Optimizing the rotor design for controlled-shear affinity filtration using computational fluid dynamics

Controlled shear affinity filtration (CSAF) is a novel integrated processing technology that positions a rotor directly above an affinity membrane chromatography column to permit protein capture and purification directly from cell culture. The conical rotor is intended to provide a uniform and tunable shear stress at the membrane surface that inhibits membrane fouling and cell cake formation by providing a hydrodynamic force away from and a drag force parallel to the membrane surface. Computational fluid dynamics (CFD) simulations are used to show that the rotor in the original CSAF device (Vogel et al., 2002) does not provide uniform shear stress at the membrane surface. This results in the need to operate the system at unnecessarily high rotor speeds to reach a required shear stress of at least 0.17 Pa at every radial position of the membrane surface, compromising the scale-up of the technology. Results from CFD simulations are compared with particle image velocimetry (PIV) experiments and a numerical solution for low Reynolds number conditions to confirm that our CFD model accurately describes the hydrodynamics in the rotor chamber of the CSAF device over a range of rotor velocities, filtrate fluxes, and (both laminar and turbulent) retentate flows. CFD simulations were then carried out in combination with a root-finding method to optimize the shape of the CSAF rotor. The optimized rotor geometry produces a nearly constant shear stress of 0.17 Pa at a rotational velocity of 250 rpm, 60% lower than the original CSAF design. This permits the optimized CSAF device to be scaled up to a maximum rotor diameter 2.5 times larger than is permissible in the original device, thereby providing more than a sixfold increase in volumetric throughput.     

Analysis of flow in a cone-and-plate apparatus with respect to spatial and temporal effects on endothelial cells

Endothelial cells, covering the inner surface of vessels and the heart, are permanently exposed to fluid flow, which affects the endothelial structure and the function. The response of endothelial cells to fluid shear stress is frequently investigated in cone-plate systems. For this type of device, we performed an analytical and numerical analysis of the steady, laminar, three-dimensional flow of a Newtonian fluid at low Reynolds numbers. Unsteady oscillating and pulsating flow was studied numerically by taking the geometry of a corresponding experimental setup into account. Our investigation provides detailed information with regard to shear-stress distribution at the plate as well as secondary flow. We show that: (i) there is a region on the plate where shear stress is almost constant and an analytical approach can be applied with high accuracy; (ii) detailed information about the flow in a real cone-plate device can only be obtained by numerical simulations; (iii) the pulsating flow is quasi-stationary; and (iv) there is a time lag on the order of 10(-3) s between cone rotation and shear stress generated on the plate.     

Three-Dimensional Computational Modeling of an Extra-Descending Aortic Assist Device Using Fluid-Structure Interaction

BackgroundThe incidence of heart failure is anticipated to rise by 2030, resulting in more than 8 million adults with this condition in US. Despite the advancement in pharmacological and surgical treatments, some patients progress to severe forms of cardiac dysfunction requiring cardiac transplantation as a last-resort treatment. Cardiac assist devices play an essential role in the recovery of normal cardiac performance through reversible remodeling or in assisting the weak organ to prolong survival rate. However, these devices need to be monitored carefully, as prolonged use may lead to physiological maladaptation and further cardiac complications. The optimization of such devices has done through the development and use of numerical simulations that allow the analysis of in-vivo hemodynamic patterns of blood flow. This study aims to investigate the performance of a model of extra-aortic assist device surrounding the descending aorta through three-dimensional patient-specific modeling.MethodsA three-dimensional model of the aorta was constructed from patient-specific cardiac CT images of a 60-year-old male diagnosed with left ventricular failure at the Tehran Heart Center (THC). Numerical simulation was conducted for two complete cardiac cycles using fluid-structure interaction (FSI) analysis under the assumption that the balloon and the aortic vessel behave as linear elastic materials, and that blood is a Newtonian and incompressible fluid.ResultsThe numerical simulation demonstrated a high correlation between the FSI analysis and clinical data of the patient-specific anatomical and physiological conditions. Blood velocity, pressure, deformation, and strain contours were simulated and analyzed through three-dimensional modeling. Compared to the unassisted aorta, the device provided an increase in blood flow displacement of an additional 15 ml of blood in the descending aorta, brachiocephalic, carotid, and subclavian arteries. The maximum von Mises stress distribution across the aortic vessel was higher than the stress imposed on the system in the unassisted heart, with values of 3.3 MPa and 0.28 MPa, respectively. Numerical investigation of structural responses revealed that no remarkable force was exerted on the aortic valve by the device at the descending aorta.ConclusionWe present the numerical investigation of a counterpulsation device around the descending aorta that has not previously been tested on human or animal models. While this extra-aortic balloon pump (EABP) did not show a significant improvement in coronary perfusion, there is room for improvement in further studies to optimize the geometry of the balloon. Additional investigations are required to determine the efficacy of this device and its safety before in-vivo experimental studies are pursued. This simulation has clinical relevance when choosing an appropriate cardiac assist device to address patient-specific physiological and pathological conditions.     

