Flow of Red Blood Cells in Stenosed Microvessels

Eulerian- lagrangian dense discrete phase model (DDPM) of stenotic LAD coronary arteries in comparison with single phase modeling

In computational fluid dynamic studies related to blood flow, investigating the behavior of blood particles is crucial, especially red blood cells as they constitute a significant proportion of blood particles. Additionally, studying red blood cell movements is necessary, especially in stenotic artery geometries. A new multiphase scheme was utilized to demonstrate the effect of red blood cells on hemodynamics in complex coronary arteries and investigate the consequence of their motion. To investigate the effect of red blood cell movement on flow, the dense discrete phase model (DDPM) was used. This simulation was performed in 3D coronary arteries with different degrees of stenosis, utilizing blood pressure as inlet and outlet boundary conditions while assuming the arterial wall to be rigid. The model prediction shows good agreement with experimental data. Velocity values were comparable in both single-phase and two-phase flow simulations, but the shear stress in two-phase modeling had higher values. In the two-phase DDPM modeling, the recirculation areas indicated a higher probability of atherosclerosis plaque re-formation in the pre-stenosis area compared to the stenosis and post-stenosis areas. The DDPM model was found to be more effective in obtaining shear stress values in the artery. Additionally, this model provides good results compared to the single-phase model in investigating the movement of particles along the artery as well as recirculation areas that lead to the deposition of particles.

The volume of healthy red blood cells is optimal for advective oxygen transport in arterioles

Red blood cells (RBCs) are vital for transporting oxygen from the lungs to the body's tissues through the intricate circulatory system. They achieve this by binding and releasing oxygen molecules to the abundant hemoglobin within their cytosol. The volume of RBCs affects the amount of oxygen they can carry, yet whether this volume is optimal for transporting oxygen through the circulatory system remains an open question. This study explores, through high-fidelity numerical simulations, the impact of RBC volume on advective oxygen transport efficiency through arterioles, which form the area of greatest flow resistance in the circulatory system. The results show that, strikingly, RBCs with volumes similar to those found in vivo are most efficient to transport oxygen through arterioles. The flow resistance is related to the cell-free layer thickness, which is influenced by the shape and the motion of the RBCs: at low volumes, RBCs deform and fold, while at high volumes, RBCs collide and follow more diffuse trajectories. In contrast, RBCs with a healthy volume maximize the cell-free layer thickness, resulting in a more efficient advective transport of oxygen.

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

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

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.

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

Axial shear rate: A hemorheological factor for erythrocyte aggregation under Womersley flow in an elastic vessel based on numerical simulation

Erythrocyte aggregation (EA) is a highly dynamic, vital phenomenon to interpreting human hemorheology, which would be helpful for the diagnosis and prediction of circulatory anomalies. Previous studies of EA on erythrocyte migration and the Fåhraeus Effect are based on the microvasculature. They have not considered the natural pulsatility of the blood flow or large vessels and mainly focused on shear rate along radial direction under steady flow to comprehend the dynamic properties of EA. To our knowledge, the rheological characteristics of non-Newtonian fluids under Womersley flow have not reflected the spatiotemporal behaviors of EA or the distribution of erythrocyte dynamics (ED). Hence, it needs to interpret the ED affected by temporal and spatial flow variation to understand the effect of EA under Womersley flow. Here, we demonstrated the numerically simulated ED to decipher EA's rheological role in axial shear rate under Womersley flow. In the present study, the temporal and spatial variations of the local EA were found to mainly depend on the axial shear rate under Womersley flow in an elastic vessel, while mean EA decreased with radial shear rate. The localized distribution of parabolic or M-shape clustered EA was found in a range of the axial shear rate profile (-15 to 15s^-1) at low radial shear rates during a pulsatile cycle. However, the linear formation of rouleaux was realized without local clusters in a rigid wall where the axial shear rate is zero. In vivo, the axial shear rate is usually considered insignificant, especially in straight arteries, but it has a great impact on the disturbed blood flow due to the geometrical properties, such as bifurcations, stenosis, aneurysm, and the cyclic variation of pressure. Our findings regarding axial shear rate provide new insight into the local dynamic distribution of EA, which is a critical player in blood viscosity. These will provide a basis for the computer-aided diagnosis of hemodynamic-based cardiovascular diseases by decreasing the uncertainty in the pulsatile flow calculation.

