Flow-dependent rheological properties of blood in capillaries

Confinement effect on the microcapillary flow and shape of red blood cells

The ability to change shape is essential for the proper functioning of red blood cells (RBCs) within the microvasculature. The shape of RBCs significantly influences blood flow and has been employed in microfluidic lab-on-a-chip devices, serving as a diagnostic biomarker for specific pathologies and enabling the assessment of RBC deformability. While external flow conditions, such as the vessel size and the flow velocity, are known to impact microscale RBC flow, our comprehensive understanding of how their shape-adapting ability is influenced by channel confinement in biomedical applications remains incomplete. This study explores the impact of various rectangular and square channels, each with different confinement and aspect ratios, on the in vitro RBC flow behavior and characteristic shapes. We demonstrate that rectangular microchannels, with a height similar to the RBC diameter in combination with a confinement ratio exceeding 0.9, are required to generate distinctive well-defined croissant and slipper-like RBC shapes. These shapes are characterized by their equilibrium positions in the channel cross section, and we observe a strong elongation of both stable shapes in response to the shear rate across the different channels. Less confined channel configurations lead to the emergence of unstable other shape types that display rich shape dynamics. Our work establishes an experimental framework to understand the influence of channel size on the single-cell flow behavior of RBCs, providing valuable insights for the design of biomicrofluidic single-cell analysis applications.

Emerging Microfluidic Devices for Sample Preparation of Undiluted Whole Blood to Enable the Detection of Biomarkers

Blood testing allows for diagnosis and monitoring of numerous conditions and illnesses; it forms an essential pillar of the health industry that continues to grow in market value. Due to the complex physical and biological nature of blood, samples must be carefully collected and prepared to obtain accurate and reliable analysis results with minimal background signal. Examples of common sample preparation steps include dilutions, plasma separation, cell lysis, and nucleic acid extraction and isolation, which are time-consuming and can introduce risks of sample cross-contamination or pathogen exposure to laboratory staff. Moreover, the reagents and equipment needed can be costly and difficult to obtain in point-of-care or resource-limited settings. Microfluidic devices can perform sample preparation steps in a simpler, faster, and more affordable manner. Devices can be carried to areas that are difficult to access or that do not have the resources necessary. Although many microfluidic devices have been developed in the last 5 years, few were designed for the use of undiluted whole blood as a starting point, which eliminates the need for blood dilution and minimizes blood sample preparation. This review will first provide a short summary on blood properties and blood samples typically used for analysis, before delving into innovative advances in microfluidic devices over the last 5 years that address the hurdles of blood sample preparation. The devices will be categorized by application and the type of blood sample used. The final section focuses on devices for the detection of intracellular nucleic acids, because these require more extensive sample preparation steps, and the challenges involved in adapting this technology and potential improvements are discussed.

Flow-driven competition between two capsules passing through a narrow pore

By incorporating a distance function into the finite element simulation, we investigate the flow-driven competition between two soft capsules passing through a narrow pore, employing the arbitrary Lagrangian-Eulerian formulation to satisfy the boundary conditions for fluid flow and capsule deformation. In our simulations, the motion and deformation of the capsules can be described in an intuitive manner, and the order in which capsules of different sizes pass through a pore can be clearly determined. Meanwhile, when the capsules are near the narrow pore, the change of the flow field is also very interesting and can be expressed intuitively. It is shown that, driven by the Poiseuille flow, the larger capsule has a stronger tendency to pass through the pore than the small one, which can be attributed to the greater resistance and the volume advantage of the larger capsule. In addition, we demonstrate that this tendency can be reversed by changing the inlet velocity and setting the initial position of the smaller capsule closer to the axis of the pore. And as long as the large one passes through first, the small one will offset the axis to the same orientation as the initial, while the large one always moves along the axis.

Influence of Hydrodynamics and Hematocrit on Ultrasound-Induced Blood Plasmapheresis

Acoustophoretic blood plasma separation is based on cell enrichment processes driven by acoustic radiation forces. The combined influence of hematocrit and hydrodynamics has not yet been quantified in the literature for these processes acoustically induced on blood. In this paper, we present an experimental study of blood samples exposed to ultrasonic standing waves at different hematocrit percentages and hydrodynamic conditions, in order to enlighten their individual influence on the acoustic response of the samples. The experiments were performed in a glass capillary (700 µm-square cross section) actuated by a piezoelectric ceramic at a frequency of 1.153 MHz, hosting 2D orthogonal half-wavelength resonances transverse to the channel length, with a single-pressure-node along its central axis. Different hematocrit percentages Hct = 2.25%, 4.50%, 9.00%, and 22.50%, were tested at eight flow rate conditions of Q = 0:80 µL/min. Cells were collected along the central axis driven by the acoustic radiation force, releasing plasma progressively free of cells. The study shows an optimal performance in a flow rate interval between 20 and 80 µL/min for low hematocrit percentages Hct ≤ 9.0%, which required very short times close to 10 s to achieve cell-free plasma in percentages over 90%. This study opens new lines for low-cost personalized blood diagnosis.

