A multiscale red blood cell model with accurate mechanics, rheology, and dynamics

Probing wrapping dynamics of spherical nanoparticles by 3D vesicles using force-based simulations

Nanoparticles present in various environments can interact with living organisms, potentially leading to deleterious effects. Understanding how these nanoparticles interact with cell membranes is crucial for rational assessment of their impact on diverse biological processes. While previous research has explored particle-membrane interactions, the dynamic processes of particle wrapping by fluid vesicles remain incompletely understood. In this study, we introduce a force-based, continuum-scale model utilizing triangulated mesh representation and discrete differential geometry to investigate particle-vesicle interaction dynamics. Our model captures the transformation of vesicle shape and nanoparticle wrapping by calculating the forces arising from membrane bending energy and particle adhesion energy. Inspired by cell phagocytosis of large particles, we focus on establishing a quantitative understanding of large-scale vesicle deformation induced by the interaction with particles of comparable sizes. We first examine the interactions between spherical vesicles and individual nanospheres, both externally and internally, and quantify energy landscapes across different wrapping fractions of the nanoparticles. Furthermore, we explore multiple particle interactions with biologically relevant fluid vesicles with nonspherical shapes. Our study reveals that initial particle positions and interaction sequences are critical in determining the final equilibrium shapes of the vesicle-particle complexes in these interactions. These findings emphasize the importance of nanoparticle positioning and wrapping fractions in the dynamics of particle-vesicle interactions, providing crucial insights for future research in the field.

Numerical study of ultra-large von Willebrand factor multimers in coagulopathy

An excessive von Willebrand factor (VWF) secretion, coupled with a moderate to severe deficiency of ADAMTS13 activity, serves as a linking mechanism between inflammation to thrombosis. The former facilitates platelet adhesion to the vessel wall and the latter is required to cleave VWF multimers. As a result, the ultra-large VWF (UL-VWF) multimers released by Weibel-Palade bodies remain uncleaved. In this study, using a computational model based on first principles, we quantitatively show how the uncleaved UL-VWF multimers interact with the blood cells to initiate microthrombosis. We observed that platelets first adhere to unfolded and stretched uncleaved UL-VWF multimers anchored to the microvessel wall. By the end of this initial adhesion phase, the UL-VWF multimers and platelets make a mesh-like trap in which the red blood cells increasingly accumulate to initiate a gradually growing microthrombosis. Although high-shear rate and blood flow velocity are required to activate platelets and unfold the UL-VWFs, during the initial adhesion phase, the blood velocity drastically drops after thrombosis, and as a result, the wall shear stress is elevated near UL-VWF roots, and the pressure drops up to 6 times of the healthy condition. As the time passes, these trends progressively continue until the microthrombosis fully develops and the effective size of the microthrombosis and these flow quantities remain almost constant. Our findings quantitatively demonstrate the potential role of UL-VWF in coagulopathy.

Computational analysis of cancer cell adhesion in curved vessels affected by wall shear stress for prediction of metastatic spreading

Introduction: The dynamics of circulating tumor cells (CTCs) within blood vessels play a pivotal role in predicting metastatic spreading of cancer within the body. However, the limited understanding and method to quantitatively investigate the influence of vascular architecture on CTC dynamics hinders our ability to predict metastatic process effectively. To address this limitation, the present study was conducted to investigate the influence of blood vessel tortuosity on the behaviour of CTCs, focusing specifically on establishing methods and examining the role of shear stress in CTC-vessel wall interactions and its subsequent impact on metastasis. Methods: We computationally simulated CTC behaviour under various shear stress conditions induced by vessel tortuosity. Our computational model, based on the lattice Boltzmann method (LBM) and a coarse-grained spectrin-link membrane model, efficiently simulates blood plasma dynamics and CTC deformability. The model incorporates fluid-structure interactions and receptor-ligand interactions crucial for CTC adhesion using the immersed boundary method (IBM). Results: Our findings reveal that uniform shear stress in straight vessels leads to predictable CTC-vessel interactions, whereas in curved vessels, asymmetrical flow patterns and altered shear stress create distinct adhesion dynamics, potentially influencing CTC extravasation. Quantitative analysis shows a 25% decrease in the wall shear stress in low-shear regions and a 58.5% increase in the high-shear region. We observed high-shear regions in curved vessels to be potential sites for increased CTC adhesion and extravasation, facilitated by elevated endothelial expression of adhesion molecules. This phenomenon correlates with the increased number of adhesion bonds, which rises to approximately 40 in high-shear regions, compared to around 12 for straight vessels and approximately 5-6 in low-shear regions. The findings also indicate an optimal cellular stiffness necessary for successful CTC extravasation in curved vessels. Discussion: By the quantitative assessment of the risk of CTC extravasation as a function of vessel tortuosity, our study offers a novel tool for the prediction of metastasis risk to support the development of personalized therapeutic interventions based on individual vascular characteristics and tumor cell properties.