An improved reduced-order model for pressure drop across arterial stenoses

Quantification of pressure drop across stenotic arteries is a major element in the functional assessment of occlusive arterial disease. Accurate estimation of the pressure drop with a numerical model allows the calculation of Fractional Flow Reserve (FFR), which is a haemodynamic index employed for guiding coronary revascularisation. Its non-invasive evaluation would contribute to safer and cost-effective diseases management. In this work, we propose a new formulation of a reduced-order model of trans-stenotic pressure drop, based on a consistent theoretical analysis of the Navier-Stokes equation. The new formulation features a novel term that characterises the contribution of turbulence effect to pressure loss. Results from three-dimensional computational fluid dynamics (CFD) showed that the proposed model produces predictions that are significantly more accurate than the existing reduced-order models, for large and small symmetric and eccentric stenoses, covering mild to severe area reductions. FFR calculations based on the proposed model produced zero classification error for three classes comprising positive (≤ 0.75), negative (≥ 0.8) and intermediate (0.75 − 0.8) classes.

A pair of particles in inertial microfluidics: effect of shape, softness, and position

Lab-on-a-chip devices based on inertial microfluidics have emerged as a promising technique to manipulate particles in a precise way. Inertial microfluidics exploits internal hydrodynamic forces and the mechanical structure of particles to achieve separation and focusing. The article focuses on the hydrodynamic interaction of two particles. This will help to develop an understanding of the dynamics of particle trains in inertial microfluidics, which are typical structures in multi-particle systems. We perform three-dimensional lattice Boltzmann simulations combined with the immersed boundary method to unravel the dynamics of various mono- and bi-dispersed pairs in inertial microfluidics. We study the influence of different starting positions for mono- and bi-dispersed pairs. We also change their deformability from relatively soft to rigid and choose spherical and biconcave particle shapes. The observed two-particle motions in the present work can be categorized into four types: stable pair, stable pair with damped oscillations, stable pair with bounded oscillations, and unstable pair. We show that stable pairs become unstable when increasing the particle stiffness. Furthermore, a pair with both capsules in the same channel half is more prone to become unstable than a pair with capsules in opposite channel halves.

Hemodynamic analysis for stenosis microfluidic model of thrombosis with refined computational fluid dynamics simulation

Disturbed blood flow has been increasingly recognized for its critical role in platelet aggregation and thrombosis. Microfluidics with hump shaped contractions have been developed to mimic microvascular stenosis and recapitulate the prothrombotic effect of flow disturbance. However the physical determinants of microfluidic hemodynamics are not completely defined. Here, we report a refined computational fluid dynamics (CFD) simulation approach to map the shear rate (γ) and wall shear stress (τ) distribution in the stenotic region at high accuracy. Using ultra-fine meshing with sensitivity verification, our CFD results show that the stenosis level (S) is dominant over the bulk shear rate (γ₀) and contraction angle (α) in determining γ and τ distribution at stenosis. In contrast, α plays a significant role in governing the shear rate gradient (γ^′) distribution while it exhibits subtle effects on the peak γ. To investigate the viscosity effect, we employ a Generalized Power-Law model to simulate blood flow as a non-Newtonian fluid, showing negligible difference in the γ distribution when compared with Newtonian simulation with water medium. Together, our refined CFD method represents a comprehensive approach to examine microfluidic hemodynamics in three dimensions and guide microfabrication designs. Combining this with hematological experiments promises to advance understandings of the rheological effect in thrombosis and platelet mechanobiology.

Effect of Temperature and Flow Rate on the Cell-Free Area in the Microfluidic Channel

Blood cell manipulation in microdevices is an interesting task for the separation of particles, by their size, density, or to remove them from the buffer, in which they are suspended, for further analysis, and more. This study highlights the cell-free area (CFA) widening based on experimental results of red blood cell (RBC) flow, suspended in a microfluidic device, while temperature and flow rate incrementally modify RBC response within the microflow. Studies of human red blood cell flow, at a concentration of 20%, suspended in its autologous plasma and phosphate-buffered saline (PBS) buffer, were carried out at a wide flow rate, varying between 10 and 230 μL/min and a temperature range of 23 °C to 50 °C. The plotted measures show an increment in a CFA near the channel wall due to cell flow inertia after a constricted channel, which becomes more significant as temperature and flow rate increase. The temperature increment widened the CFA up to three times. In comparison, flow rate increment increased the CFA up to 20 times in PBS and 11 times in plasma.

