Numerical study of the phase separation in binary lipid membrane containing protein inclusions under stationary shear flow

The phase separation of lipids is believed to be responsible for the formation of lipid rafts in biological cell membrane. In the present work, a continuum model and a particle model are constructed to study the phase separation in binary lipid membrane containing inclusions under stationary shear flow. In each model, employing the cell dynamical system (CDS) approach, the kinetic equations of the confusion-advection process are numerically solved. Snapshot figures of the phase morphology are performed to intuitively display such phase evolving process. Considering the effects from both the inclusions and the shear flow, the time growth law of the characteristic domain size is discussed.     

Flow profiles and wall shear stress distribution at a hemodialysis venous anastomosis: preliminary study

The phasic velocity field in the vicinity of the venous anastomosis in a hemodialysis angioaccess arteriovenous fistula loop graft (AVLG) is investigated employing a laser Doppler anemometer (LDA) system. Detailed LDA velocity profiles are obtained by sectional survey performed in a transparent, elastic flow model which was fabricated to represent the geometry of the AVLG system under physiological pressure and flow waveforms. The geometry of the flow model was based on a silicone rubber cast obtained from an experimental dog model. In the present study, detailed distribution of velocity profiles is obtained. The distribution of wall shear stress in the model is computed from the slope of the local velocity profiles near the wall. The relationship between the results obtained by flow visualization and the LDA measurement is discussed.     

Numerical simulations of steady flow inside a three dimensional aortic bifurcation model

A finite element formulation of the Navier-Stokes equations for three dimensional flow is presented. The equations are solved using the finite element method. The model is constructed from a cast of a human aortic bifurcation. The numerical problems introduced by solving the equation system are discussed and special attention is paid to the selection of the linear equation solver. The simulations of the steady blood flow patterns in an aortic bifurcation is shown. The results of the numerical analysis are presented as three dimensional plots of velocity vectors, wall shear vectors, streamlines and pressure isobars. The flow simulations are done for Reynolds number 10. The flow patterns found in the bifurcation model are discussed in connection with proposed theories to explain the event of early atherosclerosis.     

Rheology and ultrasound scattering from aggregated red cell suspensions in shear flow

The shear flow dynamics of reversible red cell aggregates in dense suspensions were investigated by ultrasound scattering, to study the shear disruption processes of Rayleigh clusters and examine the effective mean field approximation used in microrheological models. In a first section, a rheo-acoustical model, in the Rayleigh scattering regime, is proposed to describe the shear stress dependence of the low frequency scattered power in relation to structural parameters. The fractal scattering regime characterizing the anisotropic scattering from flocs of size larger than the ultrasound wavelength is further discussed. In the second section, we report flow-dependent changes in the low-frequency scattering coefficient in a plane-plane flow geometry to analyze the shear disruption processes of hardened or deformable red cell aggregates in neutral dextran polymer solution. Rheo-acoustical experiments are examined on the basis of the rheo-acoustical model and the effective medium approximation. The ability of ultrasound scattering technique to determine the critical disaggregation shear stress and to give quantitative information on particle surface adhesive energy is analyzed. Lastly, the shear-thinning behavior of weakly aggregated hardened or deformable red cells is described.     

A displacement-based model for estimating the shear resistance of root-permeated soils

Aims

This paper presents a displacement-based model for predicting the relationship between the increase in shear resistance and shear displacement for soils permeated with an entire plant root system.

Methods

The root force in the root system is estimated based on the shear deformation developed in the soil. This displacement-based model takes a number of factors into account, including the distribution of the shear deformation in the soil, the root orientation, the mobilized root forces, and the root properties.

Results

The proposed model reasonably captures the relationship between the increase in the shear resistance (ΔS) and the shear displacement, as shown by a comparison of the predicted results with data from in situ shear tests.

Conclusions

Major findings are the following: (1) the ΔS value increases considerably with increasing b coefficients, which are used to describe the deformed shape of the shear zone, and Young’s moduli of roots at the early stage of shearing; (2) the ΔS value increases significantly with the τ value at large shear deformations; (3) short roots play an important role in the contribution of root systems to the shear resistance of the soil. However, the success of the model relies on the appropriate estimate of the deformation characteristics on the shear zone and the soil-root bond strength.     

