and experimental conditions, e.g., stomatocytes and echinocytes. Stomatocytes and echinocytes are formed from discocytes and in addition can revert back to being discocytes; this shape change is known as the stomatocyte–discocyte–echinocyte (SDE) transformation. To-date, limited research has been conducted on the numerical prediction of the full SDE transformation. Spring-particle RBC (SP-RBC) models are commonly used to numerically predict RBC mechanics and rheology. However, these models are incapable of predicting the full SDE transformation because the typically employed bending model always leads to numerical instability with severely deformed shapes. In this work, an enhanced SP-RBC model is proposed in order to extend the capability of this model type and so that the full SDE transformation can be reproduced. This is achieved through the leveraging of an advanced bending model. Transformed vesicle and RBC shapes are predicted for a range of reduced volume and reduced membrane area difference (MAD), and very good agreement is obtained in the comparison of predicted shapes with experimental observations. Through these predictions, vesicle and SDE transformation phase diagrams are developed and, importantly, in the SDE case, shape boundaries are proposed for the first time relating RBC shape categories to RBC reduced volume and reduced MAD.

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.

Cellular Level In-silico Modeling of Blood Rheology with An Improved Material Model for Red Blood Cells

Many of the intriguing properties of blood originate from its cellular nature. Therefore, accurate modeling of blood flow related phenomena requires a description of the dynamics at the level of individual cells. This, however, presents several computational challenges that can only be addressed by high performance computing. We present Hemocell, a parallel computing framework which implements validated mechanical models for red blood cells and is capable of reproducing the emergent transport characteristics of such a complex cellular system. It is computationally capable of handling large domain sizes, thus it is able to bridge the cell-based micro-scale and macroscopic domains. We introduce a new material model for resolving the mechanical responses of red blood cell membranes under various flow conditions and compare it with a well established model. Our new constitutive model has similar accuracy under relaxed flow conditions, however, it performs better for shear rates over 1,500 s^-1. We also introduce a new method to generate randomized initial conditions for dense mixtures of different cell types free of initial positioning artifacts.

Dynamic fatigue measurement of human erythrocytes using dielectrophoresis

Erythrocytes must undergo severe deformation to pass through narrow capillaries and submicronic splenic slits for several hundred thousand times in their normal lifespan. Studies of erythrocyte biomechanics have been mainly focused on cell deformability and rheology measured from a single application of stress and mostly under a static or quasi-static state using classical biomechanical techniques, such as optical tweezers and micropipette aspiration. Dynamic behavior of erythrocytes in response to cyclic stresses that contributes to the membrane failure in blood circulation is not fully understood. This paper presents a new experimental method for dynamic fatigue analysis of erythrocytes, using amplitude modulated electrokinetic force field in a microfluidic platform. We demonstrate the capability of this new technique using a low cycle fatigue analysis of normal human erythrocytes and ATP-depleted erythrocytes. Cyclic tensile stresses are generated to induce repeated uniaxial stretching and extensional recovery of single erythrocytes. Results of morphological and biomechanical parameters of individually tracked erythrocytes show strong correlations with the number of the loading cycles. Under a same strength of electric field, after 180 stress cycles, for normal erythrocytes, maximum stretch ratio decreases from 3.80 to 2.86, characteristic time of cellular extensional recovery increases from 0.16s to 0.37s, membrane shear viscosity increases from 1.0(µN/m)s to 1.6(µN/m)s. Membrane deformation in a small number of erythrocytes becomes irreversible after large deformation for about 200 cyclic loads. ATP-depleted cells show similar trends in decreased deformation and increased characteristic time with the loading cycles. These results show proof of concept of the new microfluidics technique for dynamic fatigue analysis of human erythrocytes.

STATEMENT OF SIGNIFICANCE

Red blood cells (RBCs) experience a tremendous number of deformation in blood circulation before losing their mechanical deformability and eventually being degraded in the reticuloendothelial system. Prior efforts in RBC biomechanics have mostly focused on a single-application of stress, or quasi-static loading through physical contact to deform cell membranes, thus with limited capabilities in probing cellular dynamic responses to cyclic stresses. We present a unique electrokinetic microfluidic system for the study of dynamic fatigue behavior of RBCs subjected to cyclic loads. Our work shows quantitatively how the cyclic stretching loads cause membrane mechanical degradation and irreversibly deformed cells. This new technique can be useful to identify biomechanical markers for prediction of the mechanical stability and residual lifespan of circulating RBCs.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Study of in vitro RBCs membrane elasticity with AOD scanning optical tweezers

The elasticity of red cell membrane is a critical physiological index for the activity of RBC. Study of the inherent mechanism for RBCs membrane elasticity transformation is attention-getting all along. This paper proposes an optimized measurement method of erythrocytes membrane shear modulus incorporating acousto-optic deflector (AOD) scanning optical tweezers system. By use of this method, both membrane shear moduli and sizes of RBCs with different in vitro times were determined. The experimental results reveal that the RBCs membrane elasticity and size decline with in vitro time extension. In addition, semi quantitative measurements of S-nitrosothiol content in blood using fluorescent spectrometry during in vitro storage show that RBCs membrane elasticity change is positively associated with the S-nitrosylation level of blood. The analysis considered that the diminished activity of the nitric oxide synthase makes the S-nitrosylation of in vitro blood weaker gradually. The main reason for worse elasticity of the in vitro RBCs is that S-nitrosylation effect of spectrin fades. These results will provide a guideline for further study of in vitro cells activity and other clinical applications.

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of [Formula: see text] diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor-ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.