Singularity solution of Lanir's osmoelasticity: verification of discontinuity simulations in soft tissues

The literature characterizes cartilaginous tissues as osmoviscoelastic. Understanding the damage and failure of these tissues is essential for designing treatments. To determine tissue strength and local stresses, experimental studies—both clinical and animal—are generally supported by computational studies. Verification methods for computational studies of ionized porous media including cracks are hardly available. This study provides a method for verification and shows its performance. For this purpose, shear loading of a finite crack is addressed analytically and through a commercial finite element code. Impulsive shear loading by two-edge dislocation of a crack was considered in a 2D plane strain model for an ionized porous medium. To derive the analytical solution, the system of equation is decoupled by stress functions. The shear stress distribution at the plane of the crack is derived using Fourier and Laplace transformations. The analytical solution for the shear stress distribution is compared with computer simulations in ABAQUS version 6.4-5. Decoupling of the equations makes it possible to solve some boundary value problems in porous media taking chemical effects into account. The numerical calculations underestimate the shear stress at the crack-tips. Mesh refinement increases accuracy, but is still low in the neighborhood of the crack-tips.     

Degradation of supercoiled plasmid DNA within a capillary device

Supercoiled plasmid DNA is susceptible to fluid stress in large-scale manufacturing processes. A capillary device was used to generate controlled shear conditions and the effects of different stresses on plasmid DNA structure were investigated. Computational fluid dynamics (CFD) analysis was employed to characterize the flow environment in the capillary device and different analytical techniques were used to quantify the DNA breakage. It was found that the degradation of plasmid DNA occurred at the entrance of the capillary and that the shear stress within the capillary did not affect the DNA structure. The degradation rate of plasmids was well correlated with the average elongational strain rate or the pressure drop at the entrance region. The conclusion may also be drawn that laminar shear stress does not play a significant role in plasmid DNA degradation.     

Analysis of cell flux in the parallel plate flow chamber: implications for cell capture studies.

The parallel plate flow chamber provides a controlled environment for determinations of the shear stress at which cells in suspension can bind to endothelial cell monolayers. By decreasing the flow rate of cell-containing media over the monolayer and assessing the number of cells bound at each wall shear stress, the relationship between shear force and binding efficiency can be determined. The rate of binding should depend on the delivery of cells to the surface as well as the intrinsic cell-surface interactions; thus, only if the cell flux to the surface is known can the resulting binding curves be interpreted correctly. We present the development and validation of a mathematical model based on the sedimentation rate and velocity profile in the chamber for the delivery of cells from a flowing suspension to the chamber surface. Our results show that the flux depends on the bulk cell concentration, the distance from the entrance point, and the flow rate of the cell-containing medium. The model was then used in a normalization procedure for experiments in which T cells attach to TNF-alpha-stimulated HUVEC monolayers, showing that a threshold for adhesion occurs at a shear stress of about 3 dyn/cm2.     