Numerical analysis of blood flow through stenosed microvessels using a multi-phase model

Blood flow in arterioles have attracted considerable research attention due to their clinical implications. However, the fluid structure interaction between red blood cells and plasma in the blood poses formidable difficulty to the computational efforts. In this contribution, we seek to represent the red blood cells in the blood as a continuous non-Newtonian phase and construct a multi-phase model for the blood flow in microvessels. The methods are presented and validated using a channel with sudden expansion. And the resulting blood flow inside a stenosed microvessel is investigated at different inlet velocity amplitudes and hematocrits. It is show that the increase of both inlet velocity amplitude and inlet hematocrit leads to longer and thicker cell-rich layer downstream the stenosis. Besides, it is found that the maximum values of wall shear stress scales up with inlet velocity amplitudes and hematocrits. These results show the validity of the proposed computational model and provide helpful insights into blood flow behaviors inside stenosed vessels.

Two-component macrophage model for active phagocytosis with pseudopod formation

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

Collective behavior of squirmers in thin films

Bacteria in biofilms form complex structures and can collectively migrate within mobile aggregates, which is referred to as swarming. This behavior is influenced by a combination of various factors, including morphological characteristics and propulsive forces of swimmers, their volume fraction within a confined environment, and hydrodynamic and steric interactions between them. In our study, we employ the squirmer model for microswimmers and the dissipative particle dynamics method for fluid modeling to investigate the collective motion of swimmers in thin films. The film thickness permits a free orientation of non-spherical squirmers, but constraints them to form a two-layered structure at maximum. Structural and dynamic properties of squirmer suspensions confined within the slit are analyzed for different volume fractions of swimmers, motility types (e.g., pusher, neutral squirmer, puller), and the presence of a rotlet dipolar flow field, which mimics the counter-rotating flow generated by flagellated bacteria. Different states are characterized, including a gas-like phase, swarming, and motility-induced phase separation, as a function of increasing volume fraction. Our study highlights the importance of an anisotropic swimmer shape, hydrodynamic interactions between squirmers, and their interaction with the walls for the emergence of different collective behaviors. Interestingly, the formation of collective structures may not be symmetric with respect to the two walls. Furthermore, the presence of a rotlet dipole significantly mitigates differences in the collective behavior between various swimmer types. These results contribute to a better understanding of the formation of bacterial biofilms and the emergence of collective states in confined active matter.