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

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

Numerical computation of blood hemodynamic through constricted human left coronary artery: Pulsatile simulations

BACKGROUND AND OBJECTIVE

The accumulation of plaque in the coronary artery of the human heart restricts the path of blood flow in that region and leads to Coronary Artery Disease. This study's goal is to present the pulsatile blood flow conduct through four different levels of constrictions, i.e., healthy, 25%, 50%, and 75% in human left coronary arteries.

METHODS

Using CT scan data of a healthy person, the two-dimensional coronary model is constructed. A non-Newtonian Carreau model is used to study the maximum flow velocity, streamline effect, and maximum Wall Shear Stress at the respective constricted areas over the entire cardiac cycle. Finite Volume Method is executed for solving the governing equations. The fluctuating Wall Shear Stress (WSS) at different levels was assessed using Computational Fluid Dynamics (CFD).

RESULTS

The comparative study of the diseased arteries showcases that at the systolic phase, the 75% blocked artery attains the maximum velocity of 0.14 m/s and 0.53 m/s at t=0.005 s and t=0.115 s, respectively. While the maximum velocity takes a significant drop at t=0.23 s and t=0.345 s, this marks the diastolic phase. The streamline contour showcased the blood flow conduct at different phases of the cardiac cycle. At the peak systolic phase, a dense flow separation was observed near the blocked regions. It highlights the disturbed flow in that particular region. The most severely diseased artery acquires the maximum WSS of 18.81 Pa at the peak systolic phase, i.e., at t=0.115 s.

CONCLUSIONS

The computational study of the hemodynamic parameters can aid in the early anticipation of the degree of the severity of the diseased arteries. This study, in a way, could benefit doctors/surgeons to plan an early treatment/surgery on the grounds of the severity of the disease. Thus, a before time prognosis could restrain the number of deaths caused due to Coronary Artery Disease.

Possible Differential Diagnosis of the Degrees of Rheological Disturbances in Patients with Type 2 Diabetes Mellitus by Dielectrophoresis of Erythrocytes

Hemorheological disorders in structural and functional parameters of erythrocytes are involved in the pathological process in type 2 diabetes mellitus (DM). Aim: to investigate the feasibility of differential diagnosis of the degrees of rheological disturbances in patients with type 2 DM by dielectrophoresis of erythrocytes. Methods: 62 subjects (58.7 ± 1.6 years) with type 2 DM diagnosed according to the criteria of the ADA were subdivided into two groups: medium (n = 47) and high (n = 15) risk of microcirculatory disturbances (EASD, 2013). Electric and viscoelastic parameters of erythrocytes were determined by dielectrophoresis using an electric optical system of cell detection. Results: the progression of rheological disturbances in the patients with type 2 DM was accompanied by significant decreases in deformation amplitude; dipole moment; polarizability; and membrane capacity; and increases in conductivity, viscosity, rigidity, hemolysis, and formation of aggregates (p < 0.05). Combined use of the parameters increased sensitivity (97.8%) and specificity (86.7%) for diagnosis of rheological disturbances in type 2 DM. Conclusion: the proposed experimental approach possesses low invasiveness, high productivity, shorter duration, vividness of the results. The method allows to evaluate not only local (renal and ocular) but also systemic status of microcirculation using more than 20 parameters of erythrocytes.