A monolithic fluid-structure interaction framework applied to red blood cells

A parallel fully coupled (monolithic) fluid-structure interaction (FSI) algorithm has been applied to the deformation of red blood cells (RBCs) in capillaries, where cell deformability has significant effects on blood rheology. In the present FSI algorithm, fluid domain is discretized using the side-centered unstructured finite volume method based on the Arbitrary Lagrangian-Eulerian (ALE) formulation; meanwhile, solid domain is discretized with the classical Galerkin finite element formulation for the Saint Venant-Kirchhoff material in a Lagrangian frame. In addition, the compatible kinematic boundary condition is enforced at the fluid-solid interface in order to conserve the mass of cytoplasmic fluid within the red cell at machine precision. In order to solve the resulting large-scale algebraic linear systems in a fully coupled manner, a new matrix factorization is introduced similar to that of the projection method, and the parallel algebraic multigrid solver BoomerAMG is used for the scaled discrete Laplacian provided by the HYPRE library, which we access through the PETSc library. Three important physical parameters for the blood flow are simulated and analyzed: (1) the effect of capillary diameter, (2) the effect of red cell membrane thickness, and (3) the effect of red cell spacing (hematocrit). The numerical calculations initially indicate a shape deformation in which biconcave discoid shape changes to a parachute-like shape. Furthermore, the parachute-like cell shape in small capillaries undergoes a cupcake-shaped buckling instability, which has not been observed in the literature. The instability forms thin riblike features, and the red cell deformation is not axisymmetric but three-dimensional.

Influence of feeding hematocrit and perfusion pressure on hematocrit reduction (Fåhraeus effect) in an artificial microvascular network

OBJECTIVE

Hct in narrow vessels is reduced due to concentration of fast-flowing RBCs in the center, and of slower flowing plasma along the wall of the vessel, which in combination with plasma skimming at bifurcations leads to the striking heterogeneity of local Hct in branching capillary networks known as the network Fåhraeus effect. We analyzed the influence of feeding Hct and perfusion pressure on the Fåhraeus effect in an AMVN.

METHODS

RBC suspensions in plasma with Hcts between 20% and 70% were perfused at pressures of 5-60 cm H₂ O through the AMVN. A microscope and high-speed camera were used to measure RBC velocity and Hct in microchannels of height of 5 μm and widths of 5-19 μm.

RESULTS

Channel Hcts were reduced compared with Hct_feeding in 5 and 7 μm microchannels, but not in larger microchannels. The magnitude of Hct reduction increased with decreasing Hct_feeding and decreasing ΔP (flow velocity), showing an about sevenfold higher effect for 40% Hct_feeding and low pressure/flow velocity than for 60% Hct_feeding and high pressure/flow velocity.

CONCLUSIONS

The magnitude of the network Fåhraeus effect in an AMVN is inversely related to Hct_feeding and ΔP.

Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel

Red blood cells flowing through capillaries assume a wide variety of different shapes owing to their high deformability. Predicting the realized shapes is a complex field as they are determined by the intricate interplay between the flow conditions and the membrane mechanics. In this work we construct the shape phase diagram of a single red blood cell with a physiological viscosity ratio flowing in a microchannel. We use both experimental in vitro measurements as well as 3D numerical simulations to complement the respective other one. Numerically, we have easy control over the initial starting configuration and natural access to the full 3D shape. With this information we obtain the phase diagram as a function of initial position, starting shape and cell velocity. Experimentally, we measure the occurrence frequency of the different shapes as a function of the cell velocity to construct the experimental diagram which is in good agreement with the numerical observations. Two different major shapes are found, namely croissants and slippers. Notably, both shapes show coexistence at low (<1 mm s^-1) and high velocities (>3 mm s^-1) while in-between only croissants are stable. This pronounced bistability indicates that RBC shapes are not only determined by system parameters such as flow velocity or channel size, but also strongly depend on the initial conditions.

On the Mechanism of Human Red Blood Cell Longevity: Roles of Calcium, the Sodium Pump, PIEZO1, and Gardos Channels

In a healthy adult, the transport of O₂ and CO₂ between lungs and tissues is performed by about 2 · 10¹³ red blood cells, of which around 1.7 · 10¹¹ are renewed every day, a turnover resulting from an average circulatory lifespan of about 120 days. Cellular lifespan is the result of an evolutionary balance between the energy costs of maintaining cells in a fit functional state versus cell renewal. In this Review we examine how the set of passive and active membrane transporters of the mature red blood cells interact to maximize their circulatory longevity thus minimizing costs on expensive cell turnover. Red blood cell deformability is critical for optimal rheology and gas exchange functionality during capillary flow, best fulfilled when the volume of each human red blood cell is kept at a fraction of about 0.55-0.60 of the maximal spherical volume allowed by its membrane area, the optimal-volume-ratio range. The extent to which red blood cell volumes can be preserved within or near these narrow optimal-volume-ratio margins determines the potential for circulatory longevity. We show that the low cation permeability of red blood cells allows volume stability to be achieved with extraordinary cost-efficiency, favouring cell longevity over cell turnover. We suggest a mechanism by which the interplay of a declining sodium pump and two passive membrane transporters, the mechanosensitive PIEZO1 channel, a candidate mediator of P_sickle in sickle cells, and the Ca²⁺-sensitive, K⁺-selective Gardos channel, can implement red blood cell volume stability around the optimal-volume-ratio range, as required for extended circulatory longevity.

New insights into shear stress-induced endothelial signalling and barrier function: cell-free fluid versus blood flow

Aims

Fluid shear stress (SS) is known to regulate endothelial cell (EC) function. Most of the studies, however, focused on the effects of cell-free fluid-generated wall SS on ECs. The objective of this study was to investigate how changes in blood flow altered EC signalling and endothelial function directly through wall SS and indirectly through SS effects on red blood cells (RBCs).