Motion of microswimmers in cylindrical microchannels

Biological and artificial microswimmers often have to propel through a variety of environments, ranging from heterogeneous suspending media to strong geometrical confinement. Under confinement, local flow fields generated by microswimmers, and steric and hydrodynamic interactions with their environment determine the locomotion. We propose a squirmer-like model to describe the motion of microswimmers in cylindrical microchannels, where propulsion is generated by a fixed surface slip velocity. The model is studied using an approximate analytical solution for cylindrical swimmer shapes, and by numerical hydrodynamics simulations for spherical and spheroidal shapes. For the numerical simulations, we employ the dissipative particle dynamics method for modelling fluid flow. Both the analytical model and simulations show that the propulsion force increases with increasing confinement. However, the swimming velocity under confinement remains lower than the swimmer speed without confinement for all investigated conditions. In simulations, different swimming modes (i.e. pusher, neutral, puller) are investigated, and found to play a significant role in the generation of propulsion force when a swimmer approaches a dead end of a capillary tube. Propulsion generation in confined systems is local, such that the generated flow field generally vanishes beyond the characteristic size of the swimmer. These results contribute to a better understanding of microswimmer force generation and propulsion under strong confinement, including the motion in porous media and in narrow channels.

Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives

With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics and the interactions of fluid-filled bodies, several methods have been developed. The objective of this review is to present a compact foundation of the methods used in the literature in the context of lattice Boltzmann methods. For hydrodynamics, we focus on the lattice Boltzmann method due to its specific ability to treat time- and spatial-dependent boundary conditions and to incorporate new physical models in a computationally efficient way. We split the existing methods into two groups with regard to the interfacial boundary: fluid-structure and fluid-fluid methods. The fluid-structure methods are characterised by the coupling between fluid dynamics and mechanics of the flowing body, often used in applications involving membranes and similar flexible solid boundaries. We further divide fluid-structure-based methods into two subcategories, those which treat the fluid-structure boundary as a continuum medium and those that treat it as a discrete collection of individual springs and particles. Next, we discuss the fluid-fluid methods, particularly useful for the simulations of fluid-fluid interfaces. We focus on models for immiscible droplets and their interaction in a suspending fluid and describe benchmark tests to validate the models for fluid-filled bodies.

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

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

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

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

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

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

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

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

Numerical investigation on red blood cell flow based on unstructured grid

Prediction of blood cell flow is known as the difficult research by reason of the complexity of blood vessel. In this study, considering the complex structure of blood vessels, a mechanical model for red blood cell (RBC) based on unstructured grid has been established to study the flow characteristics of RBCs in complex blood vessels. In the model, the strain-energy function by Skalak is employed to model the shear elasticity and surface-area conservation of the membrane, and the hinge spring is used to describe the forces originating from local bending of the membrane. The immersed boundary method is utilized to couple the interphase force. Using the model, the stretching test of RBC is compared with the experiment data, and the good agreement verified the validation of the present model. The morphology of red blood cell and the blood viscosity in micro-vessel are studied. RBCs move with a symmetric shape (parachute shape) in small blood vessels, and the buckling instability is observed when the RBC flow slowly through a micro-vessel or a converging-diverging capillary. When the vessel diameter is around 10 μm, the reverse Fahraeus-Lindqvist effect is presented. The blood apparent viscosity shows linear increase with the blood hematocrit. In addition, Malaria infection can make the RBC deformability decreased and the blood apparent viscosity increased.

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.

Active buckling of pressurized spherical shells: Monte Carlo simulation

We study the buckling of pressurized spherical shells by Monte Carlo simulations in which the detailed balance is explicitly broken-thereby driving the shell to be active, out of thermal equilibrium. Such a shell typically has either higher (active) or lower (sedate) fluctuations compared to one in thermal equilibrium depending on how the detailed balance is broken. We show that, for the same set of elastic parameters, a shell that is not buckled in thermal equilibrium can be buckled if turned active. Similarly a shell that is buckled in thermal equilibrium can unbuckle if sedated. Based on this result, we suggest that it is possible to experimentally design microscopic elastic shells whose buckling can be optically controlled.

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.

