Quantifying the biophysical characteristics of Plasmodium-falciparum-parasitized red blood cells in microcirculation

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.

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.

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

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

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

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

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

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

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.

Conformations and dynamic behaviors of confined wormlike chains in a pressure-driven flow

The conformations and dynamic behaviors of wormlike chains confined by a slit in a pressure-driven flow were investigated using dissipative particle dynamics method. The wormlike chains exhibit varying conformations due to the varying shear stresses across the slit. The wormlike chain solution can be well described by the power-law fluid, and the power-law index decreases with the increase in chain rigidity. We also presented that the wormlike chain undergoes tumbling motion in the vicinity of the wall in the presence of pressure-driven flow. We also found that the wormlike chains can migrate both away from the wall and slightly away from the slit center, and the migration away from the slit center increases as the chain rigidity is increased because of hydrodynamic interactions induced in a more rigid wormlike chain.

Distributed Acceleration of Adhesive Dynamics Simulations

Cell adhesion plays a critical role in processes ranging from leukocyte migration to cancer cell transport during metastasis. Adhesive cell interactions can occur over large distances in microvessel networks with cells traveling over distances much greater than the length scale of their own diameter. Therefore, biologically relevant investigations necessitate efficient modeling of large field-of-view domains, but current models are limited by simulating such geometries at the sub-micron scale required to model adhesive interactions which greatly increases the computational requirements for even small domain sizes. In this study we introduce a hybrid scheme reliant on both on-node and distributed parallelism to accelerate a fully deformable adhesive dynamics cell model. This scheme leads to performant system usage of modern supercomputers which use a many-core per-node architecture. On-node acceleration is augmented by a combination of spatial data structures and algorithmic changes to lessen the need for atomic operations. This deformable adhesive cell model accelerated with hybrid parallelization allows us to bridge the gap between high-resolution cell models which can capture the sub-micron adhesive interactions between the cell and its microenvironment, and large-scale fluid-structure interaction (FSI) models which can track cells over considerable distances. By integrating the sub-micron simulation environment into a distributed FSI simulation we enable the study of previously unfeasible research questions involving numerous adhesive cells in microvessel networks such as cancer cell transport through the microcirculation.

The role of adhesive receptor patterns on cell transport in complex microvessels

Cell transport is governed by the interaction of fluid dynamic forces and biochemical factors such as adhesion receptor expression and concentration. Although the effect of endothelial receptor density is well understood, it is not clear how the spacing and local spatial distribution of receptors affect cell adhesion in three-dimensional microvessels. To elucidate the effect of vessel shape on cell trajectory and the arrangement of endothelial receptors on cell adhesion, we employed a three-dimensional deformable cell model that incorporates microscale interactions between the cell and the endothelium. Computational cellular adhesion models are systematically altered to assess the influence of receptor spacing. We demonstrate that the patterns of receptors on the vessel walls are a key factor guiding cell movement. In straight microvessels, we show a relationship between cell velocity and the spatial distribution of adhesive endothelial receptors, with larger receptor patches producing lower translational velocities. The joint effect of the complex vessel topology seen in microvessel shapes such as curved and bifurcated vessels when compared to straight tubes is explored with results which showed the spatial distribution of receptors affecting cell trajectory. Our findings here represent demonstration of the previously undescribed relationship between receptor pattern and geometry that guides cellular movement in complex microenvironments.

Biophysical Tools and Concepts Enable Understanding of Asexual Blood Stage Malaria

Forces and mechanical properties of cells and tissues set constraints on biological functions, and are key determinants of human physiology. Changes in cell mechanics may arise from disease, or directly contribute to pathogenesis. Malaria gives many striking examples. Plasmodium parasites, the causative agents of malaria, are single-celled organisms that cannot survive outside their hosts; thus, thost-pathogen interactions are fundamental for parasite’s biological success and to the host response to infection. These interactions are often combinations of biochemical and mechanical factors, but most research focuses on the molecular side. However, Plasmodium infection of human red blood cells leads to changes in their mechanical properties, which has a crucial impact on disease pathogenesis because of the interaction of infected red blood cells with other human tissues through various adhesion mechanisms, which can be probed and modelled with biophysical techniques. Recently, natural polymorphisms affecting red blood cell biomechanics have also been shown to protect human populations, highlighting the potential of understanding biomechanical factors to inform future vaccines and drug development. Here we review biophysical techniques that have revealed new aspects of Plasmodium falciparum invasion of red blood cells and cytoadhesion of infected cells to the host vasculature. These mechanisms occur differently across Plasmodium species and are linked to malaria pathogenesis. We highlight promising techniques from the fields of bioengineering, immunomechanics, and soft matter physics that could be beneficial for studying malaria. Some approaches might also be applied to other phases of the malaria lifecycle and to apicomplexan infections with complex host-pathogen interactions.