Biofabrication Strategies and Engineered In Vitro Systems for Vascular Mechanobiology

The vascular system is integral for maintaining organ-specific functions and homeostasis. Dysregulation in vascular architecture and function can lead to various chronic or acute disorders. Investigation of the role of the vascular system in health and disease has been accelerated through the development of tissue-engineered constructs and microphysiological on-chip platforms. These in vitro systems permit studies of biochemical regulation of vascular networks and parenchymal tissue and provide mechanistic insights into the biophysical and hemodynamic forces acting in organ-specific niches. Detailed understanding of these forces and the mechanotransductory pathways involved is necessary to develop preventative and therapeutic strategies targeting the vascular system. This review describes vascular structure and function, the role of hemodynamic forces in maintaining vascular homeostasis, and measurement approaches for cell and tissue level mechanical properties influencing vascular phenomena. State-of-the-art techniques for fabricating in vitro microvascular systems, with varying degrees of biological and engineering complexity, are summarized. Finally, the role of vascular mechanobiology in organ-specific niches and pathophysiological states, and efforts to recapitulate these events using in vitro microphysiological systems, are explored. It is hoped that this review will help readers appreciate the important, but understudied, role of vascular-parenchymal mechanotransduction in health and disease toward developing mechanotherapeutics for treatment strategies.

Numerical Model for the Determination of Erythrocyte Mechanical Properties and Wall Shear Stress in vivo From Intravital Microscopy

The mechanical properties and deformability of Red Blood Cells (RBCs) are important determinants of blood rheology and microvascular hemodynamics. The objective of this study is to quantify the mechanical properties and wall shear stress experienced by the RBC membrane during capillary plug flow in vivo utilizing high speed video recording from intravital microscopy, biomechanical modeling, and computational methods. Capillaries were imaged in the rat cremaster muscle pre- and post-RBC transfusion of stored RBCs for 2-weeks. RBC membrane contours were extracted utilizing image processing and parametrized. RBC parameterizations were used to determine updated deformation gradient and Lagrangian Green strain tensors for each point along the parametrization and for each frame during plug flow. The updated Lagrangian Green strain and Displacement Gradient tensors were numerically fit to the Navier-Lame equations along the parameterized boundary to determined Lame's constants. Mechanical properties and wall shear stress were determined before and transfusion, were grouped in three populations of erythrocytes: native cells (NC) or circulating cells before transfusion, and two distinct population of cells after transfusion with stored cells (SC1 and SC2). The distinction, between the heterogeneous populations of cells present after the transfusion, SC1 and SC2, was obtained through principle component analysis (PCA) of the mechanical properties along the membrane. Cells with the first two principle components within 3 standard deviations of the mean, were labeled as SC1, and those with the first two principle components greater than 3 standard deviations from the mean were labeled as SC2. The calculated shear modulus average was 1.1±0.2, 0.90±0.15, and 12 ± 8 MPa for NC, SC1, and SC2, respectively. The calculated young's modulus average was 3.3±0.6, 2.6±0.4, and 32±20 MPa for NC, SC1, and SC2, respectively. o our knowledge, the methods presented here are the first estimation of the erythrocyte mechanical properties and shear stress in vivo during capillary plug flow. In summary, the methods introduced in this study may provide a new avenue of investigation of erythrocyte mechanics in the context of hematologic conditions that adversely affect erythrocyte mechanical properties.

Cross-sectional focusing of red blood cells in a constricted microfluidic channel

Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of cell focusing in the channel cross-section remains poorly investigated. Here, we explore the cross-sectional distribution of living and rigid red blood cells passing a constricted microfluidic channel by tracking individual cells in multiple layers across the channel depth and across the channel width. While cells are homogeneously distributed in the channel cross-section pre-contraction, we observe a strong geometry-induced focusing towards the four channel faces post-contraction. The magnitude of this cross-sectional focusing effect increases with increasing Reynolds number for both living and rigid red blood cells. We discuss how this non-uniform cell distribution downstream of the contraction results in an apparent double-peaked velocity profile in particle image velocimetry analysis and show that trapping of red blood cells in the recirculation zones of the abrupt construction depends on cell deformability.

Numerical investigation of unsteady pulsatile Newtonian/non-Newtonian blood flow through curved stenosed arteries

A numerical investigation of Newtonian/non-Newtonian unsteady pulsatile entry blood flow inside a 3D curved stenosed artery is presented. For considering the non-Newtonian effect (shear thinning or shear thickening behavior), the blood viscosity is characterized by the power-law model (Ostwald de Waele Equation). At the inlet of the artery, a realistic pulsatile waveform is utilized according to the experimental data reported by other researchers. This study belongs to the analysis of the curvature ratios, percentage and length ratio of stenosis, and blood thickening on hemodynamic characteristics of the flow. The results emphasize that the maximum wall shear stress happens near the stenosis neck and as expected, by decreasing the stenosis length, the maximum value of wall shear stress increases. In addition, the results indicate that the shear thickening fluid shows a more stable velocity profile rather than the shear thinning fluid flow.