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

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

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

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

Effect of Cell Age and Membrane Rigidity on Red Blood Cell Shape in Capillary Flow

Blood flow in the microcirculatory system is crucially affected by intrinsic red blood cell (RBC) properties, such as their deformability. In the smallest vessels of this network, RBCs adapt their shapes to the flow conditions. Although it is known that the age of RBCs modifies their physical properties, such as increased cytosol viscosity and altered viscoelastic membrane properties, the evolution of their shape-adapting abilities during senescence remains unclear. In this study, we investigated the effect of RBC properties on the microcapillary in vitro flow behavior and their characteristic shapes in microfluidic channels. For this, we fractioned RBCs from healthy donors according to their age. Moreover, the membranes of fresh RBCs were chemically rigidified using diamide to study the effect of isolated graded-membrane rigidity. Our results show that a fraction of stable, asymmetric, off-centered slipper-like cells at high velocities decreases with increasing age or diamide concentration. However, while old cells form an enhanced number of stable symmetric croissants at the channel centerline, this shape class is suppressed for purely rigidified cells with diamide. Our study provides further knowledge about the distinct effects of age-related changes of intrinsic cell properties on the single-cell flow behavior of RBCs in confined flows due to inter-cellular age-related cell heterogeneity.

Competition between deformation and free volume quantified by 3D image analysis of red blood cell

Cells in living organisms are subjected to mechanical strains caused by external forces like overcrowding, resulting in strong deformations that affect cell function. We study the interplay between deformation and crowding of red blood cells (RBCs) in dispersions of nonabsorbing rod-like viruses. We identify a sequence of configurational transitions of RBC doublets, including configurations that can only be induced by long-ranged attraction: highly fluctuating T-shaped and face-to-face configurations at low, and doublets approaching a complete spherical configuration at high, rod concentrations. Complementary simulations are used to explore different energy contributions to deformation as well as the stability of RBC doublet configurations. Our advanced analysis of 3D reconstructed confocal images of RBC doublets quantifies the depletion interaction and the resulting deformation energy. Thus, we introduce a noninvasive, high-throughput platform that is generally applicable to investigate the mechanical response of biological cells to external forces and characterize their mechanical properties.

Mechano-immunology in microgravity

Life on Earth has evolved to thrive in the Earth's natural gravitational field; however, as space technology advances, we must revisit and investigate the effects of unnatural conditions on human health, such as gravitational change. Studies have shown that microgravity has a negative impact on various systemic parts of humans, with the effects being more severe in the human immune system. Increasing costs, limited experimental time, and sample handling issues hampered our understanding of this field. To address the existing knowledge gap and provide confidence in modelling the phenomena, in this review, we highlight experimental works in mechano-immunology under microgravity and different computational modelling approaches that can be used to address the existing problems.

Conformability of flexible sheets on spherical surfaces

Three-dimensional surface-conformable electronics is a burgeoning technology with potential applications in curved displays, bioelectronics, and biomimetics. Flexible electronics are notoriously difficult to fully conform to nondevelopable surfaces such as spheres. Although stretchable electronics can well conform to nondevelopable surfaces, they need to sacrifice pixel density for stretchability. Various empirical designs have been explored to improve the conformability of flexible electronics on spherical surfaces. However, no rational design guidelines exist. This study uses a combination of experimental, analytical, and numerical approaches to systematically investigate the conformability of both intact and partially cut circular sheets on spherical surfaces. Through the analysis of thin film buckling on curved surfaces, we identify a scaling law that predicts the conformability of flexible sheets on spherical surfaces. We also quantify the effects of radial slits on enhancing conformability and provide a practical guideline for using these slits to improve conformability from 40% to more than 90%.

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

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

The stress-free state of human erythrocytes: Data-driven inference of a transferable RBC model

The stress-free state (SFS) of red blood cells (RBCs) is a fundamental reference configuration for the calibration of computational models, yet it remains unknown. Current experimental methods cannot measure the SFS of cells without affecting their mechanical properties, whereas computational postulates are the subject of controversial discussions. Here, we introduce data-driven estimates of the SFS shape and the visco-elastic properties of RBCs. We employ data from single-cell experiments that include measurements of the equilibrium shape of stretched cells and relaxation times of initially stretched RBCs. A hierarchical Bayesian model accounts for these experimental and data heterogeneities. We quantify, for the first time, the SFS of RBCs and use it to introduce a transferable RBC (t-RBC) model. The effectiveness of the proposed model is shown on predictions of unseen experimental conditions during the inference, including the critical stress of transitions between tumbling and tank-treading cells in shear flow. Our findings demonstrate that the proposed t-RBC model provides predictions of blood flows with unprecedented accuracy and quantified uncertainties.