Blood Viscosity in Subjects With Type 2 Diabetes Mellitus: Roles of Hyperglycemia and Elevated Plasma Fibrinogen

The viscosity of blood is an indicator in the understanding and treatment of disease. An elevated blood viscosity has been demonstrated in patients with Type 2 Diabetes Mellitus (T2DM), which might represent a risk factor for cardiovascular complications. However, the roles of glycated hemoglobin (HbA1c) and plasma fibrinogen levels on the elevated blood viscosity in subjects with T2DM at different chronic glycemic conditions are still not clear. Here, we evaluate the relationship between the blood viscosity and HbA1c as well as plasma fibrinogen levels in patients with T2DM. The experimental data show that the mean values of the T2DM blood viscosity are higher in groups with higher HbA1c levels, but the correlation between the T2DM blood viscosity and the HbA1c level is not obvious. Instead, when we investigate the influence of plasma fibrinogen level on the blood viscosity in T2DM subjects, we find that the T2DM blood viscosity is significantly and positively correlated with the plasma fibrinogen level. Further, to probe the combined effects of multiple factors (including the HbA1c and plasma fibrinogen levels) on the altered blood viscosity in T2DM, we regroup the experimental data based on the T2DM blood viscosity values at both the low and high shear rates, and our results suggest that the influence of the elevated HbA1c level on blood viscosity is quite limited, although it is an important indicator of glycemic control in T2DM patients. Instead, the elevated blood hematocrit, the enhanced red blood cell (RBC) aggregation induced by the increased plasma fibrinogen level, and the reduced RBC deformation play key roles in the determination of blood viscosity in T2DM. Together, these experimental results are helpful in identifying the key determinants for the altered T2DM blood viscosity, which can be used in future studies of the hemorheological disturbances of T2DM patients.

Dependence of red blood cell dynamics in microvessel bifurcations on the endothelial surface layer's resistance to flow and compression

Red blood cells (RBCs) make up 40-45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5-1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL's resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell-cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL's resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.

Hemorheology: the critical role of flow type in blood viscosity measurements

The crucial role of the hemorheological characteristics of blood in a range of diagnoses, treatments and drug delivery mechanisms is widely accepted. Nonetheless, the literature on blood rheology remains inconclusive and sometimes even contradictory. This is in part due to natural variance of blood samples from one study to another, but also stems from fundamental differences in the consequences of the choice of rheometric flow employed. Here, and using a detailed and accurate computational scheme, we thoroughly study the role of flow type in measurement of blood viscosity. Performing these in silico measurements, we isolate the role of flow type and geometry at different hematocrit levels. We show that flow curves obtained in pressure-driven flows relevant to laminar circulatory flows deviate greatly from ones obtained in drag flow at the same hematocrit level. Our numerical platform also allows for the yield stress to be measured under quiescent conditions and without imposing any flow for different hematocrits. We discuss the scaling of the yield stress with the hematocrit level, and show that the differences in pressure vs. drag flows stem from the Red Blood Cell (RBC) orientation at different flow rates as well as the existence of a cell free layer close to the walls.

Model systems for optical trapping: the physical basis and biological applications

The micromechanical methods, among which optical trapping and atomic force microscopy have a special place, are widespread currently in biology to study molecular interactions between different biological objects. Optical trapping is reported to be quite applicable to study the mechanical properties of surface structures onto bacterial (pili and flagella) and eukaryotic (filopodia) cells. The review briefly summarizes the physical basis of optical trapping, as well as the principles of calculating the van der Waals, electrostatic, and donor-acceptor forces when two microparticles or a microparticle and a flat surface are used. Three main types of model systems (abiotic, biotic, and mixed) used in trapping experiments are described, and the peculiarities of manipulation with living (bacteria, fungal spores, etc.) and non-spherical objects (e.g., rod-shaped bacteria) are summarized.

Real-time red blood cell counting and osmolarity analysis using a photoacoustic-based microfluidic system

Counting the number of red blood cells (RBCs) in blood samples is a common clinical diagnostic procedure, but conventional methods are unable to provide the size and other physical properties of RBCs at the same time. In this work, we explore photoacoustic (PA) detection as a rapid label-free and noninvasive analysis technique that can potentially be used for single RBC characterization based on their photoabsorption properties. We have demonstrated an on-chip PA flow cytometry system using a simple microfluidic chip combined with a PA imaging system to count and characterize up to ∼60 RBCs per second. Compared with existing microfluidic-based RBC analysis methods, which typically use camera-captured image sequences to characterize cell morphology and deformation, the PA method discussed here requires only the processing of one-dimensional time-series data instead of two- or three-dimensional time-series data acquired by computer vision methods. Therefore, the PA method will have significantly lower computational requirements when large numbers of RBCs are to be analyzed. Moreover, we have demonstrated that the PA signals of RBCs flowing in a microfluidic device could be directly used to acquire the osmolarity conditions (in the range of 124 to 497 mOsm L-1) of the medium surrounding the RBCs. This finding suggests a potential extension of applicability to blood tests via PA-based biomedical detection.