Antimargination of Microparticles and Platelets in the Vicinity of Branching Vessels

We investigate the margination of microparticles/platelets in blood flow through complex geometries typical for in vivo vessel networks: a vessel confluence and a bifurcation. Using three-dimensional lattice Boltzmann simulations, we confirm that behind the confluence of two vessels, a cell-free layer devoid of red blood cells develops in the channel center. Despite its small size of roughly 1 μm, this central cell-free layer persists for up to 100 μm after the confluence. Most importantly, we show from simulations that this layer also contains a significant amount of microparticles/platelets and validate this result by in vivo microscopy in mouse venules. At bifurcations, however, a similar effect does not appear, and margination is largely unaffected by the geometry. This antimargination toward the vessel center after a confluence may explain earlier in vivo observations, which found that platelet concentrations near the vessel wall are seen to be much higher on the arteriolar side (containing bifurcations) than on the venular side (containing confluences) of the vascular system.

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

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

The Margination of Particles in Areas of Constricted Blood Flow

Stroke is a leading cause of death globally and is caused by stenoses, abnormal narrowings of blood vessels. Recently, there has been an increased interest in shear-activated particle clusters for the treatment of stenosis, but there is a lack of literature investigating the impact of different stenosis geometries on particle margination. Margination refers to the movement of particles toward the blood vessel wall and is desirable for drug delivery. The current study investigated ten different geometries and their effects on margination. Microfluidic devices with a constricted area were fabricated to mimic a stenosed blood vessel with different extent of occlusion, constricted length, and eccentricity (gradualness of the constriction and expansion). Spherical fluorescent particles with a diameter of 2.11 μm were suspended in blood and tracked as they moved into, through, and out of the constricted area. A margination parameter, M, was used to quantify margination based on the particle distribution after velocity normalization. Experimental results suggested that a constriction leads to an enhanced margination, whereas an expansion is responsible for a decrease in margination. Further, margination was found to increase with increasing percent occlusion and constriction length, likely a result of higher shear rate and longer residence time, respectively. Margination decreases as the stenosis geometry becomes more gradual (eccentricity increases) with the exception of a sudden constriction/expansion geometry. The findings demonstrate the importance of geometric effects on margination and call for detailed numerical modeling and geometric characterization of the stenosed areas to fully understand the underlying physics.

Variations in pulsatile flow around stenosed microchannel depending on viscosity

In studying blood flow in the vessels, the characteristics of non-Newtonian fluid are important, considering the role of viscosity in rheology. Stenosis, which is an abnormal narrowing of the vessel, has an influence on flow behavior. Therefore, analysis of blood flow in stenosed vessels is essential. However, most of them exist as simulation outcomes. In this study, non-Newtonian fluid was observed in stenosed microchannels under the pulsatile flow condition. A polydimethylsiloxane channel with 60% stenosis was fabricated by combining an optic fiber and a petri dish, resembling a mold. Three types of samples were prepared by changing the concentrations of xanthan gum, which induces a shear thinning effect (phosphate buffered saline (PBS) solution as the Newtonian fluid and two non-Newtonian fluids mimicking normal blood and highly viscous blood analog). The viscosity of the samples was measured using a Y-shaped microfluidic viscometer. Thereafter, velocity profiles were analyzed under the pulsatile flow condition using the micro-particle image velocimetry (PIV) method. For the Newtonian fluid, the streamline was skewed more to the wall of the channel. The velocity profile of the non-Newtonian fluid was generally blunter than that of the Newtonian fluid. A highly oscillating wall shear stress (WSS) during the pulsatile phase may be attributed to such a bluntness of flow under the same wall shear rate condition with the Newtonian fluid. In addition, a highly viscous flow contributes to the variation in the WSS after passing through the stenosed structures. A similar tendency was observed in simulation results. Such a variation in the WSS was associated with plaque instability or rupture and damage of the tissue layer. These results, related to the influence on the damage to the endothelium or stenotic lesion, may help clinicians understand relevant mechanisms.