Hemolysis prediction in bio-microfluidic applications using resolved CFD-DEM simulations

BACKGROUND AND OBJECTIVE

Hemolysis, namely hemoglobin leakage from red blood cells (RBCs), is one of the major sources of incorrect results in clinical tests, especially when passive microfluidics is involved. This is due to small characteristic dimensions which could cause strong RBCs deformation. Prediction of hemolysis is essential in the design and optimization of lab-on-a-chip devices for cell sorting and plasma separation. The aim of this work is to provide a numerical simulation tool this purpose applicable to real-scale bio-microfluidic devices with affordable computational cost.

METHODS

Blood is modelled as a suspension of biological cells, mainly RBCs, in liquid plasma assumed as a Newtonian, incompressible carrier fluid. Therefore, the physics of cells and carrier fluid is coupled by means of an immersed boundary concept known as resolved CFD-DEM. In this approach, the Navier-Stokes equations are numerically solved through a finite volume method with an additional penalty term to account for the presence of RBCs. RBCs' positions and velocities are updated by solving Newton and Euler equations for conservation of linear and angular momentum. To model the RBCs deformation, a reduced-order model is employed, where each RBC is represented by a clump of overlapping rigid spheres connected by fictional numerical bonds, whose properties are tuned to reproduce the ones of RBCs viscoelastic membrane. This coupled approach allows access to cell-level information and facilitates the usage of strain-based hemolysis models.

RESULTS

Different micro-channel geometries and blood hematocrits are simulated, to explore the influence of these factors on RBCs damage. Statistical analysis is performed to extract relevant biophysical quantities from numerical simulations such as hemolysis index distribution at the channel exit. Finally, the effect of carrier fluid viscosity is studied in relation to cell-cell interactions.

CONCLUSIONS

Simulation results show that hemolysis occurrence is almost independent of the hematocrit values in the microchannel, implying the possibility to speed up calculation using low hematocrit values. Nevertheless, using whole blood viscosity for the carrier fluid overestimates the value of the hemolysis index by almost one order of magnitude.

Red blood cell sublethal damage: haemocompatibility is not the absence of haemolysis

Blood is a complex fluid owing to its two-phase suspension of formed cellular elements within a protein-rich plasma. Vital to its role in distributing nutrients throughout the circulatory system, the mechanical properties of blood - and particularly red blood cells (RBC)-primarily determine bulk flow characteristics and microcirculatory flux. Various factors impair the physical properties of RBC, including cellular senescence, many diseases, and exposure to mechanical forces. Indeed, the latter is increasingly relevant following the advent of modern life support, such as mechanical circulatory support (MCS), which induce unique interactions between blood and artificial environments that leave blood cells with the signature of aging, albeit accelerated, and crucially underlie various serious complications, including death. Accumulating evidence indicates that these complications appear to be associated with mechanical shear forces present within MCS that are not extreme enough to overtly rupture cells, yet may still induce "sublethal" injury and "fatigue" to vital blood constituents. Impaired RBC physical properties following elevated shear exposure-a hallmark of sublethal injury to blood-are notable and may explain, at least in part, systemic complications and premature mortality associated with MCS. Design of optimal next-generation MCS devices thus requires consideration of biocompatibility and blood-device interactions to minimize potential blood complications and promote clinical success. Presented herein is a contemporary understanding of "blood damage," with emphasis on shear exposures that alter microrheological function but do not overtly destroy cells (ie, sublethal damage). Identification of key cellular factors perturbed by supraphysiological shear exposure are examined, offering potential pathways to enhance design of MCS and blood-contacting medical devices.