Loading and relaxation dynamics of a red blood cell

We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the loading (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the relaxation (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., t_L and t_R. When the intensity of the mechanical load is small enough, the two kinds of dynamics are symmetrical (t_L≈t_R) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an asymmetry is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times t_L and t_R. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.

Machine learning of lubrication correction based on GPR for the coupled DPD-DEM simulation of colloidal suspensions

Hydrodynamic interactions have a major impact on the suspension properties, but they are absent in atomic and molecular fluids due to a lack of intervening medium at close range. To reproduce the correct hydrodynamic interactions, lubrication correction is essential to compensate the missing short-range hydrodynamics from the fluids. However, lubrication correction requires many simulations in particle-based simulations of colloidal suspensions. To address the problem, we employ an active learning strategy based on Gaussian process regression (GPR) for normal and tangential lubrication corrections to significantly reduce the number of necessary simulations and apply the correction to the coupled multiscale simulation of monodisperse hard-sphere colloidal suspensions. In particular, a single-particle dissipative particle dynamics (DPD) model with parameter correction is used to describe the solvent-solvent and colloid-solvent interactions, and a discrete element method (DEM) model to depict the colloid-colloid frictional contacts. The lubrication correction results demonstrate that only six and four independent simulations (observation points for GPR training) are required to achieve accurate normal and tangential lubrication corrections, respectively. To validate the machine learning of lubrication correction based on GPR, we investigate the self-diffusion coefficients of colloids, suspension rheology and microstructure using the coupled DPD-DEM model with GPR lubrication correction. Our simulation results show that the machine learning of lubrication correction based on GPR is effective and the lubrication corrected DPD-DEM model is indeed capable of accurately capturing hydrodynamic interactions and correctly reproducing dynamical and rheological properties of colloidal suspensions. Moreover, the machine learning of lubrication correction based on GPR is not limited to the coupled DPD-DEM simulation of colloidal suspensions presented here, but can be easily applied to other particle-based simulations of particulate suspensions.

Multiparametric biophysical profiling of red blood cells in malaria infection

Biophysical separation promises label-free, less-invasive methods to manipulate the diverse properties of live cells, such as density, magnetic susceptibility, and morphological characteristics. However, some cellular changes are so minute that they are undetectable by current methods. We developed a multiparametric cell-separation approach to profile cells with simultaneously changing density and magnetic susceptibility. We demonstrated this approach with the natural biophysical phenomenon of Plasmodium falciparum infection, which modifies its host erythrocyte by simultaneously decreasing density and increasing magnetic susceptibility. Current approaches have used these properties separately to isolate later-stage infected cells, but not in combination. We present biophysical separation of infected erythrocytes by balancing gravitational and magnetic forces to differentiate infected cell stages, including early stages for the first time, using magnetic levitation. We quantified height distributions of erythrocyte populations-27 ring-stage synchronized samples and 35 uninfected controls-and quantified their unique biophysical signatures. This platform can thus enable multidimensional biophysical measurements on unique cell types.

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

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

In silico biophysics and hemorheology of blood hyperviscosity syndrome

Hyperviscosity syndrome (HVS) is characterized by an increase of the blood viscosity by up to seven times the normal blood viscosity, resulting in disturbances to the circulation in the vasculature system. HVS is commonly associated with an increase of large plasma proteins and abnormalities in the properties of red blood cells, such as cell interactions, cell stiffness, and increased hematocrit. Here, we perform a systematic study of the effect of each biophysical factor on the viscosity of blood by employing the dissipative particle dynamic method. Our in silico platform enables manipulation of each parameter in isolation, providing a unique scheme to quantify and accurately investigate the role of each factor in increasing the blood viscosity. To study the effect of these four factors independently, each factor was elevated more than its values for a healthy blood while the other factors remained constant, and viscosity measurement was performed for different hematocrits and flow rates. Although all four factors were found to increase the overall blood viscosity, these increases were highly dependent on the hematocrit and the flow rates imposed. The effect of cell aggregation and cell concentration on blood viscosity were predominantly observed at low shear rates, in contrast to the more magnified role of cell rigidity and plasma viscosity at high shear rates. Additionally, cell-related factors increase the whole blood viscosity at high hematocrits compared with the relative role of plasma-related factors at lower hematocrits. Our results, mapped onto the flow rates and hematocrits along the circulatory system, provide a correlation to underpinning mechanisms for HVS findings in different blood vessels.

