Deformation mechanism of leukocyte adhering to vascular surface under steady shear flow

The adhesion of leukocytes to vascular surface is an important biomedical problem and has drawn extensive attention. In this study, we propose a compound drop model to simulate a leukocyte with a nucleus adhering to the surface of blood vessel under steady shear flow. A two-dimensional computational fluid dynamics (CFD) is conducted to determine the local distribution of pressure on the surface of the adherent model cell. By introducing the parameter of deformation index (DI), we investigate the deformation of the leukocyte and its nucleus under controlled conditions. Our numerical results show that: (i) the leukocyte is capable of deformation under external exposed flow field. The deformation index increases with initial contact angle and Reynolds number of external exposed flow. (ii) The nucleus deforms with the cell, and the deformation index of the leukocyte is greater than that of the nucleus. The leukocyte is more deformable while the nucleus is more capable of resisting external shear flow. (iii) The leukocyte and the nucleus are not able to deform infinitely with the increase of Reynolds number because the deformation index reaches a maximum. (iv) Pressure distribution confirms that there exists a region downstream of the cell, which produces high pressure to retard continuous deformation and provide a positive lift force on the cell. Meanwhile, we have measured the deformation of human leukocytes exposed to shear flow by using a flow chamber system. We found that the numerical results are well consistent with those of experiment. We conclude that the nucleus with high viscosity plays a particular role in leukocyte deformation.     

Mechanical behavior of an individual adherent MLO-Y4 osteocyte under shear flow

Mechanical properties of a single cell and its mechanical response under stimulation play an important role in regulating interactions between cell and extracellular matrix and affecting mechanotransduction. Osteocytes exhibit solid-like viscoelastic behavior in response to the interstitial fluid shear resulting from tissue matrix deformation. This study intends to quantitatively describe the mechanical behavior of osteocytes combining in vitro experiment and fluid–structure interaction (FSI) finite element (FE) model. The cell is configured in the FSI FE model using the observed data from quasi-3D images. Instead of simply assigning the cellular viscoelastic parameters by statistical data, the mechanical parameters are determined by an iterative algorithm comparing the experimental and the computational results from the FE model. The viscoelastic parameters of osteocytes are obtained as: the equilibrium elasticity modulus \(k_{1}=0.15\pm 0.038\,\hbox {kPa}\), instantaneous elasticity modulus \((k_{1}+k_{2})=0.77\pm 0.23\,\hbox {kPa}\), viscosity coefficient \(\eta =1.38\pm 0.33\,\hbox {kPa}\,\hbox {s}\). A novel index to quantify the cell adhesion is also put forward. In addition, an interesting competition phenomenon is revealed on the cell surface concerning stress and strain, i.e., the place with high stress has low strain and that with low stress has high strain. The proposed method provides a novel technique to study the mechanical behavior of individual adherent cell in vitro. It is believed that this quantitative technique not only determines cell mechanical behavior but also helps elucidate the mechanism of mechanotransduction in various types of cells.     

Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.     

Shape optimization in steady blood flow: a numerical study of non-Newtonian effects

We investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks, motivated by optimal design problems in biomedical engineering. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. We apply sensitivity-based optimization procedure to a flow through an idealized arterial graft. For this problem we study the influence of the inflow velocity, and thus the shear rate. Furthermore, we introduce an additional factor in the form of a geometric parameter, and study its effect on the optimal shape obtained.     

A numerical simulation of steady flow fields in a bypass tube.

Steady flow in a complete by-pass tube was simulated numerically. The study was to consider a complete flow field, which included both the by-pass and the host tubes. The changes of the hemodynamics were investigated with three parameters: the inlet flow Reynolds number (Re), anastomotic angle (alpha) and the position of the occlusion in the host tube. The baseline flow field was set up with Re=200, alpha=45 degrees and the centered position of occlusion. The parametric study was then conducted on combination of Re=100, 200, 400, alpha=35 degrees, 45 degrees, 60 degrees, 75 degrees, 90 degrees and three occlusion positions: left, center and right. It was found that in the baseline case, large slow/recirculation flows could be seen in the host tube both upstream and downstream of the occlusion. The separation points were on the opposite walls to the junctions. Recirculation zones were also found near the toe and in the proximal outer wall of the by-pass tube. Their sizes were about one diameter of the tube or smaller. In some cases, pairing vortices could be seen in the host tube upstream of the occlusion. The shear rate distribution associated with the flow fields was presented. The flow pattern obtained was agreeable to those observed experimentally by other investigators. The difference of the flow fields between a complete bypass and simple anastomosis was discussed. The present numerical code provides a preliminary simulation/design tool for bypass graft flows.     