In silico modeling for the hepatic circulation and transport: From the liver organ to lobules

The function of the liver depends critically on its blood supply. Numerous in silico models have been developed to study various aspects of the hepatic circulation, including not only the macro-hemodynamics at the organ level, but also the microcirculation at the lobular level. In addition, computational models of blood flow and bile flow have been used to study the transport, metabolism, and clearance of drugs in pharmacokinetic studies. These in silico models aim to provide insights into the liver organ function under both healthy and diseased states, and to assist quantitative analysis for surgical planning and postsurgery treatment. The purpose of this review is to provide an update on state-of-the-art in silico models of the hepatic circulation and transport processes. We introduce the numerical methods and the physiological background of these models. We also discuss multiscale frameworks that have been proposed for the liver, and their linkage with the large context of systems biology, systems pharmacology, and the Physiome project. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering Cardiovascular Diseases > Computational Models.

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.

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.

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

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

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

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

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

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

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

Tank-treading dynamics of red blood cells in shear flow: On the membrane viscosity rheology

In this article, extensive three-dimensional simulations are conducted for tank-treading (TT) red blood cells (RBCs) in shear flow with different cell viscous properties and flow conditions. Apart from recent numerical studies on TT RBCs, this research considers the uncertainty in cytoplasm viscosity, covers a more complete range of shear flow situations of available experiments, and examines the TT behaviors in more details. Key TT characteristics, including the rotation frequency, deformation index, and inclination angle, are compared with available experimental results of similar shear flow conditions. Fairly good simulation-experiment agreements for these parameters can be obtained by adjusting the membrane viscosity values; however, different rheological relationships between the membrane viscosity and the flow shear rate are noted for these comparisons: shear thinning from the TT frequency, Newtonian from the inclination angle, and shear thickening from the cell deformation. Previous studies claimed a shear-thinning membrane viscosity model based on the TT frequency results; however, such a conclusion seems premature from our results and more carefully designed and better controlled investigations are required for the RBC membrane rheology. In addition, our simulation results reveal complicate RBC TT features and such information could be helpful for a better understanding of in vivo and in vitro RBC dynamics.

Circulating cell clusters aggravate the hemorheological abnormalities in COVID-19

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

Interaction of the Blood Components with Ascending Thoracic Aortic Aneurysm Wall: Biomechanical and Fluid Analyses

Background: Ascending thoracic aortic aneurysm (ATAA) is an asymptomatic localized dilation of the aorta that is prone to rupture with a high rate of mortality. While diameter is the main risk factor for rupture assessment, it has been shown that the peak wall stress from finite element (FE) simulations may contribute to refinement of clinical decisions. In FE simulations, the intraluminal boundary condition is a single-phase blood flow that interacts with the thoracic aorta (TA). However, the blood is consisted of red blood cells (RBCs), white blood cells (WBCs), and plasma that interacts with the TA wall, so it may affect the resultant stresses and strains in the TA, as well as hemodynamics of the blood. Methods: In this study, discrete elements were distributed in the TA lumen to represent the blood components and mechanically coupled using fluid–structure interaction (FSI). Healthy and aneurysmal human TA tissues were subjected to axial and circumferential tensile loadings, and the hyperelastic mechanical properties were assigned to the TA and ATAA FE models. Results: The ATAA showed larger tensile and shear stresses but smaller fluid velocity compared to the ATA. The blood components experienced smaller shear stress in interaction with the ATAA wall compared to TA. The computational fluid dynamics showed smaller blood velocity and wall shear stress compared to the FSI. Conclusions: This study is a first proof of concept, and future investigations will aim at validating the novel methodology to derive a more reliable ATAA rupture risk assessment considering the interaction of the blood components with the TA wall.