Adhesive rolling of nanoparticles in a lateral flow inspired from diagnostics of COVID-19

Due to the lack of therapeutics and vaccines, diagnostics of COVID-19 emerges as one of the primary tools for controlling the spread of SARS-COV-2. Here we aim to develop a theoretical model to study the detection process of SARS-COV-2 in lateral flow device (LFD), which can achieve rapid antigen diagnostic tests. The LFD is modeled as the adhesion of a spherical nanoparticle (NP) coated with ligands on the surface, mimicking the SARS-COV-2, on an infinite substrate distributed with receptors under a simple shear flow. The adhesive behaviors of NPs in the LFD are governed by the ligand-receptor binding (LRB) and local hydrodynamics. Through energy balance analysis, three types of motion are predicted: (i) firm-adhesion (FA); (ii) adhesive-rolling (AR); and (iii) free-rolling (FR), which correspond to LRB-dominated, LRB-hydrodynamics-competed, and hydrodynamics-dominated regimes, respectively. The transitions of FA-to-AR and AR-to-FR are found to be triggered by overcoming LRB barrier and saturation of LRB torque, respectively. Most importantly, in the AR regime, the smaller NPs can move faster than their larger counterparts, induced by the LRB effect that depends on the radius R of NPs. In addition, a scaling law is found in the AR regime that v ∝ γ ˙ R α (rolling velocity v and shear rate γ ˙ ), with an approximate scaling factor α ∼ - 0 . 2 ± 0 . 05 identified through fitting both theoretical and numerical results. The scaling factor emerges from the energy-based stochastic LRB model, and is confirmed to be universal by examining selections of different LRB model parameters. This size-dependent rolling behavior under the control of flow strength may provide the theoretical guidance for designing efficient LFD in detecting infectious disease.

Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease

Understanding the mechanics of blood flow is necessary for developing insights into mechanisms of physiology and vascular diseases in microcirculation. Given the limitations of technologies available for assessing in vivo flow fields, in vitro methods based on traditional microfluidic platforms have been developed to mimic physiological conditions. However, existing methods lack the capability to provide accurate assessment of these flow fields, particularly in vessels with complex geometries. Conventional approaches to quantify flow fields rely either on analyzing only visual images or on enforcing underlying physics without considering visualization data, which could compromise accuracy of predictions. Here, we present artificial-intelligence velocimetry (AIV) to quantify velocity and stress fields of blood flow by integrating the imaging data with underlying physics using physics-informed neural networks. We demonstrate the capability of AIV by quantifying hemodynamics in microchannels designed to mimic saccular-shaped microaneurysms (microaneurysm-on-a-chip, or MAOAC), which signify common manifestations of diabetic retinopathy, a leading cause of vision loss from blood-vessel damage in the retina in diabetic patients. We show that AIV can, without any a priori knowledge of the inlet and outlet boundary conditions, infer the two-dimensional (2D) flow fields from a sequence of 2D images of blood flow in MAOAC, but also can infer three-dimensional (3D) flow fields using only 2D images, thanks to the encoded physics laws. AIV provides a unique paradigm that seamlessly integrates images, experimental data, and underlying physics using neural networks to automatically analyze experimental data and infer key hemodynamic indicators that assess vascular injury.

Digital blood in massively parallel CPU/GPU systems for the study of platelet transport

We propose a highly versatile computational framework for the simulation of cellular blood flow focusing on extreme performance without compromising accuracy or complexity. The tool couples the lattice Boltzmann solver Palabos for the simulation of blood plasma, a novel finite-element method (FEM) solver for the resolution of deformable blood cells, and an immersed boundary method for the coupling of the two phases. The design of the tool supports hybrid CPU-GPU executions (fluid, fluid-solid interaction on CPUs, deformable bodies on GPUs), and is non-intrusive, as each of the three components can be replaced in a modular way. The FEM-based kernel for solid dynamics outperforms other FEM solvers and its performance is comparable to state-of-the-art mass-spring systems. We perform an exhaustive performance analysis on Piz Daint at the Swiss National Supercomputing Centre and provide case studies focused on platelet transport, implicitly validating the accuracy of our tool. The tests show that this versatile framework combines unprecedented accuracy with massive performance, rendering it suitable for upcoming exascale architectures.

Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels

OBJECTIVE

The flow behavior of blood is strongly affected by red blood cell (RBC) properties, such as the viscosity ratio C between cytosol and suspending medium, which can significantly be altered in several pathologies (e.g. sickle-cell disease, malaria). The main objective of this study is to understand the effect of C on macroscopic blood flow properties such as flow resistance in microvessels, and to link it to the deformation and dynamics of single RBCs.

METHODS

We employ mesoscopic hydrodynamic simulations to investigate flow properties of RBC suspensions with different cytosol viscosities for various flow conditions in cylindrical microchannels.