Methods and results

Experiments were conducted in individually perfused rat venules. We experimentally induced changes in SS that were quantified by measured flow velocity and fluid viscosity. The concomitant changes in EC [Ca2+]i and nitric oxide (NO) were measured with fluorescent markers, and EC barrier function was assessed by fluorescent microsphere accumulation at EC junctions using confocal imaging. EC eNOS activation was evaluated by immunostaining. In response to changes in SS, increases in EC [Ca2+]i and gap formation occurred only in blood or RBC solution perfused vessels, whereas SS-dependent NO production and eNOS-Ser1177 phosphorylation occurred in both plasma and blood perfused vessels. A bioluminescent assay detected SS-dependent ATP release from RBCs. Pharmacological inhibition and genetic modification of pannexin-1 channels on RBCs abolished SS-dependent ATP release and SS-induced increases in EC [Ca2+]i and gap formation.

Conclusions

SS-induced EC NO production occurs in both cell free fluid and blood perfused vessels, whereas SS-induced increases in EC [Ca2+]i and EC gap formation require the presence of RBCs, attributing to SS-induced pannexin-1 channel dependent release of ATP from RBCs. Thus, changes in blood flow alter vascular EC function through both wall SS and SS exerted on RBCs, and RBC released ATP contributes to SS-induced changes in EC barrier function.

Pressure-driven occlusive flow of a confined red blood cell

When red blood cells (RBCs) move through narrow capillaries in the microcirculation, they deform as they flow. In pathophysiological processes such as sickle cell disease and malaria, RBC motion and flow are severely restricted. To understand this threshold of occlusion, we use a combination of experiment and theory to study the motion of a single swollen RBC through a narrow glass capillary of varying inner diameter. By tracking the movement of the squeezed cell as it is driven by a controlled pressure drop, we measure the RBC velocity as a function of the pressure gradient as well as the local capillary diameter, and find that the effective blood viscosity in this regime increases with both decreasing RBC velocity and tube radius by following a power-law that depends upon the length of the confined cell. Our observations are consistent with a simple elasto-hydrodynamic model and highlight the role of lateral confinement in the occluded pressure-driven slow flow of soft confined objects.

Rheology of red blood cells under flow in highly confined microchannels: I. effect of elasticity

We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high confinement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.

FDA's nozzle numerical simulation challenge: non-Newtonian fluid effects and blood damage

Data from FDA's nozzle challenge-a study to assess the suitability of simulating fluid flow in an idealized medical device-is used to validate the simulations obtained from a numerical, finite-differences code. Various physiological indicators are computed and compared with experimental data from three different laboratories, getting a very good agreement. Special care is taken with the derivation of blood damage (hemolysis). The paper is focused on the laminar regime, in order to investigate non-Newtonian effects (non-constant fluid viscosity). The code can deal with these effects with just a small extra computational cost, improving Newtonian estimations up to a ten percent. The relevance of non-Newtonian effects for hemolysis parameters is discussed.

Theoretical analysis of the determinants of lung oxygen diffusing capacity

The process of pulmonary oxygen uptake is analyzed to obtain an explicit equation for lung oxygen diffusing capacity in terms of hematocrit and pulmonary capillary diameter. An axisymmetric model with discrete cylindrical erythrocytes is used to represent radial diffusion of oxygen from alveoli through the alveolar-capillary membrane into pulmonary capillaries, through the plasma, and into erythrocytes. Analysis of unsteady diffusion due to the passage of the erythrocytes shows that transport of oxygen through the alveolar-capillary membrane occurs mainly in the regions adjacent to erythrocytes, and that oxygen transport through regions adjacent to plasma gaps can be neglected. The model leads to an explicit formula for diffusing capacity as a function of geometric and oxygen transport parameters. For normal hematocrit and a capillary diameter of 6.75 μm, the predicted diffusing capacity is 102 ml O₂ min⁻¹ mmHg⁻¹. This value is 30-40% lower than values estimated previously by the morphometric method, which considers the total membrane area and the specific uptake rate of erythrocytes. Diffusing capacity is shown to increase with increasing hematocrit and decrease with increasing capillary diameter and increasing thickness of the membrane. Simulations of pulmonary oxygen uptake in humans under conditions of exercise or hypoxia based show closer agreement with experimental data than previous models, but still overestimate oxygen uptake. The remaining discrepancy may reflect effects of heterogeneity of perfusion and ventilation in the lung.

Blood viscosity in microvessels: experiment and theory

The apparent viscosity of blood flowing through narrow glass tubes decreases strongly with decreasing tube diameter over the range from about 300 μm to about 10 μm. This phenomenon, known as the Fåhraeus-Lindqvist effect, occurs because blood is a concentrated suspension of deformable red blood cells with a typical dimension of about 8 μm. Most of the resistance to blood flow through the circulatory system resides in microvessels with diameters in this range. Apparent viscosity of blood in microvessels in vivo has been found to be significantly higher than in glass tubes with corresponding diameters. Here we review experimental observations of blood's apparent viscosity in vitro and in vivo, and progress towards a quantitative theoretical understanding of the mechanisms involved.

Chemical composition of hepatic lipids mediates reperfusion injury of the macrosteatotic mouse liver through thromboxane A(2)

BACKGROUND & AIMS

Chemical composition of hepatic lipids is an evolving player in steatotic liver ischemia/reperfusion (I/R) injury. Thromboxane A(2) (TXA(2)) is a vasoactive pro-inflammatory lipid mediator derived from arachidonic acid (AA), an omega-6 fatty acid (Ω-6 FA). Reduced tolerance of the macrosteatotic liver to I/R may be related to increased TXA(2) synthesis due to the predominance of Ω-6 FAs.