A cell-resolved, Lagrangian solver for modeling red blood cell dynamics in macroscale flows

When red blood cells (RBCs) experience non-physiologically high stresses, e.g., in medical devices, they can rupture in a process called hemolysis. Directly simulating this process is computationally unaffordable given that the length scales of a medical device are several orders of magnitude larger than that of a RBC. To overcome this separation of scales, the present work introduces an affordable computational framework that accurately resolves the stress and deformation of a RBC in a spatially and temporally varying macroscale flow field such as those found in a typical medical device. The underlying idea of the present framework is to treat RBCs as one-way coupled tracers in the macroscale flow by capturing the effect of the flow on their dynamics but neglecting their effect on the flow at the macroscale. As a result, the RBC dynamics are simulated after those of the flow in a postprocessing step by receiving the fluid velocity gradient tensor measured along the RBC trajectory as the input. To resolve the fluid velocity in the immediate vicinity of the RBC as well as the motion of the membrane, we employ the boundary integral method coupled to a structural solver. The governing equations are discretized in space using spherical harmonics, yielding spectral integration accuracy. The predictions produced by this formulation are in good agreement with those obtained from simulations of spherical capsules in shear flows and optical tweezers experiments. The accuracy of the present method is evaluated using unbounded shear flow as a benchmark. Its computational cost grows proportional to p ⁵, where p is the degree of the spherical harmonic. It also exhibits a fast convergence rate that is approximately O ( p 6 ) for p ⪅ 20.

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.

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

Malaria is one of the deadliest infectious diseases and its symptoms are related to the blood stage, when the parasite multiplies within red blood cells. In order to avoid clearance by the spleen, the parasite produces specific factors like the adhesion receptor PfEMP1 and the multifunctional protein KAHRP that lead to the formation of adhesive knobs on the surface of the red blood cells and thus increase residence time in the vasculature. We have developed a computational model for the parasite-induced remodelling of the actin-spectrin network to quantitatively predict the dynamical changes in the mechanical properties of the infected red blood cells and the spatial distribution of the different protein components of the membrane skeleton. Our simulations show that KAHRP can relocate to actin junctions due to dynamical changes in binding affinities, in good qualitative agreement with super-resolution imaging experiments. In the future, our simulation framework can be used to gain further mechanistic insight into the way malaria parasites attack the red blood cell cytoskeleton.

Technologies for measuring red blood cell deformability

Human red blood cells (RBCs) are approximately 8 μm in diameter, but must repeatedly deform through capillaries as small as 2 μm in order to deliver oxygen to all parts of the body. The loss of this capability is associated with the pathology of many diseases, and is therefore a potential biomarker for disease status and treatment efficacy. Measuring RBC deformability is a difficult problem because of the minute forces (∼pN) that must be exerted on these cells, as well as the requirements for throughput and multiplexing. The development of technologies for measuring RBC deformability date back to the 1960s with the development of micropipette aspiration, ektacytometry, and the cell transit analyzer. In the past 10 years, significant progress has been made using microfluidics by leveraging the ability to precisely control fluid flow through microstructures at the size scale of individual RBCs. These technologies have now surpassed traditional methods in terms of sensitivity, throughput, consistency, and ease of use. As a result, these efforts are beginning to move beyond feasibility studies and into applications to enable biomedical discoveries. In this review, we provide an overview of both traditional and microfluidic techniques for measuring RBC deformability. We discuss the capabilities of each technique and compare their sensitivity, throughput, and robustness in measuring bulk and single-cell RBC deformability. Finally, we discuss how these tools could be used to measure changes in RBC deformability in the context of various applications including pathologies caused by malaria and hemoglobinopathies, as well as degradation during storage in blood bags prior to blood transfusions.

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.