Dynamic deformation and recovery response of red blood cells to a cyclically reversing shear flow: Effects of frequency of cyclically reversing shear flow and shear stress level

Dynamic deformation and recovery responses of red blood cells (RBCs) to a cyclically reversing shear flow generated in a 30-microm clearance, with the peak shear stress of 53, 108, 161, and 274 Pa at the frequency of 1, 2, 3, and 5 Hz, respectively, were studied. The RBCs' time-varying velocity varied after the glass plate velocity without any time lag, whereas the L/W change, where L and W were the major and minor axes of RBCs' ellipsoidal shape, exhibited a rapid increase and gradual decay during the deformation and recovery phase. The time of minimum L/W occurrence lagged behind the zero-velocity time of the glass plate (zero stress), and the delay time normalized to the one-cycle duration remained constant at 8.0%. The elongation of RBCs at zero stress time became larger with the reversing frequency. A simple mechanical model consisting of an elastic linear element during a rapid elongation period and a parallel combination of elements such as a spring and dashpot during the nonlinear recovery phase was suggested. The dynamic response behavior of RBCs under a cyclically reversing shear flow was different from the conventional shape change where a steplike force was applied to and completely released from the RBCs.     

Oscillatory deformation of human erythrocytes in sinusoidally modulated shear flow

The red cell deformation under oscillatory shear stress was studied. Shear stress was sinusoidally modulated between 8 and 32 dyn/cm2, thus, the extent of cellular deformation altered sinusoidally. At a low modulation frequency (less than 1.8 Hz), intact red cells perfectly responded to the shear stress applied on cells, and they could deform as much as the deformation in stationary shear flow. Above 2 Hz, the cellular deformation could not follow changes in shear stress along up-phase in the shear stress cycle. As decreasing the intracellular hemoglobin concentration, the cellular response to oscillatory shear stress became better. Treatment of cells with low concentrations of diamide impaired the response of intact cells to oscillatory shear stress, but unaffected the response of partially hemolyzed cells. These data suggest that the cellular response to oscillatory shear stress is determined by the cytoskeletal structure and the intracellular viscosity.     

A noninvasive approach to determine viscoelastic properties of an individual adherent cell under fluid flow

Mechanical properties of cells play an important role in their interaction with the extracellular matrix as well as the mechanotransduction process. Several in vitro techniques have been developed to determine the mechanical properties of cells, but none of them can measure the viscoelastic properties of an individual adherent cell in fluid flow non-invasively. In this study, techniques of fluid–structure interaction (FSI) finite element method and quasi-3-dimensional (quasi-3D) cell microscopy were innovatively applied to the frequently used flow chamber experiment, where an adherent cell was subjected to fluid flow. A new non-invasive approach, with cells at close to physiological conditions, was established to determine the viscoelastic properties of individual cells. The results showed an instantaneous modulus of osteocytes of 0.49±0.11 kPa, an equilibrium modulus of 0.31±0.044 kPa, and an apparent viscosity coefficient of 4.07±1.23 kPa s. This new quantitative approach not only provides an excellent means to measure cell mechanical properties, but also may help to elucidate the mechanotransduction mechanisms for a variety of cells under fluid flow stimulation.     

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.     

Motion and deformation of a red blood cell in a shear flow: a two-dimensional simulation of the wall effect

The motion and deformation of a single red blood cell in a simple shear flow between two parallel walls is studied theoretically. A two-dimensional deformable microcapsule is adopted as a model for the cell, which has a thin moving membrane, like a tank-tread, around the interior and is deformed into an elliptical shape with a constant area. Applying the finite element method to the Stokes equations, the tank-tread motion and deformation is determined in a stationary motion, under fluid dynamic interaction between the cell and the walls. It is shown that the motion and deformation of the microcapsule crucially depends on the channel width between the two walls. As the width decreases, the microcapsule is more elongated and the frequency of tank-tread motion decreases at a constant shear rate. In addition, the angle of inclination decreases at the low range of the viscosity ratio of internal to external fluids and increases at the high range. The results obtained are compared with experimental observations and applied to the behavior of cells under mutual interaction.     

PIV measurements of flow in a centrifugal blood pump: steady flow

Magnetically suspended left ventricular assist devices have only one moving part, the impeller. The impeller has absolutely no contact with any of the fixed parts, thus greatly reducing the regions of stagnant or high shear stress that surround a mechanical or fluid bearing. Measurements of the mean flow patterns as well as viscous and turbulent stresses were made in a shaft-driven prototype of a magnetically suspended centrifugal blood pump at several constant flow rates (3-9 L/min) using particle image velocimetry (PIV). The chosen range of flow rates is representative of the range over which the pump may operate while implanted. Measurements on a three-dimensional measurement grid within several regions of the pump, including the inlet, blade passage, exit volute, and diffuser are reported. The measurements are used to identify regions of potential blood damage due to high shear stress and/or stagnation of the blood, both of which have been associated with blood damage within artificial heart valves and diaphragm-type pumps. Levels of turbulence intensity and Reynolds stresses that are comparable to those in artificial heart valves are reported. At the design flow rate (6 L/min), the flow is generally well behaved (no recirculation or stagnant flow) and stress levels are below levels that would be expected to contribute to hemolysis or thrombosis. The flow at both high (9 L/min) and low (3 L/min) flow rates introduces anomalies into the flow, such as recirculation, stagnation, and high stress regions. Levels of viscous and Reynolds shear stresses everywhere within the pump are below reported threshold values for damage to red cells over the entire range of flow rates investigated; however, at both high and low flow rate conditions, the flow field may promote activation of the clotting cascade due to regions of elevated shear stress adjacent to separated or stagnant flow.     

Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.     

A numerical simulation of intimal thickening under shear in arteries.

A model of intima thickening proposed by Friedman and his coworkers (1,2) is incorporated in our computer code to simulate the growth of intima under shear. The computer code is based on a finite volume method in a boundary-fitted coordinate system. It is found that the model yields an evenly-distributed thickening over a straight, smooth vessel wall. However, in a stenosed or a curved artery, thicker intima can be formed in preferential regions due to unevenly-distributed wall shear stresses. The results clearly demonstrate the correlations among the geometry, wall shear rate and the plaque localization in arteries. The model is applied to a straight artery with a stenosis or sinus, a smooth curved artery and a stenosed curved artery. The effects of stenosis/sinus and lumen curvature on the flows and the intimal thickening are studied. The simulation provides a numerical visualization of the intimal thickening in a dynamic way.     

Adhesion of leukocytes under oscillating stagnation point conditions: a numerical study

Leukocyte recruitment from blood to the endothelium plays an important role in atherosclerotic plaque formation. Cells show a primary and secondary adhesive process with primary bonds responsible for capture and rolling and secondary bonds for arrest. Our objective was to investigate the role played by this process on the adhesion of leukocytes in complex flow. Cells were modelled as rigid spheres with spring like adhesion molecules which formed bonds with endothelial receptors. Models of bond kinetics and Newton's laws of motion were solved numerically to determine cell motion. Fluid force was obtained from the local shear rate obtained from a CFD simulation of the flow over a backward facing step.In stagnation point flow the shear rate near the stagnation point has a large gradient such that adherent cells in this region roll to a high shear region preventing permanent adhesion. This is enhanced if a small time dependent perturbation is imposed upon the stagnation point. For lower shear rates the cell rolling velocity may be such that secondary bonds have time to form. These bonds resist the lower fluid forces and consequently there is a relatively large permanent adhesion region.     

Alpha 6 beta 1 integrin (VLA-6) mediates leukocyte tether and arrest on laminin under physiological shear flow

Polymorphonuclear leukocytes (PMN) were perfused over extracellular matrix protein substrates under laminar shear flow. Under shear below 1.5 dyn/cm(2), many PMN tethered to immobilized laminin but not to fibronectin or vitronectin. Almost all the tethered PMN immediately arrested on laminin. The number of tethered PMN was mostly abrogated by mAbs to integrin alpha 6 or beta 1 chains at concentrations of more than 5 microg/ml. Addition of the two mAbs together produced no further inhibition compared with each mAb alone. In contrast, none of the mAbs to alpha 2, alpha 3, and beta 4 chains showed significant inhibition, indicating that PMN tethering to laminin is mostly dependent on alpha 6 beta 1 integrin. The addition of 10-100 ng/ml IL-8 in the assay medium before perfusion partially reduced PMN tethering to laminin. Stimulation with IL-8 also induced detachment of some tethered PMN within 30 s. Thus, IL-8 partially weakens the adhesiveness of alpha 6 beta 1 integrin on PMN in flow conditions.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

The CD81 tetraspanin facilitates instantaneous leukocyte VLA-4 adhesion strengthening to vascular cell adhesion molecule 1 (VCAM-1) under shear flow

Leukocyte integrins must rapidly strengthen their binding to target endothelial sites to arrest rolling adhesions under physiological shear flow. We demonstrate that the integrin-associated tetraspanin, CD81, regulates VLA-4 and VLA-5 adhesion strengthening in monocytes and primary murine B cells. CD81 strengthens multivalent VLA-4 contacts within subsecond integrin occupancy without altering intrinsic adhesive properties to low density ligand. CD81 facilitates both VLA-4-mediated leukocyte rolling and arrest on VCAM-1 under shear flow as well as VLA-5-dependent adhesion to fibronectin during short stationary contacts. CD81 also augments VLA-4 avidity enhancement induced by either chemokine-stimulated Gi proteins or by protein kinase C activation, although it is not required for Gi protein or protein kinase C signaling activities. In contrast to other proadhesive integrin-associated proteins, CD81-promoted integrin adhesiveness does not require its own ligand occupancy or ligation. These results provide the first demonstration of an integrin-associated transmembranal protein that facilitates instantaneous multivalent integrin occupancy events that promote leukocyte adhesion to an endothelial ligand under shear flow.