RESULTS

Starting from a dispersed cell configuration which approximates RBC dispersion at vessel bifurcations in the microvasculature, we find that the flow convergence and development of RBC-free layer (RBC-FL) depend only weakly on C, and require a convergence length in the range of 25D-50D, where D is channel diameter. In vessels with D ≤ 20 μ m , the final resistance of developed flow is nearly the same for C = 5 and C = 1, while for D = 40 μ m , the flow resistance for C = 5 is about 10% larger than for C = 1. The similarities and differences in flow resistance can be explained by viscosity-dependent RBC-FL thicknesses, which are associated with the viscosity-dependent dynamics of single RBCs.

CONCLUSIONS

The weak effect on the flow resistance and RBC-FL explains why RBCs can contain a high concentration of hemoglobin for efficient oxygen delivery, without a pronounced increase in the flow resistance. Furthermore, our results suggest that significant alterations in microvascular flow in various pathologies are likely not due to mere changes in cytosolic viscosity.

Artemisinin-Ginkgo biloba extract combination therapy for Plasmodium yoelii

Malaria remains a widespread life-threatening infectious disease, leading to an estimated 219 million cases and around 435,000 deaths. After an unprecedented success, the antimalarial progress is at a standstill. Therefore, new methods are urgently needed to decrease drug resistant and enhance antimalarial efficacy. According to the alteration of erythrocyte biomechanical properties and the immune evasion mechanism of parasites, drugs, which can improve blood circulation, can be chosen to combine with antimalarial drugs for malaria treatment. Ginkgo biloba extract (GBE), one of drug for vascular disease, was used to combine with artemisinin for Plasmodium yoelii therapy. Artemisinin-GBE combination therapy (AGCT) demonstrated remarkable antimalarial efficacy by decreasing infection rate, improving blood microcirculation and modulating immune system. Besides, the expression of invasion related genes, such as AMA1, MSP1 and Py01365, can be suppressed by AGCT, hindering invasion process of merozoites. This new antimalarial strategy, combining antimalarial drugs with drugs that improve blood circulation, may enhance the antimalarial efficacy and ameliorate restoration ability, proving a potential method for finding ideal compatible drugs to improve malaria therapy.

Searching for the Mechanical Fingerprint of Pre-diabetes in T1DM: A Case Report Study

We report the case of a 38 year-old Caucasian man enrolled in a study aimed at investigating the physical properties of red blood cells (RBCs) using advanced microscopy techniques, including Atomic Force Microscopy (AFM). At the time of his first enrolment in the study, he had normal Fasting Plasma Glucose (FPG) values, a BMI of 24.1, and no other symptoms of diabetes, including fatigue, high triglycerides, low HDL cholesterol, and altered inflammatory and corpuscular RBC indices. The subject reported no family history of diabetes, obesity, and cardiovascular diseases. Despite his apparently healthy conditions, the biomechanics of his RBCs was altered, showing increased values of stiffness and viscosity. More than 1 year after the mechanical measurements, the subject was admitted to the Operational Unit of Diabetology of the Policlinico Gemelli Hospital with high blood glucose and glycosylated hemoglobin (HbA1c) levels and diagnosed with type 1 diabetes (T1DM). Here, we show these data, and we discuss the hypothesis that RBC mechanical properties could be sensitive to changes occurring during the pre-diabetic phase of T1DM.

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

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

A 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.

Neglected interstitial space in malaria recurrence and treatment

The interstitial space, a widespread fluid-filled compartment throughout the body, is related to many pathophysiological alterations and diseases, attracting increasing attention. The vital role of interstitial space in malaria infection and treatment has been neglected current research efforts. We confirmed the reinfection capacity of parasites sequestrated in interstitial space, which replenish the mechanism of recurrence. Malaria parasite-infected mice were treated with artemisinin-loaded liposomes through the interstitial space and exhibited a better therapeutic response. Notably, compared with oral administration, interstitial administration showed an unexpectedly high activation and recruitment of immune cells, and resulted in better clearance of sequestered parasites from organs, and enhanced pathological recovery. The interstitial route of administration prolongs the blood circulation time of artemisinin and increases its plasma concentration, and may compensate for the inefficiency of oral administration and the nanotoxicity of intravenous administration, providing a potential strategy for infectious disease therapy.

Multi-GPU Immersed Boundary Method Hemodynamics Simulations

Large-scale simulations of blood flow that resolve the 3D deformation of each comprising cell are increasingly popular owing to algorithmic developments in conjunction with advances in compute capability. Among different approaches for modeling cell-resolved hemodynamics, fluid structure interaction (FSI) algorithms based on the immersed boundary method are frequently employed for coupling separate solvers for the background fluid and the cells within one framework. GPUs can accelerate these simulations; however, both current pre-exascale and future exascale CPU-GPU heterogeneous systems face communication challenges critical to performance and scalability. We describe, to our knowledge, the largest distributed GPU-accelerated FSI simulations of high hematocrit cell-resolved flows with over 17 million red blood cells. We compare scaling on a fat node system with six GPUs per node and on a system with a single GPU per node. Through comparison between the CPU- and GPU-based implementations, we identify the costs of data movement in multiscale multi-grid FSI simulations on heterogeneous systems and show it to be the greatest performance bottleneck on the GPU.