The effect of stiffened diabetic red blood cells on wall shear stress in a reconstructed 3D microaneurysm

Blood flow within the vasculature of the retina has been found to influence the progression of diabetic retinopathy. In this research cell resolved blood flow simulations are used to study the pulsatile flow of whole blood through a segmented retinal microaneurysm. Images were collected using adaptive optics optical coherence tomography of the retina of a patient with diabetic retinopathy, and a sidewall (sacciform) microaneurysm was segmented from the volumetric data. The original microaneurysm neck width was varied to produce two additional aneurysm geometries in order to probe the influence of neck width on the transport of red blood cells and platelets into the aneurysm. Red blood cell membrane stiffness was also increased to resolve the impact of rigid red blood cells, as a result of diabetes, in blood flow. Wall shear stress and wall shear stress gradients were calculated throughout the aneurysm domains, and the quantification of the influence of the red blood cells is presented. Average wall shear stress and wall shear stress gradients increased due to the increase of red blood cell membrane stiffness. Stiffened red blood cells were also found to induce higher local wall shear stress and wall shear stress gradients as they passed through the leading and draining parental vessels. Stiffened red blood cells were found to penetrate the aneurysm sac more than healthy red blood cells, as well as decreasing the margination of platelets to the vessel walls of the parental vessel, which caused a decrease in platelet penetration into the aneurysm sac.

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.

Erythrocyte sedimentation: Effect of aggregation energy on gel structure during collapse

The erythrocyte (or red blood cell) sedimentation rate (ESR) is commonly interpreted as a measure of cell aggregation and as a biomarker of inflammation. It is well known that an increase of fibrinogen concentration, an aggregation-inducing protein for erythrocytes, leads to an increase of the sedimentation rate of erythrocytes, which is generally explained through the formation and faster settling of large disjoint aggregates. However, many aspects of erythrocyte sedimentation conform well with the collapse of a particle gel rather than with the sedimentation of disjoint aggregates. Using experiments and cell-level numerical simulations, we systematically investigate the dependence of ESR on fibrinogen concentration and its relation to the microstructure of the gel-like erythrocyte suspension. We show that for physiological aggregation interactions, an increase in the attraction strength between cells results in a cell network with larger void spaces. This geometrical change in the network structure occurs due to anisotropic shape and deformability of erythrocytes and leads to an increased gel permeability and faster sedimentation. Our results provide a comprehensive relation between the ESR and the cell-level structure of erythrocyte suspensions and support the gel hypothesis in the interpretation of blood sedimentation.

Dynamics of Individual Red Blood Cells Under Shear Flow: A Way to Discriminate Deformability Alterations

In this work, we compared the dynamics of motion in a linear shear flow of individual red blood cells (RBCs) from healthy and pathological donors (Sickle Cell Disease (SCD) or Sickle Cell-β-thalassemia) and of low and high densities, in a suspending medium of higher viscosity. In these conditions, at lower shear rates, biconcave discocyte-shaped RBCs present an unsteady flip-flopping motion, where the cell axis of symmetry rotates in the shear plane, rocking to and fro between an orbital angle ±ϕ observed when the cell is on its edge. We show that the evolution of ϕ depends solely on RBC density for healthy RBCs, with denser RBCs displaying lower ϕ values than the lighter ones. Typically, at a shear stress of 0.08 Pa, ϕ has values of 82 and 72° for RBCs with average densities of 1.097 and 1.115, respectively. Surprisingly, we show that SCD RBCs display the same ϕ-evolution as healthy RBCs of same density, showing that the flip-flopping behavior is unaffected by the SCD pathology. When the shear stress is increased further (above 0.1 Pa), healthy RBCs start going through a transition to a fluid-like motion, called tank-treading, where the RBC has a quasi-constant orientation relatively to the flow and the membrane rotates around the center of mass of the cell. This transition occurs at higher shear stresses (above 0.2 Pa) for denser cells. This shift toward higher stresses is even more remarkable in the case of SCD RBCs, showing that the transition to the tank-treading regime is highly dependent on the SCD pathology. Indeed, at a shear stress of 0.2 Pa, for RBCs with a density of 1.097, 100% of healthy RBCs have transited to the tank-treading regime vs. less than 50% SCD RBCs. We correlate the observed differences in dynamics to the alterations of RBC mechanical properties with regard to density and SCD pathology reported in the literature. Our results suggest that it might be possible to develop simple non-invasive assays for diagnosis purpose based on the RBC motion in shear flow and relying on this millifluidic approach.

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

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