Adaptive regulation of wall shear stress optimizing vascular tree function

The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm²), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.     

Transient shear stresses on a suspension cell in turbulence

A model flow field representative of Kolmogorov eddies in turbulence is proposed, and its two parameters are expressed in terms of the known bioreactor variables epsilon, the rate of turbulent power dissipation, and nu, the fluid kinematic viscosity. The trajectory through this flow field of a small sphere representing a cell is determined, and from that the time-varying local shear rate can be found. This allows calculation of the shear stress at any point on the sphere's surface as it rotates in and moves through the model eddy. The maximum shear stress imposed on the cell by the surrounding turbulence has a range of 0.5-5 dyn/cm(2), and can be estimated by 5.33rho(epsilonnu)(1/2). The shear stress has two major frequency components with ranges of 1-4 and 20-80 s(-1); the higher frequency component is estimated by 0.678(epsilon/nu)(1/2). The rotation of the direction of the shear stress vector at each point on the cell's surface is also discussed. Two ways in which external stresses might affect cell growth are proposed.     

Theoretical model and experimental study of red blood cell (RBC) deformation in microchannels

The motion and deformation of red blood cells (RBCs) flowing in a microchannel were studied using a theoretical model and a novel automated rheoscope. The theoretical model was developed to predict the cells deformation under shear as a function of the cells geometry and mechanical properties. Fluid dynamics and membrane mechanics are incorporated, calculating the traction and deformation in an iterative manner. The model was utilized to evaluate the effect of different biophysical parameters, such as: inner cell viscosity, membrane shear modulus and surface to volume ratio on deformation measurements. The experimental system enables the measurement of individual RBCs velocity and their deformation at defined planes within the microchannel. Good agreement was observed between the simulation results, the rheoscope measurements and published ektacytometry results. The theoretical model results imply that such deformability measuring techniques are weakly influenced by changes in the inner viscosity of the cell or the ambient fluid viscosity. However, these measurements are highly sensitive to RBC shear modulus. The shear modulus, estimated by the model and the rheoscope measurements, falls between the values obtained by micropipette aspiration and laser trapping. The study demonstrates the integration of a theoretical model with a microfabricated device in order to achieve a better understanding of RBC mechanics and their measurement using microfluidic shear assays. The system and the model have the potential of serving as quantitative clinical tools for diagnosing deformability disorders in RBCs.     

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.     

Bend propagation in flagella. I. Derivation of equations of motion and their simulation.

A set of nonlinear differential equations describing flagellar motion in an external viscous medium is derived. Because of the local nature of these equations and the use of a Crank-Nicolson-type forward time step, which is stable for large deltat, numerical solution of these equations on a digital computer is relatively fast. Stable bend initiation and propagation, without internal viscous resistance, is demonstrated for a flagellum containing a linear elastic bending resistance and an elastic shear resistance that depends on sliding. The elastic shear resistance is derived from a plausible structural model of the radial link system. The active shear force for the dynein system is specified by a history-dependent functional of curvature characterized by the parameters m0, a proportionality constant between the maximum active shear moment and curvature, and tau, a relaxation time which essentially determines the delay between curvature and active moment.     

Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress

Cultured vascular endothelial cells undergo significant morphological changes when subjected to sustained fluid shear stress. The cells elongate and align in the direction of applied flow. Accompanying this shape change is a reorganization at the intracellular level. The cytoskeletal actin filaments reorient in the direction of the cells' long axis. How this external stimulus is transmitted to the endothelial cytoskeleton still remains unclear. In this article. we present a theoretical model accounting for the cytoskeletal reorganization under the influence of fluid shear stress. We develop a system of integro-partial-differential equations describing the dynamics of actin filaments, the actin-binding proteins, and the drift of transmembrane proteins due to the fluid shear forces applied on the plasma membrane. Numerical simulations of the equations show that under certain conditions, initially randomly oriented cytoskeletal actin filaments reorient in structures parallel to the externally applied fluid shear forces. Thus, the model suggests a mechanism by which shear forces acting on the cell membrane can be transmitted to the entire cytoskeleton via molecular interactions alone.     