Stochastic bond dynamics facilitates alignment of malaria parasite at erythrocyte membrane upon invasion

Malaria parasites invade healthy red blood cells (RBCs) during the blood stage of the disease. Even though parasites initially adhere to RBCs with a random orientation, they need to align their apex toward the membrane in order to start the invasion process. Using hydrodynamic simulations of a RBC and parasite, where both interact through discrete stochastic bonds, we show that parasite alignment is governed by the combination of RBC membrane deformability and dynamics of adhesion bonds. The stochastic nature of bond-based interactions facilitates a diffusive-like re-orientation of the parasite at the RBC membrane, while RBC deformation aids in the establishment of apex-membrane contact through partial parasite wrapping by the membrane. This bond-based model for parasite adhesion quantitatively captures alignment times measured experimentally and demonstrates that alignment times increase drastically with increasing rigidity of the RBC membrane. Our results suggest that the alignment process is mediated simply by passive parasite adhesion.

The influence of red blood cell deformability on hematocrit profiles and platelet margination

The influence of red blood cell (RBC) deformability in whole blood on platelet margination is investigated using confocal microscopy measurements of flowing human blood and cell resolved blood flow simulations. Fluorescent platelet concentrations at the wall of a glass chamber are measured using confocal microscopy with flowing human blood containing varying healthy-to-stiff RBC fractions. A decrease is observed in the fluorescent platelet signal at the wall due to the increase of stiffened RBCs in flow, suggesting a decrease of platelet margination due to an increased fraction of stiffened RBCs present in the flow. In order to resolve the influence of stiffened RBCs on platelet concentration at the channel wall, cell-pair and bulk flow simulations are performed. For homogeneous collisions between RBC pairs, a decrease in final displacement after a collision with increasing membrane stiffness is observed. In heterogeneous collisions between healthy and stiff RBC pairs, it is found that the stiffened RBC is displaced most. The influence of RBC deformability on collisions between RBCs and platelets was found to be negligible due to their size and mass difference. For a straight vessel geometry with varying healthy-to-stiff RBC ratios, a decrease was observed in the red blood cell-free layer and platelet margination due to an increase in stiffened RBCs present in flow.

A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.

Evidence against a Role of Elevated Intracellular Ca2+ during Plasmodium falciparum Preinvasion

Severe malaria is primarily caused by Plasmodium falciparum parasites during their asexual reproduction cycle within red blood cells. One of the least understood stages in this cycle is the brief preinvasion period during which merozoite-red cell contacts lead to apical alignment of the merozoite in readiness for penetration, a stage of major relevance in the control of invasion efficiency. Red blood cell deformations associated with this process were suggested to be active plasma membrane responses mediated by transients of elevated intracellular calcium. Few studies have addressed this hypothesis because of technical challenges, and the results remained inconclusive. Here, Fluo-4 was used as a fluorescent calcium indicator with optimized protocols to investigate the distribution of the dye in red blood cell populations used as P. falciparum invasion targets in egress-invasion assays. Preinvasion dynamics was observed simultaneously under bright-field and fluorescence microscopy by recording egress-invasion events. All the egress-invasion sequences showed red blood cell deformations of varied intensities during the preinvasion period and the echinocytic changes that follow during invasion. Intraerythrocytic calcium signals were absent throughout this interval in over half the records and totally absent during the preinvasion period, regardless of deformation strength. When present, calcium signals were of a punctate modality, initiated within merozoites already poised for invasion. These results argue against a role of elevated intracellular calcium during the preinvasion stage. We suggest an alternative mechanism of merozoite-induced preinvasion deformations based on passive red cell responses to transient agonist-receptor interactions associated with the formation of adhesive coat filaments.

Shear stress in the microvasculature: influence of red blood cell morphology and endothelial wall undulation

The effect of red blood cells and the undulation of the endothelium on the shear stress in the microvasculature is studied numerically using the lattice Boltzmann-immersed boundary method. The results demonstrate a significant effect of both the undulation of the endothelium and red blood cells on wall shear stress. Our results also reveal that morphological alterations of red blood cells, as occur in certain pathologies, can significantly affect the values of wall shear stress. The resulting fluctuations in wall shear stress greatly exceed the nominal values, emphasizing the importance of the particulate nature of blood as well as a more realistic description of vessel wall geometry in the study of hemodynamic forces. We find that within the channel widths investigated, which correspond to those found in the microvasculature, the inverse minimum distance normalized to the channel width between the red blood cell and the wall is predictive of the maximum wall shear stress observed in straight channels with a flowing red blood cell. We find that the maximum wall shear stress varies several factors more over a range of capillary numbers (dimensionless number relating strength of flow to membrane elasticity) and reduced areas (measure of deflation of the red blood cell) than the minimum wall shear stress. We see that waviness reduces variation in minimum and maximum shear stresses among different capillary and reduced areas.

