Effects of stiffness and volume on the transit time of an erythrocyte through a slit

Dynamics of erythrocytes in oscillatory shear flows: effects of S/V ratio

By combining a multiscale structural model of erythrocyte with a fluid-cell interaction model based on the boundary-integral method, we numerically investigate the dynamic response of erythrocytes in oscillatory shear flows (OSFs). The goal is to develop a novel experimental method to test the structural robustness of erythrocytes in transient mechanical loads with small time scales, conditions closely imitating the mechanical environment in vivo. Following the discovery of multiple response modes (wheeling, mode 1 tank treading, and mode 2 tank treading) under these conditions (Zhu & Asaro, 2019), we concentrate on deformation and stress inside RBCs driven by OSF, especially shear deformation of the membrane and the skeleton-bilayer dissociation stress, parameters that are related to mechanically induced structural remodeling such as vesiculation. Effects related to changes in surface area-to-volume (S/V) ratio are considered. Our results show that with the variation of the S/V ratio there could be significant change in terms of the occurrence of response modes even if other parameters are kept unchanged. For example, by reducing the S/V ratio of the cell, an asymmetric mode featuring a mixture of the wheeling and mode 2 tank treading responses is discovered. This mode is found to be associated with large skeleton-bilayer dissociation stress so that its potential impact on OSF-driven vesiculation should not be overlooked. By systematically examining the dependencies of skeleton deformation and skeleton-bilayer dissociation stress upon S/V, this study is critical for the development of the OSF technique in applications such as diagnosis since cell conditions are often reflected in its geometric properties.

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

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

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

Computational modeling of biomechanics and biorheology of heated red blood cells

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

Tethering, evagination, and vesiculation via cell-cell interactions in microvascular flow

Vesiculation is a ubiquitous process undergone by most cell types and serves a variety of vital cell functions; vesiculation from erythrocytes, in particular, is a well-known example and constitutes a self-protection mechanism against premature clearance, inter alia. Herein, we explore a paradigm that red blood cell derived vesicles may form within the microvascular, in intense shear flow, where cells become adhered to either other cells or the extracellular matrix, by forming tethers or an evagination. Adherence may be enhanced, or caused, by diseased states or chemical anomalies as are discussed herein. The mechanisms for such processes are detailed via numerical simulations that are patterned directly from video-recorded cell microflow within the splenic venous sinus (MacDonald et al. 1987), as included, e.g., as Supplementary Material. The mechanisms uncovered highlight the necessity of accounting for remodeling of the erythrocyte's membrane skeleton and, specifically, for the time scales associated with that process that is an integral part of cell deformation. In this way, the analysis provides pointed, and vital, insights into the notion of what the, often used phrase, cell deformability actually entails in a more holistic manner. The analysis also details what data are required to make further quantitative descriptions possible and suggests experimental pathways for acquiring such.

Flow-induced translocation of vesicles through a narrow pore

We use finite element method to investigate the flow-induced translocation of vesicles through a narrow pore from a dynamic point of view. In order to complete the coupling between fluid flow and the vesicle membranes, we employ the fluid-structure interactions with the arbitrary Lagrangian-Eulerian method. Our results demonstrate that the vesicle shows similar shape change from bullet-like to dumbbell-like, dumbbell-like to bulb-like, and bulb-like to parachute-like if it is pushed by flow field to pass through a narrow pore smaller than its size. We further find that the strain energy exhibits a higher peak and a lower peak in the whole translocation process, where the higher peak corresponds to the dumbbell-like shape and the lower peak corresponds to the parachute-like shape due to more stretching of the membrane for the dumbbell-like shape than that of the parachute-like shape. The translocation time of the vesicle from one side to the other side of the narrow pore decreases with the increase of inlet velocity, but the strain energy exhibits an increase, which implies that the vesicle needs more time to complete the translocation with the lower inlet velocity, but the requirement for the mechanical properties of the membrane is lower. Our work answers the mapping between the positions of the vesicles and deformed states with the stress distribution and change of strain energy, which can provide helpful information on the utilization of vesicles in pharmaceutical, chemical, and physiological processes.