Numerical design of a microfluidic chip for probing mechanical properties of cells

Microfluidic chips have been widely used to probe the mechanical properties of cells, which are recognized as a promising label-free biomarker for some diseases. In our previous work (Ye et al., 2018), we have studied the relationships between the transit time and the mechanical properties of a cell flowing through a microchannel with a single constriction, which potentially forms a basis for a microfluidic chip to measure cell's mechanical properties. Here, we investigate this microfluidic chip design and examine its potential in performances. We first develop the simultaneous dependence of the transit time on both the shear and bending moduli of a cell, and then examine the chip sensitivity with respect to the cell mechanical properties while serializing a single constriction along the flow direction. After that, we study the effect of the flow velocity on the transit time, and also test the chip's ability to identify heterogeneous cells with different mechanical properties. The results show that the microfluidic chip designed is capable of identifying heterogeneous cells, even when only one unhealthy cell is included. The serialization of chip can greatly increase the chip sensitivity with respect to the mechanical properties of cells. The flow with a higher velocity helps in not only promoting the chip throughput, but also in providing more accurate transit time measurements, because the cell prefers a symmetric deformation under a high velocity.

The dynamics of a healthy and infected red blood cell in flow through constricted channels: A DPD simulation

Understanding the dynamics of red blood cell (RBC) motion under in silico conditions is central to the development of cost-effective diagnostic tools. Specifically, unraveling the relationship between the rheological properties and the nature of shape change in the RBC (healthy or infected) can be extremely useful. In case of malarial infection, RBC progressively loses its deformability and tends to occlude the microvessel. In the present study, detailed mesoscopic simulations are performed to investigate the deformation dynamics of an RBC in flow through a constricted channel. Specifically, the manifestation of viscous forces (through flow rates) on the passage and blockage characteristics of a healthy red blood cell (hRBC) vis-á-vis an infected red blood cell (iRBC) are investigated. A finite-sized dissipative particle dynamics framework is used to model plasma in conjunction with a discrete model for the RBC. Instantaneous wall boundary method was used to model no-slip wall boundary conditions with a good control on the near-wall density fluctuations and compressibility effects. To investigate the microvascular occlusion, the RBC motion through 2 types of constricted channels, viz, (1) a tapered microchannel and (2) a stenosed-type microchannel, were simulated. It was observed that the deformation of an infected cell was much less compared with a healthy cell, with an attendant increase in the passage time. Apart from the qualitative features, deformation indices were obtained. The deformation of hRBC was sudden, while the iRBC deformed slowly as it traversed through the constriction. For higher flow rates, both hRBC and iRBC were found to undergo severe deformation. Even under low flow rates, hRBC could easily traverse past the constricted channel. However, for sufficiently slow flow rates (eg, capillary flows), the microchannel was found to be completely blocked by the iRBC.

How viscoelastic is human blood plasma?

Blood plasma has been considered a Newtonian fluid for decades. Recent experiments (Brust et al., Phys. Rev. Lett., 2013, 110) revealed that blood plasma has a pronounced viscoelastic behavior. This claim was based on purely elastic effects observed in the collapse of a thin plasma filament and the fast flow of plasma inside a contraction-expansion microchannel. However, due to the fact that plasma is a solution with very low viscosity, conventional rotational rheometers are not able to stretch the proteins effectively and thus, provide information about the viscoelastic properties of plasma. Using computational rheology and a molecular-based constitutive model, we predict accurately the rheological response of human blood plasma in strong extensional and constriction complex flows. The complete rheological characterization of plasma yields the first quantitative estimation of its viscoelastic properties in shear and extensional flows. We find that although plasma is characterized by a spectrum of ultra-short relaxation times (on the order of 10-3-10-5 s), its elastic nature dominates in flows that feature high shear and extensional rates, such as blood flow in microvessels. We show that plasma exhibits intense strain hardening when exposed to extensional deformations due to the stretch of the proteins in its bulk. In addition, using simple theoretical considerations we propose fibrinogen as the main candidate that attributes elasticity to plasma. These findings confirm that human blood plasma features bulk viscoelasticity and indicate that this non-Newtonian response should be seriously taken into consideration when examining whole blood flow.

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.

Red blood cell motion and deformation in a curved microvessel

The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.

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.

Theory and algorithms to compute Helfrich bending forces: a review

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