Endothelial glycocalyx regulates cytoadherence in Plasmodium falciparum malaria

Malaria is associated with significant microcirculation disorders, especially when the infection reaches its severe stage. This can lead to a range of fatal conditions, from cerebral malaria to multiple organ failure, of not fully understood pathogenesis. It has recently been proposed that a breakdown of the glycocalyx, the carbohydrate-rich layer lining the vascular endothelium, plays a key role in severe malaria, but direct evidence supporting this hypothesis is still lacking. Here, the interactions between Plasmodium falciparum infected red blood cells ( PfRBCs) and endothelial glycocalyx are investigated by developing an in vitro, physiologically relevant model of human microcirculation based on microfluidics. Impairment of the glycocalyx is obtained by enzymatic removal of sialic acid residues, which, due to their terminal location and net negative charge, are implicated in the initial interactions with contacting cells. We show a more than twofold increase of PfRBC adhesion to endothelial cells upon enzymatic treatment, relative to untreated endothelial cells. As a control, no effect of enzymatic treatment on healthy red blood cell adhesion is found. The increased adhesion of PfRBCs is also associated with cell flipping and reduced velocity as compared to the untreated endothelium. Altogether, these results provide a compelling evidence of the increased cytoadherence of PfRBCs to glycocalyx-impaired vascular endothelium, thus supporting the advocated role of glycocalyx disruption in the pathogenesis of this disease.

Quantifying Shear-Induced Deformation and Detachment of Individual Adherent Sickle Red Blood Cells

Vaso-occlusive crisis, a common painful complication of sickle cell disease, is a complex process triggered by intercellular adhesive interactions among blood cells and the endothelium in all human organs (e.g., the oxygen-rich lung as well as hypoxic systems such as liver and kidneys). We present a combined experimental-computational study to quantify the adhesive characteristics of sickle mature erythrocytes (SMEs) and irreversibly sickled cells (ISCs) under flow conditions mimicking those in postcapillary venules. We employed an in vitro microfluidic cell adherence assay, which is coated uniformly with fibronectin. We investigated the adhesion dynamics of SMEs and ISCs in pulsatile flow under well-controlled hypoxic conditions, inferring the cell adhesion strength by increasing the flow rate (or wall shear stress (WSS)) until the onset of cell detachment. In parallel, we performed simulations of individual SMEs and ISCs under shear. We introduced two metrics to quantify the adhesion process, the cell aspect ratio (AR) as a function of WSS and its rate of change (the dynamic deformability index). We found that the AR of SMEs decreases significantly with the increase of WSS, consistent between the experiments and simulations. In contrast, the AR of ISCs remains constant in time and independent of the flow rate. The critical WSS value for detaching a single SME in oxygenated state is in the range of 3.9-5.5 Pa depending on the number of adhesion sites; the critical WSS value for ISCs is lower than that of SMEs. Our simulations show that the critical WSS value for SMEs in deoxygenated state is above 6.2 Pa (multiple adhesion sites), which is greater than their oxygenated counterparts. We investigated the effect of cell shear modulus on the detachment process; we found that for the same cell adhesion spring constant, the higher shear modulus leads to an earlier cell detachment from the functionalized surface. These findings may aid in the understanding of individual roles of sickle cell types in sickle cell disease vaso-occlusion.

Rheology and microrheology of deformable droplet suspensions

Dense suspensions of soft colloidal particles display a broad range of physical and rheological properties which are still far from being fully understood. To elucidate the role of deformability on colloidal flow, we employ computer simulations to measure the apparent viscosity of a system of droplets of variable surface tension subjected to a pressure-driven flow. We confirm that our suspension generically undergoes discontinuous shear thinning, and determine the dependence of the onset of the discontinuity on surface tension. We find that the effective viscosity of the suspension is mainly determined by a capillary number. We present active microrheology simulations, where a single droplet is dragged through the suspension. These also show a dynamical phase transition, analogous to the one associated with discontinuous shear thinning in our interpretation. Such a transition is signalled by a discontinuity in the droplet velocity versus applied force.

Adhesion-based sorting of blood cells: an adhesive dynamics simulation study

Blood cells can be sorted in microfluidic devices not only based on their sizes and deformability, but also based on their adhesive properties. In particular, white blood cells have been shown to be sorted out by using adhesive micropatterns made from stripes that are tilted in regard to the direction of shear flow. Here we use adhesive dynamics simulations for round cells to quantitatively investigate this effect and to predict the optimal tilt angle. We then apply our method to predict optimal sorting conditions for malaria-infected red blood cells, which like white blood cells also adhere to and roll on adhesive substrates.