METHODS

TXA(2) levels elicited by I/R in ob/ob and wild type mice were assessed by ELISA. Ob/ob mice were fed Ω-3 FAs enriched diet to reduce hepatic synthesis of AA and TXA(2) or treated with selective TXA(2) receptor blocker before I/R.

RESULTS

I/R triggered significantly higher hepatic TXA(2) production in ob/ob than wild type animals. Compared with ob/ob mice on regular diet, Ω-3 FAs supplementation markedly reduced hepatic AA levels before ischemia and consistently blunted hepatic TXA(2) synthesis after reperfusion. Sinusoidal perfusion and hepatocellular damage were significantly ameliorated despite downregulation of heme oxygenase-1. Hepatic transcript and protein levels of IL-1β and neutrophil recruitment were significantly diminished after reperfusion. Moreover, TXA(2) receptor blockage conferred similar protection without modification of the histological pattern of steatosis. A stronger protection was achieved in the steatotic compared with lean animals.

CONCLUSIONS

Enhanced I/R injury in the macrosteatotic liver is explained, at least partially, by TXA(2) mediated microcirculatory failure rather than size-related mechanical compression of the sinusoids by lipid droplets. TXA(2) blockage may be a simple strategy to include steatotic organs and overcome the shortage of donor organs for liver transplantation.

Mechanics and computational simulation of blood flow in microvessels

Blood is a concentrated suspension of red blood cells (RBCs). Motion and deformation of RBCs can be analyzed based on knowledge of their mechanical characteristics. Axisymmetric models for single-file motion of RBCs in capillaries yield predictions of apparent viscosity in good agreement with experimental results for diameters up to about 8 μm. Two-dimensional simulations, in which each RBC is represented as a set of interconnected viscoelastic elements, predict that off-centre RBCs in an 8-μm channel take asymmetric shapes and drift toward the centre-line. Predicted trajectories agree with observations in microvessels of the rat mesentery. An isolated RBC initially positioned near the wall of a 20-μm channel is deformed into an asymmetric shape, migrates away from the wall, and then enters a complex tumbling motion with continuous shape change. Realistic simulation of multiple interacting RBCs in microvessels remains as a major challenge.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Modeling and simulation of microfluid effects on deformation behavior of a red blood cell in a capillary

A modified SIMPER algorithm is developed for analysis of microfluid effects on the motion and deformation of a red blood cell (RBC) in a capillary. With consideration of very small Reynolds number in microfluidics, this algorithm not only speeds up the convergence of the momentum equations by combining the advantages of the SIMPLEC and SIMPLER algorithms together, but also satisfies the continuity equation with higher accuracy by integrating a fine adjustment technique. In order to validate the modified SIMPLER algorithm, the behavior of RBC in a capillary is simulated at different velocities. When the mean RBC velocity is 0.1mm/s, the RBC exhibits a characteristic parachute shape in the steady state, which agrees well with the numerical results previously reported. Apart from that, a quantitative validation with the experimental data is performed by examining the relationship between the mean velocity and deformation index of the RBC, showing an excellent agreement. The effects of crucial parameters are investigated systematically on the motion and deformation of the RBC, including the RBC radius, elastic modulus and bending stiffness of RBC membrane, initial velocity of suspending fluid, as well as the density and viscosity ratios of the suspending fluid to RBC. The simulation results demonstrate that all of the parameters have influences on the RBC behavior by changing the interaction between the RBC and suspending fluid.

Pericyte-mediated regulation of capillary diameter: a component of neurovascular coupling in health and disease

Because regional blood flow increases in association with the increased metabolic demand generated by localized increases in neural activity, functional imaging researchers often assume that changes in blood flow are an accurate read-out of changes in underlying neural activity. An understanding of the mechanisms that link changes in neural activity to changes in blood flow is crucial for assessing the validity of this assumption, and for understanding the processes that can go wrong during disease states such as ischaemic stroke. Many studies have investigated the mechanisms of neurovascular regulation in arterioles but other evidence suggests that blood flow regulation can also occur in capillaries, because of the presence of contractile cells, pericytes, on the capillary wall. Here we review the evidence that pericytes can modulate capillary diameter in response to neuronal activity and assess the likely importance of neurovascular regulation at the capillary level for functional imaging experiments. We also discuss evidence suggesting that pericytes are particularly sensitive to damage during pathological insults such as ischaemia, Alzheimer's disease and diabetic retinopathy, and consider the potential impact that pericyte dysfunction might have on the development of therapeutic interventions and on the interpretation of functional imaging data in these disorders.

Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries

The recent development of microfluidic devices allows the investigation and manipulation of individual liquid microdroplets, capsules, and cells. The collective behavior of several red blood cells (RBCs) or microcapsules in narrow capillaries determines their flow-induced morphology, arrangement, and effective viscosity. Of fundamental interest here is the relation between the flow behavior and the elasticity and deformability of these objects, their long-range hydrodynamic interactions in microchannels, and thermal membrane undulations. We study these mechanisms in an in silico model, which combines a particle-based mesoscale simulation technique for the fluid hydrodynamics with a triangulated-membrane model. The 2 essential control parameters are the volume fraction of RBCs (the tube hematocrit, H(T)), and the flow velocity. Our simulations show that already at very low H(T), the deformability of RBCs implies a flow-induced cluster formation above a threshold flow velocity. At higher H(T) values, we predict 3 distinct phases: one consisting of disordered biconcave-disk-shaped RBCs, another with parachute-shaped RBCs aligned in a single file, and a third with slipper-shaped RBCs arranged as 2 parallel interdigitated rows. The deformation-mediated clustering and the arrangements of RBCs and microcapsules are relevant for many potential applications in physics, biology, and medicine, such as blood diagnosis and cell sorting in microfluidic devices.