Modeling erythrocyte electrodeformation in response to amplitude modulated electric waveforms

We present a comprehensive theoretical-experimental framework for quantitative, high-throughput study of cell biomechanics. An improved electrodeformation method has been developed by combing dielectrophoresis and amplitude shift keying, a form of amplitude modulation. This method offers a potential to fully control the magnitude and rate of deformation in cell membranes. In healthy human red blood cells, nonlinear viscoelasticity of cell membranes is obtained through variable amplitude load testing. A mathematical model to predict cellular deformations is validated using the experimental results of healthy human red blood cells subjected to various types of loading. These results demonstrate new capabilities of the electrodeformation technique and the validated mathematical model to explore the effects of different loading configurations on the cellular mechanical behavior. This gives it more advantages over existing methods and can be further developed to study the effects of strain rate and loading waveform on the mechanical properties of biological cells in health and disease.

Relationship between transit time and mechanical properties of a cell through a stenosed microchannel

The changes in the mechanical properties of a cell are not only the cause of some diseases, but can also be a biomarker for some disease states. In recent times, microfluidic devices with built-in constrictions have been widely used to measure these changes. The transit time in such devices, defined as the time that a cell takes to pass through a constriction, has been found to be a crucial factor associated with the cell mechanical properties. Here, we use smoothed dissipative particle dynamics (SDPD), a particle-based numerical method, to explore the relationship between the transit time and mechanical properties of a cell. Three expressions of the transit time are developed from our simulation data, with respect to the stenosed size of constrictions, the shear modulus and bending modulus of cells, respectively. We show that a convergent constriction (the inlet is wider than the outlet), and a sharp-corner constriction (the constriction outlet is narrow) are better in identifying the differences in the transit time of cells. Moreover, the transit time increases and gradually approaches a constant as the shear modulus of cells increases, but increases first and then decreases as the bending modulus increases. These results suggest that the mechanical properties of cells can indeed be measured by analyzing their transit time, based on the recommended microfluidic device.

Probing blood cell mechanics of hematologic processes at the single micron level

Blood cells circulate in a dynamic fluidic environment, and during hematologic processes such as hemostasis, thrombosis, and inflammation, blood cells interact biophysically with a myriad of vascular matrices-blood clots and the subendothelial matrix. While it is known that adherent cells physiologically respond to the mechanical properties of their underlying matrices, how blood cells interact with their mechanical microenvironment of vascular matrices remains poorly understood. To that end, we developed microfluidic systems that achieve high fidelity, high resolution, single-micron PDMS features that mimic the physical geometries of vascular matrices. With these electron beam lithography (EBL)-based microsystems, the physical interactions of individual blood cells with the mechanical properties of the matrices can be directly visualized. We observe that the physical presence of the matrix, in and of itself, mediates hematologic processes of the three major blood cell types: platelets, erythrocytes, and leukocytes. First, we find that the physical presence of single micron micropillars creates a shear microgradient that is sufficient to cause rapid, localized platelet adhesion and aggregation that leads to complete microchannel occlusion; this response is enhanced with the presence of fibrinogen or collagen on the micropillar surface. Second, we begin to describe the heretofore unknown biophysical parameters for the formation of schistocytes, pathologic erythrocyte fragments associated with various thrombotic microangiopathies (poorly understood, yet life-threatening blood disorders associated with microvascular thrombosis). Finally, we observe that the physical interactions with a vascular matrix is sufficient to cause neutrophils to form procoagulant neutrophil extracellular trap (NET)-like structures. By combining electron beam lithography (EBL), photolithography, and soft lithography, we thus create microfluidic devices that provide novel insight into the response of blood cells to the mechanical microenvironment of vascular matrices and have promise as research-enabling and diagnostic platforms.

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

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