Flow-tissue interaction with compliance mismatch in a model stented artery

The insertion of an endovascular prosthesis is known to have a thrombogenic effect that is also a consequence of the interaction between the flowing blood and the stented arterial segment; in fact the prosthesis induces a compliance mismatch and a possible small expansion along the vessel that eventually gives rise to an anomalous distribution of wall shear stresses. The fluid dynamics inside a rectilinear elastic vessel with compliance and section variation is studied here numerically. A recently introduced perturbative approach is employed to model the interaction between the fluid and the elastic tissue; this approximate technique is first validated by comparison with a complete solution within a simple one-dimensional model of the same system. Then it is applied to an axisymmetric model in order to evaluate the flow dynamics and the distribution of wall shear stress in the stented vessel. Compliance mismatch is shown to produce more intense negative wall shear stresses in the stented segment while rapid variations of wall shear stress are found at the stent ends. These effects are enhanced when the prosthesis is accompanied by a small increase of the vessel lumen.     

Transient magneto-peristaltic flow of couple stress biofluids: A magneto-hydro-dynamical study on digestive transport phenomena

Magnetic fields are increasingly being utilized in endoscopy and gastric transport control. In this regard, the present study investigates the influence of a transverse magnetic field in the transient peristaltic rheological transport. An electrically-conducting couple stress non-Newtonian model is employed to accurately simulate physiological fluids in peristaltic flow through a sinusoidally contracting channel of finite length. This model is designed for computing the intra-bolus oesophageal and intestinal pressures during the movement of food bolus in the digestive system under magneto-hydro-dynamic effects. Long wavelength and low Reynolds number approximations have been employed to reduce the governing equations from nonlinear to linear form, this being a valid approach for creeping flows which characterizes physiological dynamics. Analytical approximate solutions for axial velocity, transverse velocity, pressure gradient, local wall shear stress and volumetric flow rate are obtained for the non-dimensional conservation equations subject to appropriate boundary conditions. The effects of couple stress parameter and transverse magnetic field on the velocity profile, pressure distribution, local wall shear stress and the averaged flow rate are discussed with the aid of computational results. The comparative study of non-integral and integral number of waves propagating along the finite length channel is also presented. Magnetic field and non-Newtonian properties are found to strongly influence peristaltic transport.     

Red cell membrane elasticity as determined by flow channel technique.

The elasticity of red cell membrane was determined in a rectangular flow channel under controlled shear flow. The relation between shear stress and cell extension ratio (lambda) has been analyzed with the use of Evans' two-dimensional model. The deformed cell shapes observed experimentally agreed well with the model with lambda up to 1.4. The best correlation was found at lambda = 1.2. The analysis suggests a nonlinear extensional membrane modulus in the low stress range encountered in the flow channel. In terms of an appropriate strain parameter, the elastic modulus is shown to rise toward the level encountered in micropipette aspiration experiments. The implications of the present findings in modeling of cell mechanics and in cell hemolysis are discussed.     

A finite element model for analyzing shear wave propagation observed in magnetic resonance elastography

Magnetic resonance elastography (MRE) is a novel non-invasive approach to determine material stiffness by using a conventional magnetic resonance imaging (MRI) system incorporated with an oscillating motion-sensitizing gradient to detect nodal displacements produced by a shear excitation wave. The effects of material properties, excitation frequency, boundary conditions, and applied tension on shear wavelength measurement must be examined before MRE can become a useful diagnostic tool. We propose finite element (FE) modeling as a robust method to systematically study the effects of these parameters. An axisymmetric FE model was generated with ABAQUS to simulate agarose gel phantoms. The effects of material stiffness, density, and excitation frequency on propagating shear wavelength were examined individually. The effect of the boundary conditions on shear wavelength was also demonstrated. Results of shear wavelength from MRE measurement were compared with the results of FE model, which showed good agreement between the methods.     

Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows

The tank-treading rotation of red blood cells (RBCs) in shear flows has been studied extensively with experimental, analytical, and numerical methods. Even for this relatively simple system, complicated motion and deformation behaviors have been observed, and some of the underlying mechanisms are still not well understood. In this study, we attempt to advance our knowledge of the relationship among cell motion, deformation, and flow situations with a numerical model. Our simulation results agree well with experimental data, and confirm the experimental finding of the decrease in frequency/shear-rate ratio with shear rate and the increase of frequency with suspending viscosity. Moreover, based on the detailed information from our simulations, we are able to interpret the frequency dependency on shear rate and suspending viscosity using a simple two-fluid shear model. The information obtained in this study thus is useful for understanding experimental observations of RBCs in shear and other flow situations; the good agreement to experimental measurements also shows the potential usefulness of our model for providing reliable results for microscopic blood flows.     

Modelling of peak-flow wall shear stress in major airways of the lung

Some respiratory diseases result in the inflammation of the lung airway epithelium. An associated chronic cough, as found in many cases of asthma and in long-term smokers, can exacerbate damage to the epithelial layer. It has been proposed that wall shear stresses, created by peak expiratory flow-rates during a coughing episode, are responsible. The work here uses a computational fluid dynamics technique to model peak expiratory flow in the trachea and major lung bronchi. Calculated wall shear stress values are compared to a limited set of published measurements taken from a physical model. The measurements are discussed in the context of a flow study of a complex bronchial network. A more complete picture is achieved by the calculation method, indicating, in some cases, higher maximum wall shear stresses than measured, confirming the original findings of the experimental work. Recommendations are made as to where further work would be beneficial to medical applications.     

A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases

Blood flow through a stenosed artery has been investigated in this paper. Blood has been represented by a non-Newtonian fluid obeying Herschel-Bulkley equation. This model has been used to study the influence of the fluid behaviour index n, shear-dependent nonlinear viscosity K and the yield stress tau H in blood flow through stenosed arteries. The variation of the wall shear stress and the flow resistance with n, K and tau H has been shown graphically. It is observed that the wall shear stress and the flow resistance increase in Herschel-Bulkley fluid in comparison with corresponding Newtonian fluid. It is of interest to note that, in the present model, the thickness of the plug core varies with the axial distance z in the stenotic region. Finally, some biological implications of the present model for some arterial diseases have been briefly discussed.     

Reconstruction of Active Regular Motion in Amoeba Extract: Dynamic Cooperation between Sol and Gel States

Amoeboid locomotion is one of the typical modes of biological cell migration. Cytoplasmic sol–gel conversion of an actomyosin system is thought to play an important role in locomotion. However, the mechanisms underlying sol–gel conversion, including trigger, signal, and regulating factors, remain unclear. We developed a novel model system in which an actomyosin fraction moves like an amoeba in a cytoplasmic extract. Rheological study of this model system revealed that the actomyosin fraction exhibits shear banding: the sol–gel state of actomyosin can be regulated by shear rate or mechanical force. Furthermore, study of the living cell indicated that the shear-banding property also causes sol–gel conversion with the same order of magnitude as that of shear rate. Our results suggest that the inherent sol–gel transition property plays an essential role in the self-regulation of autonomous translational motion in amoeba.     

A method for planar biaxial mechanical testing that includes in-plane shear.

A limitation in virtually all planar biaxial studies of soft tissues has been the inability to include the effects of in-plane shear. This is due to the inability of current mechanical testing devices to induce a state of in-plane shear, due to the added cost and complexity. In the current study, a straightforward method is presented for planar biaxial testing that induces a combined state of in-plane shear and normal strains. The method relies on rotation of the test specimen's material axes with respect to the device axes and on rotating carriages to allow the specimen to undergo in-plane shear freely. To demonstrate the method, five glutaraldehyde treated bovine pericardium specimens were prepared with their preferred fiber directions (defining the material axes) oriented at 45 deg to the device axes to induce a maximum shear state. The test protocol included a wide range of biaxial strain states, and the resulting biaxial data re-expressed in material axes coordinate system. The resulting biaxial data was then fit to the following strain energy function W: [equation: see text] where E'ij is the Green's strain tensor in the material axes coordinate system and c and Ai are constants. While W was able to fit the data very well, the constants A5 and A6 were found not to contribute significantly to the fit and were considered unnecessary to model the shear strain response. In conclusion, while not able to control the amount of shear strain independently or induce a state of pure shear, the method presented readily produces a state of simultaneous in-plane shear and normal strains. Further, the method is very general and can be applied to any anisotropic planar tissue that has identifiable material axes.