Numerical modeling of the behavior of an elastic capsule in a microchannel flow: The initial motion

The initial motion of two-dimensional capsule in microchannel flow just after release is investigated in this paper by a numerical simulation method, which combines the finite volume method with the front tracking technique. The capsule is modeled as liquid medium enclosed by a thin membrane, for which linear elastic properties are taken into consideration. Three kinds of initial capsule shapes (circle, ellipse, and biconcave) and three initial positions (center-line, near-center, and near-wall positions) are considered in the simulations. Off-center capsules (the near-center and near-wall capsules) experience tilting and membrane tank-treading, and migrate laterally while they move with the fluid flow. After initial rapid tilting, the circular and elliptic near-wall capsules reach quasistationary tilt orientation, while the biconcave near-wall capsules experience steady change in tilt orientation with time. Lateral movements of the capsules indicate the existence of lift effect causing the capsule to move away from the wall. Lift velocities, the velocity components along the transverse direction, of the circular near-wall capsules decrease as they approach the centerline, while those of the elliptic and biconcave near-wall capsules do not show this trend, which might result from the short range of the simulation time. In general, the capsule with higher membrane dilation modulus has lower lift velocity, showing the effect of capsule deformability on the capsule behavior. Both tank-treading and lift velocities are 1-2 orders lower than the capsule translational velocity. For the circular and biconcave capsules, no matter the center-line or off-center capsules, hematocrit ratio increases with the membrane dilation modulus, namely, the capsule moving velocity decreases with the increasing dilation modulus, while the elliptic capsules with nondimensional membrane dilation moduli of 2500 and 500 show inverse trend in some time range. A preliminary study is carried out for long-term simulation of a circular capsule.

Three-dimensional computational modeling of multiple deformable cells flowing in microvessels

Three-dimensional (3D) computational modeling and simulation are presented on the motion of a large number of deformable cells in microchannels. The methodology is based on an immersed boundary method, and the cells are modeled as liquid-filled elastic capsules. The model retains two important features of the blood flow in the microcirculation, that is, the particulate nature of blood and deformation of the erythrocytes. The tank-treading and tumbling motion and the lateral migration, as observed for erythrocytes in dilute suspension, are briefly discussed. We then present results on the motion of multiple cells in semidense suspension and study how their collective dynamics leads to various physiologically relevant processes such as the development of the cell-free layer and the Fahraeus-Lindqvist effect. We analyze the 3D trajectory and velocity fluctuations of individual cell in the suspension and the plug-flow velocity profile as functions of the cell deformability, hematocrit, and vessel size. The numerical results allow us to directly obtain various microrheological data, such as the width of the cell-free layer, and the variation in the apparent blood viscosity and hematocrit over the vessel cross section. We then use these results to calculate the core and plasma-layer viscosity and show that the two-phase (or core-annular) model of blood flow in microvessels underpredicts the blood velocity obtained in the simulations by as much as 40%. Based on a posteriori analysis of the simulation data, we develop a three-layer model of blood flow by taking into consideration the smooth variation in viscosity and hematocrit across the interface of the cell-free layer and the core. We then show that the blood velocity predicted by the three-layer model agrees very well with that obtained from the simulations.

Enhanced flow in smooth single-file channel

We investigate the flux of particles in a smooth single-file channel where particles cannot cross each other as well as in wider channels of varying cross section where particles execute normal diffusion. All the channels are connected to an infinite reservoir at one end and the flux of particles is measured at the other open end. We perform random walk Monte Carlo simulation using lattice model. The flux decreases monotonically as the channel cross section is increased from single-file channel to wider channel and finally reaches a constant value for a sufficiently wide channel. The observation of enhanced flux in single-file channel as compared to a wider channel can be tested for efficient separation of particles through smooth nanochannels.

Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels

A theoretical method is used to simulate the motion and deformation of mammalian red blood cells (RBCs) in microvessels, based on knowledge of the mechanical characteristics of RBCs. Each RBC is represented as a set of interconnected viscoelastic elements in two dimensions. The motion and deformation of the cell and the motion of the surrounding fluid are computed using a finite-element numerical method. Simulations of RBC motion in simple shear flow of a high-viscosity fluid show "tank-treading'' motion of the membrane around the cell perimeter, as observed experimentally. With appropriate choice of the parameters representing RBC mechanical properties, the tank-treading frequency and cell elongation agree closely with observations over a range of shear rates. In simulations of RBC motion in capillary-sized channels, initially circular cell shapes rapidly approach shapes typical of those seen experimentally in capillaries, convex in front and concave at the rear. An isolated RBC entering an 8-mum capillary close to the wall is predicted to migrate in the lateral direction as it traverses the capillary, achieving a position near the center-line after traveling a distance of about 60 mum. Cell trajectories agree closely with those observed in microvessels of the rat mesentery.