Enhanced External Counterpulsation Treatment May Intervene The Advanced Atherosclerotic Plaque Progression by Inducing The Variations of Mechanical Factors: A 3D FSI Study Based on in vivo Animal Experiment

Growing evidences suggest that long-term enhanced external counterpulsation (EECP) treatment can inhibit the initiation of atherosclerotic lesion by improving the hemodynamic environment in aortas. However, whether this kind procedure will intervene the progression of advanced atherosclerotic plaque remains elusive and causes great concern in its clinical application presently. In the current paper, a pilot study combining animal experiment and numerical simulation was conducted to investigate the acute mechanical stress variations during EECP intervention, and then to assess the possible chronic effects. An experimentally induced hypercholesterolemic porcine model was developed and the basic hemodynamic measurement was performed in vivo before and during EECP treatment. Meanwhile, A 3D fluid-structure interaction (FSI) model of blood vessel with symmetric local stenosis was developed for the numerical calculation of some important mechanical factors. The results show that EECP augmented 12.21% of the plaque wall stress (PWS), 57.72% of the time average wall shear stress (AWSS) and 43.67% of the non-dimensional wall shear stress gradient (WSSGnd) at throat site of the stenosis. We suggest that long-term EECP treatment may intervene the advanced plaque progression by inducing the significant variations of some important mechanical factors, but its proper effects will need a further research combined follow-up observation in clinic.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

Experimental technique of measuring dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. The exact cause and mechanism of the progression of AV calcification is unknown, although mechanical forces have been known to play a role. It is thus important to characterize the mechanical environment of the AV. In the current study, we establish a methodology of measuring shear stresses experienced by the aortic surface of the AV leaflets using an in vitro valve model and adapting the laser Doppler velocimetry (LDV) technique. The valve model was constructed from a fresh porcine aortic valve, which was trimmed and sutured onto a plastic stented ring, and inserted into an idealized three-lobed sinus acrylic chamber. Valve leaflet location was measured by obtaining the location of highest back-scattered LDV laser light intensity. The technique of performing LDV measurements near to biological surfaces as well as the leaflet locating technique was first validated in two phantom flow systems: (1) steady flow within a straight tube with AV leaflet adhered to the wall, and (2) steady flow within the actual valve model. Dynamic shear stresses were then obtained by applying the techniques on the valve model in a physiologic pulsatile flow loop. Results show that aortic surface shear stresses are low during early systole (<5 dyn/cm2) but elevated to its peak during mid to late systole at about 18-20 dyn/cm2. Low magnitude shear stress (<5 dyn/cm2) was observed during early diastole and dissipated to zero over the diastolic duration. Systolic shear stress was observed to elevate only with the formation of sinus vortex flow. The presented technique can also be used on other in vitro valve models such as congenitally geometrically malformed valves, or to investigate effects of hemodynamics on valve shear stress. Shear stress data can be used for further experiments investigating effects of fluid shear stress on valve biology, for conditioning tissue engineered AV, and to validate numerical simulations.     

Adhesion study of silicone coatings: the interaction of thickness, modulus and shear rate on adhesion force

Interactions between coating thickness, modulus and shear rate on pseudobarnacle adhesion to a platinum-cured silicone coating were studied using a statistical experimental design. A combined design method was used for two mixture components and two process variables. The two mixture components, vinyl end-terminated polydimethylsiloxanes (V21: MW=6 kg mole(-1) and V35: MW=4 9.5 kg mole(-1), Gelest Inc.) were mixed at five different levels to vary the modulus. The dry coating thickness was varied from 160 - 740 microm and shear tests were performed at four different shear rates (2, 7, 12, and 22 microm s(-1)). The results of the statistical analysis showed that the mixture components were significant factors on shear stress, showing an interaction with the process variable. For the soft silicone coating based on the high molecular weight polydimethylsiloxane (E=0.08 MPa), shear stress significantly increased as coating thickness decreased, while shear rate slightly impacted shear force especially at 160 microm coating thickness. As the modulus was increased (E=1.3 MPa), more force was required to detach the pseudobarnacle from the coatings, but thickness and rate dependence on shear stress became less important.     