Localized mechanical stimulation of single cells with engineered spatio-temporal profile

In vivo, cells are frequently exposed to multiple mechanical stimuli arising from the extracellular microenvironment, with a deep impact on many biological functions. On the other hand, current methods for mechanobiology do not allow one to easily replicate in vitro the complex spatio-temporal profile of such mechanical signals. Here we introduce a new platform for studying the mechanical coupling between single cells and a dynamic extracellular environment, based on active substrates for cell culture made of Fe-coated polymeric micropillars. Under the action of quasi-static external magnetic fields, each group of pillars produces synchronous mechanical stimuli at different points of the cell membrane, thanks to the highly controllable pillars' deflection. This method allows one to apply complex stress fields, resulting in the parallel application of localized forces with tunable intensity and temporal profile. The platform has been validated by studying the cellular response to periodic stimuli in NIH3T3 fibroblasts. We find that low-frequency mechanical stimulation affects the actin cytoskeleton, nuclear morphology, and H2B core-histone dynamics and induces MKL transcription-cofactor translocation from nucleus to cytoplasm. The unique capability of the proposed platform to apply stimuli with a tunable temporal profile and high parallelism on a cell culture holds great potential for the investigation of mechanotransduction mechanisms in cells and tissues.

Synergistic Integration of Laboratory and Numerical Approaches in Studies of the Biomechanics of Diseased Red Blood Cells

In red blood cell (RBC) disorders, such as sickle cell disease, hereditary spherocytosis, and diabetes, alterations to the size and shape of RBCs due to either mutations of RBC proteins or changes to the extracellular environment, lead to compromised cell deformability, impaired cell stability, and increased propensity to aggregate. Numerous laboratory approaches have been implemented to elucidate the pathogenesis of RBC disorders. Concurrently, computational RBC models have been developed to simulate the dynamics of RBCs under physiological and pathological conditions. In this work, we review recent laboratory and computational studies of disordered RBCs. Distinguished from previous reviews, we emphasize how experimental techniques and computational modeling can be synergically integrated to improve the understanding of the pathophysiology of hematological disorders.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Factors Diminishing Cytoadhesion of Red Blood Cells Infected by Plasmodium falciparum in Arterioles

Cytoadhesion of red blood cells infected by Plasmodium falciparum (Pf-IRBCs) is predominantly found in postcapillary venules, rather than in arterioles. However, factors influencing this phenomenon remain unclear. Here, we conduct a systematic study using a numerical model coupling the fluid and solid mechanics of the cells and cellular environment with the biochemical ligand-receptor interaction. Our results show that, once a Pf-IRBC adheres to the vascular wall, the Pf-IRBC can withstand even arteriole shear stresses, and exhibits either rolling or firm adhesion. We also perform a simulation of the multistep process of cytoadhesion, consisting of flow, margination, capture, and rolling or firm adhesion. This multistep simulation suggests that a lower probability of contact with the vascular wall at high shear rates may diminish adherent Pf-IRBCs in the arterioles.

Computational Biomechanics of Human Red Blood Cells in Hematological Disorders

We review recent advances in multiscale modeling of the biomechanical characteristics of red blood cells (RBCs) in hematological diseases, and their relevance to the structure and dynamics of defective RBCs. We highlight examples of successful simulations of blood disorders including malaria and other hereditary disorders, such as sickle-cell anemia, spherocytosis, and elliptocytosis.

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.

Rolling Adhesion of Schizont Stage Malaria-Infected Red Blood Cells in Shear Flow

To avoid clearance by the spleen, red blood cells infected with the human malaria parasite Plasmodium falciparum (iRBCs) adhere to the vascular endothelium through adhesive protrusions called "knobs" that the parasite induces on the surface of the host cell. However, the detailed relation between the developing knob structure and the resulting movement in shear flow is not known. Using flow chamber experiments on endothelial monolayers and tracking of the parasite inside the infected host cell, we find that trophozoites (intermediate-stage iRBCs) tend to flip due to their biconcave shape, whereas schizonts (late-stage iRBCs) tend to roll due to their almost spherical shape. We then use adhesive dynamics simulations for spherical cells to predict the effects of knob density and receptor multiplicity per knob on rolling adhesion of schizonts. We find that rolling adhesion requires a homogeneous coverage of the cell surface by knobs and that rolling adhesion becomes more stable and slower for higher knob density. Our experimental data suggest that schizonts are at the border between transient and stable rolling adhesion. They also allow us to establish an estimate for the molecular parameters for schizont adhesion to the vascular endothelium and to predict bond dynamics in the contact region.