Bursts in single-file motion mediated conduction

We present a cellular automaton (CA) model of particles in a single-file motion with free particle exchange at the boundaries of a one-dimensional channel connected to two infinite reservoirs in order to study the self-transmission of particles with excluded mutual passage. The parallel, local and homogeneous rule sets of the CA algorithm consider two different interactions of varying strength between particles, without any specific particle-channel interaction. CA model results suggest that one hallmark of single-file motion is the conduction bursts at a particular time scale, which have thus far only been discovered for hydrogen bond networked water translocation. The cumulative transport probabilities of particles through single-file channels of different length follow a single profile, which can be obtained through proper scaling of time. The universal features of our results suggest new experiments in single-file channel with fluids other than water.

Numerical simulation of cell motion in tube flow

A theoretical model is presented for describing the motion of a deformable cell encapsulating a Newtonian fluid and enclosed by an elastic membrane in tube flow. In the mathematical formulation, the interior and exterior hydrodynamics are coupled with the membrane mechanics by means of surface equilibrium equations, and the problem is formulated as a system of integral equations for the interfacial velocity, the disturbance tube-wall traction, and the pressure difference across the two ends to the tube due to the presence of the cell. Numerical solutions obtained by a boundary-element method are presented for flow in a cylindrical tube with a circular cross-section, cytoplasm viscosity equal to the ambient fluid viscosity, and cells positioned sufficiently far from the tube wall so that strong lubrication forces do not arise. In the numerical simulations, cells with spherical, oblate ellipsoidal, and biconcave unstressed shapes enclosed by membranes that obey a neo-Hookean constitutive equation are considered. Spherical cells are found to slowly migrate toward the tube centerline at a rate that depends on the mean flow velocity, whereas oblate and biconcave cells are found to develop parachute and slipper-like shapes, respectively, from axisymmetric and more general initial orientations.

Transmural microcirculatory blood flow distribution in right and left ventricular free walls of rabbits

Within-layer regional myocardial flows in the left and right ventricles (LV, RV) and in LV with increased myocardial workload (beta(1)-adrenoceptor stimulation) were studied transmurally in anesthetized rabbits. Myocardial flow distribution was visualized with resolutions between 0.1 x 0.1- and 1 x 1-mm(2) pixels, using digital radiography combined with the (3)H-labeled desmethylimipramine deposition technique. The spatial pattern of flow distribution was quantitated by the coefficient of variation of regional flows (CV, related to global flow heterogeneity) and the correlation between adjacent regional flows (CA, inversely related to local flow randomness). CV was lower in LV than in RV [P < 0.05, nonparametric 2-way analysis of variance (NANOVA)]. When resolution was lowered from 0.1 x 0.1- to 1 x 1-mm(2) pixels, CV decreased by 70% in both LV and RV. CA was higher in LV than in RV (P < 0.05, NANOVA); the interventricular difference in CA was large over the resolutions between 0.4 x 0.4- and 1 x 1-mm(2) pixels. In LV, both CV and CA increased with depth of myocardium (P < 0.05, NANOVA); in subendocardium CV was high comparable with CV in RV (P = 0.47, NANOVA). The enhancement of myocardial workload decreased CV and tended to decrease CA in LV subendocardium (P < 0.05, P = 0.06, respectively; NANOVA). We conclude that 1) microregional flow distribution is less heterogeneous and less random in LV than in RV; 2) transmurally, in LV subendocardium global flow heterogeneity was the highest whereas local flow randomness was the lowest, so that clusters of low- or high-flow regions exist in this LV layer; and 3) global flow heterogeneity decreased and local flow randomness tended to increase (flow homogenizing occurred) in LV subendocardium with increasing myocardial workload. Thus the distributed pattern of myocardial microregional flows may be adaptable to local myocardial metabolic change.

A model for red blood cell motion in glycocalyx-lined capillaries

The interior surfaces of capillaries are lined with a layer (glycocalyx) of macromolecules bound or absorbed to the endothelium. Here, a theoretical model is used to analyze the effects of the glycocalyx on hematocrit and resistance to blood flow in capillaries. The glycocalyx is represented as a porous layer that resists penetration by red blood cells. Axisymmetric red blood cell shapes are assumed, and effects of cell membrane shear elasticity are included. Lubrication theory is used to compute the flow of plasma around the cell and within the glycocalyx. The effects of the glycocalyx on tube hematocrit (Fahraeus effect) and on flow resistance are predicted as functions of the width and hydraulic resistivity of the layer. A layer of width 1 micron and resistivity 10(8) dyn.s/cm4 leads to a relative apparent viscosity of approximately 10 in a 6-micron capillary at discharge hematocrit 45% and flow velocity of approximately 1 mm/s. This is consistent with experimental observations of increased flow resistance in microvessels in vivo, relative to glass tubes with the same diameters.

Microvascular blood flow resistance: role of endothelial surface layer

Observations of blood flow in microvascular networks have shown that the resistance to blood flow is about twice that expected from studies using narrow glass tubes. The goal of the present study was to test the hypothesis that a macromolecular layer (glycocalyx) lining the endothelial surface contributes to blood flow resistance. Changes in flow resistance in microvascular networks of the rat mesentery were observed with microinfusion of enzymes targeted at oligosaccharide side chains in the glycocalyx. Infusion of heparinase resulted in a sustained decrease in estimated flow resistance of 14-21%, hydrodynamically equivalent to a uniform increase of vessel diameter by approximately 1 micron. Infusion of neuraminidase led to accumulation of platelets on the endothelium and doubled flow resistance. Additional experiments in untreated vascular networks in which microvascular blood flow was reduced by partial microocclusion of the feeding arteriole showed a substantial increase of flow resistance at low flow rates (average capillary flow velocities < 100 diameters/s). These observations indicate that the glycocalyx has significant hemodynamic relevance that may increase at low flow rates, possibly because of a shear-dependent variation in glycocalyx thickness.