剪切流动法研究表面固定化配基与目标分子的相互作用力

基于剪切流动腔技术,以微球作为受力载体,设计了一套可用于研究表面固定化配基与目标分子特异性相互作用力的实验和分析方法,并以人免疫球蛋白 G (human IgG) 和羊抗人免疫球蛋白 G (goat anti-human IgG) 分别作为模型配基和模型目标分子进行了研究 . 基于平面 Poiseuille 层流模型设计了流场参数,以数值计算结果验证了设计的合理性 . 使用牛血清白蛋白 (BSA) 作为非特异性对照,判断微球与基片表面的结合力来自配基和目标分子的生物特异性相互作用,并由进一步的目标分子灭活对比实验确认了这一结论 . 实验观察到微球与基片表面的结合力受到配基面密度的影响,说明发生结合的是多对而非单对蛋白质分子 . 将 95 ％的微球被剥离时对应的壁面剪切率设定为临界剪切率,由大量实验结果拟合得到了临界剪切率与配基面密度间的定量关系 . 在受力分析模型中,考虑到多分子的结合,以及分子键位置不同造成的力臂长度的差异,最终计算得到单对配基与目标分子的平均结合力约为 342pN.     

Design optimization of a helical endothelial cell culture device

The specific roles of mass transfer and fluid dynamic stresses on endothelial function, important in atherogenesis, are not known. Further, the effects of mass transfer and fluid dynamic stresses are difficult to separate because areas of “abnormal” mass transfer and “abnormal” wall shear stress tend to co-localize (where abnormal is defined as any deviation from the mass transfer rate or wall shear stress present in a long straight artery with the same flow rate and diameter). Our goal was to design a cell culture device which gives maximum separation between areas of abnormal shear stress and areas of abnormal mass transfer. We used design optimization principles to design a helical cell culture device. Using shear stress and mass transfer fields predicted by solving the governing equations, the area of the device which was exposed to low rates of mass transfer and normal levels of wall shear stress was determined. The design optimization method then maximized this area by varying the design variables, resulting in the optimum design. The optimum design had Reynolds number = 50, helical radius = 3.23 and helical pitch = 3.82. The area of the device which was exposed to low rates of mass transfer and regular levels of wall shear stress was about 4.5 times the inlet cross-sectional area of the device or about 5% of the device total internal surface area. An optimum design was successfully determined and the methodology used was shown to be robust. The area of the device which was exposed to low rates of mass transfer and regular levels of wall shear stress occurred in a defined region which should aid further experimental work.     

Pulsed ultrasonic Doppler velocity measurements inside a left ventricular assist device

In this study we have employed a single channel, pulsed ultrasonic Doppler velocimeter to measure instantaneous velocity distributions within the pumping chamber of a ventricular assist device. Instantaneous velocities have been decomposed into periodic mean and turbulent fluctuating components from which estimates of Reynolds stresses within the chamber and mean shear stresses along the wall of the chamber have been obtained. A review of the complete data set indicates a maximum value of the mean wall shear stress of 25 dynes/cm2 and a maximum Reynolds stress of 212 dynes/cm2. These values are lower than those measured distal to aortic valve prostheses in vitro and are well below levels known to damage blood components. Core flow patterns, wall washing patterns and flow stagnation points are also revealed.     

A numerical analysis of forces exerted by laminar flow on spreading cells in a parallel plate flow chamber assay

Exposure of spreading anchorage-dependent cells to laminar flow is a common technique to measure the strength of cell adhesion. Since cells protrude into the flow stream, the force exerted by the fluid on the cells is a function of cell shape. To assess the relationship between cell shape and the hydrodynamic force on adherent cells, we obtained numerical solutions of the velocity and stress fields around bovine aortic endothelial cells during various stages of spreading and calculated the force required to detach the cells. Morphometric parameters were obtained from light and scanning electron microscopy measurements. Cells were assumed to have a constant volume, but the surface area increased during spreading until the membrane was stretched taut. Two-dimensional models of steady flow were generated using the software packages ANSYS (mesh generation) and FIDAP (problem solution). The validity of the numerical results was tested by comparison with published results for a semicircle in contact with the surface. The drag force and torque were greatest for round cells making initial contact with the surface. During spreading, the drag force and torque declined by factors of 2 and 20, respectively. The calculated forces and moments were used in adhesion models to predict the wall shear stress at which the cells detached. Based upon published values for the bond force and receptor number, round cells should detach at shear stresses between 2.5 and 6 dyn/cm(2), whereas substantially higher stresses are needed to detach spreading and fully spread cells. Results from the simulations indicate that (1) the drag force varies little with cell shape whereas the torque is very sensitive to cell shape, and (2) the increase in the strength of adhesion during spreading is due to increased contact area and receptor densities within the contact area. (c) 1993 John Wiley & Sons, Inc.     

Nanoliter scale microbioreactor array for quantitative cell biology

A nanoliter scale microbioreactor array was designed for multiplexed quantitative cell biology. An addressable 8 x 8 array of three nanoliter chambers was demonstrated for observing the serum response of HeLa human cancer cells in 64 parallel cultures. The individual culture unit was designed with a "C" shaped ring that effectively decoupled the central cell growth regions from the outer fluid transport channels. The chamber layout mimics physiological tissue conditions by implementing an outer channel for convective "blood" flow that feeds cells through diffusion into the low shear "interstitial" space. The 2 microm opening at the base of the "C" ring established a differential fluidic resistance up to 3 orders of magnitude greater than the fluid transport channel within a single mold microfluidic device. Three-dimensional (3D) finite element simulation were used to predict fluid transport properties based on chamber dimensions and verified experimentally. The microbioreactor array provided a continuous flow culture environment with a Peclet number (0.02) and shear stress (0.01 Pa) that approximated in vivo tissue conditions without limiting mass transport (10 s nutrient turnover). This microfluidic design overcomes the major problems encountered in multiplexing nanoliter culture environments by enabling uniform cell loading, eliminating shear, and pressure stresses on cultured cells, providing stable control of fluidic addressing, and permitting continuous on-chip optical monitoring.     

The effects of elongational stress exposure on the activation and aggregation of blood platelets.

Hemodynamic shear is known to stimulate blood and endothelial cells and induce platelet activation. Many studies of shear-induced platelet stimulation have employed rotational viscometers in which secondary flow effects are assumed to be negligible. Shear induced platelet activation occurs at elevated shear rates where secondary flows may contribute a significant percentage of the total hydrodynamic force experienced by the sample. Elongational stress, one component of this secondary flow, has been shown to alter transmembrane ion flux in intact cell and the permeability of synthetic membrane preparations. Elongational flow also occurs in the vasculature at sites of elevated shear stress. Secondary flow components may contribute to platelet activation induced during shear stress application in rotational viscometry. A unique 'constrained convergence' elongational flow chamber was designed and fabricated to study platelet response to elongational stress exposure. The elongational flow chamber was capable of producing an elongation rate of 2.1 s-1 with a corresponding volume averaged shear rate of 58.33 s-1. Significant changes were observed in the total platelet volume distribution and measured response to added chemical antagonists after elongational stress exposure. The total platelet volume histogram shifted toward larger particle sizes, suggesting the formation of large aggregates as a result of elongational stress exposure. Platelets exposed to elongational stress demonstrated a dose dependent decrease in added ADP-induced aggregation rate and extent of aggregation.     