Motion of red blood cells in capillaries with variable cross-sections

Red blood cells undergo continual deformation when traversing microvessels in living tissues. This may contribute to higher resistance to blood flow observed in living microvessels, compared with that in corresponding uniform glass tubes. We use a theoretical model to simulate single-file motion of red cells though capillaries with variable cross-sections, assuming axisymmetric geometry. Effects of cell membrane shear viscosity and elasticity are included, but bending resistance is neglected. Lubrication theory is used to describe the flow of surrounding plasma. When a red cell encounters a region of capillary narrowing, additional energy is dissipated, due to membrane viscosity, and due to narrowing of the lubrication layer, increasing the flow resistance. Predicted resistance to cell motion in a vessel with periodic constrictions (diameter varying between 5 microns and 4 microns) is roughly twice that in a uniform vessel with diameter 4.5 microns. Effects of transient red cell deformations may contribute significantly to blood flow resistance in living microvessels.

Red blood cell flow cessation and diameter reductions in skeletal muscle capillaries in vivo - the role of oxygen

When perfusion pressure is reduced, red blood cell flow in the capillaries of skeletal muscle ceases at a positive pressure difference across the vascular bed, while arterioles dilate and venules are not constricted. This flow cessation (i.e., cessation of red blood cell flow) and luminal diameter changes in capillaries following femoral arterial pressure reduction were investigated in the rabbit tenuissimus muscle in situ (n = 42) using intravital video microscopy. Arterial pressure was reduced by occlusion of the aorta distal to the renal arteries. During the experiments, leg and muscle were placed in a sealed box. The muscle was exposed to low PO2 by leading a gas mixture deprived of O2 through the box. Locally at the muscle surface, i.e., under the microscope objective, PO2 was varied by varying the PO2 in the superfusion solution. In all experiments, the remainder of the muscle was kept at low (< 20 mm Hg) PO2. The incidence of flow cessation was virtually zero at low local (< 20 mm Hg) PO2 and became almost 100% at local values above 70 mm Hg. Initial equivalent capillary diameters were 3.1-5.8 microm (median 4.0 microm) and did not correlate with local O2 tension. During aorta occlusion, capillary diameters significantly (P < 0.0001) decreased by a median value of 8% at all local PO2 values; in 14 out of 54 capillaries local diameter became less than 2.8 microm. The extent of diameter reduction did not correlate with PO2. In the 14 capillaries in which the diameter became less than 2.8 microm flow cessation occurred in only four cases. The minimal diameter reached was always at the site of an endothelial nucleus. The capillary diameter reductions are probably due to passive recoil. In the 48 capillaries in which flow ceased, only in four cases did a red blood cell stop at the site of the nucleus. We conclude that capillary diameter reductions (local and generalized) lead to a considerable increase in capillary resistance which contributes to the occurrence of flow cessation but cannot solely explain it.

Heterogeneity of red blood cell perfusion in capillary networks supplied by a single arteriole in resting skeletal muscle

Flow heterogeneity within capillary beds may have two sources: (1) unequal distribution of red blood cell (RBC) supply among arterioles and (2) unique properties of RBC flow in branching networks of capillaries. Our aim was to investigate the capillary network as a source of both spatial and temporal heterogeneity of RBC flow. Five networks, each supplied by a single arteriole, were studied in frog sartorius muscle (one network per frog) by intravital video microscopy. Simultaneous data on RBC velocity (millimeters per second), lineal density (RBCs per millimeter), and supply rate (RBCs per second) were measured continuously (10 samples per second) from video recordings in 5 to 10 capillary segments per network for 10 minutes by use of automated computer analysis. To quantify heterogeneity, mean values from successive 10-second intervals were tabulated for each flow parameter in each capillary segment (ie, portion of capillary between successive bifurcations), and percent coefficient of variation (SD/mean.100%) was calculated for (1) spatial heterogeneity among vessels (CVs) every 10 seconds and for the entire 10-minute sample and (2) temporal heterogeneity within vessels for every capillary segment and for the mean flow parameter. Analysis of these data indicates that (1) capillary networks are a significant source of both spatial and temporal flow heterogeneity, and (2) continuous redistributions of flow occur within networks, resulting in substantial temporal changes in CVs, although a persistent spatial heterogeneity of perfusion still exists on a 10-minute basis. In most networks, CVs decreased as supply rate within the network increased, thus indicating that rheology plays a significant role in determining the perfusion heterogeneity.

Erythrocyte flow heterogeneity in the cerebrocortical capillary network

The heterogeneity of erythrocyte flow velocity and erythrocyte flux and their dependence on decreased cerebral perfusion pressure were studied in the rat cerebral cortex using intravital video microscopy. With decreased perfusion pressure, both mean and range of erythrocyte flow velocity of individual capillaries was reduced. Both cell velocity and cell flux decreased more in high flow capillaries than in low flow capillaries. The results are compatible with the hypothesis that redistribution of capillary flow during hypotension may help to maintain the perfusion of arterio-venous capillary flow pathways. Although the data are preliminary, they represent the first direct measurements of capillary flow path length and transit time in the capillary network of the cerebral cortex.

Blood vessel modeling

We developed a computer program for calculating hemodynamic parameters in a segment of vessel or catheter using Poiseuille's Law. The program analyzes flow, pressure, flow velocity, total fluid volume, pulse pressure, resistance and Reynolds number in a segment of vessel. The user can dilate or constrict at any position along its length for modeling stenoses or aneurysms. Viscosity, fluid density, length, and intrinsic radius can be varied to simulate atherosclerotic vessels. Idealized linear hemodynamics of an abdominal aortic aneurysm or a coarcted aorta can be modeled from angiographic data. Interactive results are displayed graphically and can be printed for future reference. The program can estimate catheter, graft or vascular resistances, flow velocity in atherogenic arteries, and the likelihood of achieving laminar flow.

Red blood cell mechanics and capillary blood rheology

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessels walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic "tank-treading" motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.

Myocardial capillaries: increase in number by splitting of existing vessels

To study myocardial vascular development, stereological parameters were estimated in 24 Wistar rat hearts of six different age groups, from newborn to adult. The vascular surface density showed a sharp increase in the first 2 weeks, a peak around the age of 2 weeks, and then a steady decrease until it flattened in adulthood. In contrast, the vascular volume percentage, when plotted against age, decreased continuously with the greatest change in the first week, after which the curve flattened. These findings are compatible with an increase in the number of capillaries with a concomitant decrease of their diameters. Qualitative scrutiny of the histology did indeed support the idea that vessels become thinner. Reconstructions of the histological sections showed the same change three dimensionally. The reconstructions also demonstrated very small holes that seemed to go through the capillaries in the younger stages. Corrosion casts of the blood vessels were made using a casting resin. This was injected into the umbilical artery of rat embryos from 15 days gestation to birth. In postnatal rats of six age groups methacrylate was injected directly into the left ventricle. These casts supported the stereological data by showing an increase in number and decrease in diameter of capillaries, while during pre- and postnatal development, the intervascular spaces lengthened from small, irregular spaces to long, rectangular ones. Small holes, the probable precursors of such spaces, were clearly visible in the wider vessels of the youngest stages. All data point to an interesting mode of capillary growth, i.e. growth by division of existing vessels.

Pulmonary artery, aortic and oesophageal pressure changes during high intensity treadmill exercise in the horse: a possible relation to exercise-induced pulmonary haemorrhage

This study investigated changes in packed cell volume (PCV), pulmonary artery and aortic pressures, and the interaction between oesophageal pressure and pulmonary artery and aortic pressures during strenuous exercise in the horse. It was hypothesised that oesophageal pressure changes summate with pulmonary artery and aortic pressures during exercise and contribute to exercise-induced pulmonary haemorrhage (EIPH). Acute treadmill exercise (10 m/sec, 3 degrees incline) produced increases in heart rate (HR) from 50 to 202 beats/min; mean pulmonary artery pressure (PAP) from 28 to 80 mmHg; mean aortic pressure (AP) from 108 to 157 mmHg; and PCV from 0.35 to 0.52 litres/litre. EIPH was observed in three of seven horses after treadmill exercise, but no differences in the above variables were observed between the two groups of horses. Electronic subtraction of the oesophageal pressure signal from PAP and AP signals indicated peak transmural pressures of approximately 150 mmHg pulmonary and 175 mmHg aortic pressure. The elevated PAP associated with exercise appeared related more to increased HR and less to PCV (blood viscosity) or AP (bronchial). Both pulmonary artery and aortic peak transmural vascular pressures were substantially influenced by oesophageal pressure changes; peak and mean pulmonary artery and aortic pressures were significantly higher than resting pressures, and may conceivably contribute to EIPH.

Erythrocyte rheology

Two main subjects of erythrocyte rheology, deformation and aggregation, are discussed in detail, on the basis of biochemical structure. The close relationship between the life span (or cell aging) and the rheology of individual erythrocytes is also briefly described. A currently important problem is emphasized, that is, the molecular aspect of the dynamic cytoskeletal structure and the mechanism of its regulation. This concerns not only the rheological function and the survival of circulating erythrocytes, but also the pathophysiology of abnormal erythrocytes.

Variation in axial velocity profile of red cells passing through a single capillary

We have used an analysis of the velocity of individual red cells as the cells pass through a capillary in order to estimate the variability in cross-sectional area of the capillary lumen available for flow along the length of the vessel. The purpose of the study was to determine if there were irregularities of sufficient magnitude and frequency to support Secomb's hypothesis that local constrictions in the capillary lumen could hinder blood flow at low driving pressure, due to the energy required to deform red cells as they pass through the constriction. All capillary segments analyzed to date, in both rat and frog, have shown regions where the velocity of individual cells is consistently faster or slower than that of the mean velocity of all other cells in the same segment. There are approximately two constrictions per 100 microns in the rat and one per 100 microns in the frog. On average these constrictions appear to reduce the cross-sectional area by 30% in the rat and 16% in the frog. These results provide evidence in support of Secomb's hypothesis. In addition, our results from one bifurcation indicate that the capillary lumen increases in cross-sectional area as one moves from the parent vessel to the region of the bifurcation. Downstream of the bifurcation the lumen rapidly decreases in area by 45 to 54%. Thus a red cell must undergo even greater deformation as it passes through a capillary bifurcation than it will in most other sections of the capillary network.(ABSTRACT TRUNCATED AT 250 WORDS)