Force versus axial deflection of pipette-aspirated closed membranes

The axial deformation of a pipette-pressurized fluid membrane bag produces minuscule yet well-defined, reproducible forces. The stiffness of this ultrasensitive force transducer is tunable and largely independent of the constitutive membrane behavior. Based on a rigorous variational treatment, we present both numerical as well as approximate analytical solutions for the force-deflection relation of this unique biophysical force probe. Our numerical results predict a measurably nonlinear force-deflection behavior at moderate-to-large deformations, which we confirm experimentally using red blood cells. Furthermore, considering nearly spherical membrane shapes and enforcing proper boundary conditions, we derive an analytical solution valid at small deformations. In this linear regime the pressurized membrane bag behaves like a Hookean spring, with a spring constant that is significantly larger than previously published for the biomembrane force probe.     

Modeling and design of optimal flow perfusion bioreactors for tissue engineering applications

Perfusion bioreactors have been used in different tissue engineering applications because of their consistent distribution of nutrients and flow-induced shear stress within the tissue-engineering scaffold. A widely used configuration uses a scaffold with a circular cross-section enclosed within a cylindrical chamber and inlet and outlet pipes which are connected to the chamber on either side through which media is continuously circulated. However, fluid-flow experiments and simulations have shown that the majority of the flow perfuses through the center. This pattern creates stagnant zones in the peripheral regions as well as in those of high flow rate near the inlet and outlet. This non-uniformity of flow and shear stress, owing to a circular design, results in limited cell proliferation and differentiation in these areas. The focus of this communication is to design an optimized perfusion system using computational fluid dynamics as a mathematical tool to overcome the time-consuming trial and error experimental method. We compared the flow within a circular and a rectangular bioreactor system. Flow simulations within the rectangular bioreactor are shown to overcome the limitations in the circular design. This communication challenges the circular cross-section bioreactor configuration paradigm and provides proof of the advantages of the new design over the existing one.     

Optimization of ski jumper's posture considering lift-to-drag ratio and stability

An optimization analysis of a ski jumper's posture has been performed to improve the lift-to-drag ratio, and to examine aerodynamic stability to ensure flight control and safety. Three-dimensional Reynolds-averaged Navier-Stokes equations were discretized using finite volume approximations for the flow analysis, and the shear stress transport k-ω turbulence model was used for a turbulence closure. The Airfoil theory and principles of aircraft stability were used to examine the stability mechanism. Two ski jumper posture angles were chosen as design variables through a preliminary test, and the lift-to-drag ratio was used as an objective function for the optimization problem. Thirteen design points within design spaces are selected by Latin hypercube sampling. In order to predict the objective function values in the design space, the Kriging model was constructed using the numerical results on the design points. By the sequential quadratic programming, the optimal point was found from the constructed the Kriging model. The Kriging model predicted the objective function value at the optimum point with a 1.1% error compared to the value obtained by numerical analysis. The optimum design showed a considerable lift-to-drag ratio improvement compared to the reference design.     

Shear forces during blast, not abrupt changes in pressure alone, generate calcium activity in human brain cells

Blast-Induced Traumatic Brain Injury (bTBI) describes a spectrum of injuries caused by an explosive force that results in changes in brain function. The mechanism responsible for primary bTBI following a blast shockwave remains unknown. We have developed a pneumatic device that delivers shockwaves, similar to those known to induce bTBI, within a chamber optimal for fluorescence microscopy. Abrupt changes in pressure can be created with and without the presence of shear forces at the surface of cells. In primary cultures of human central nervous system cells, the cellular calcium response to shockwaves alone was negligible. Even when the applied pressure reached 15 atm, there was no damage or excitation, unless concomitant shear forces, peaking between 0.3 to 0.7 Pa, were present at the cell surface. The probability of cellular injury in response to a shockwave was low and cell survival was unaffected 20 hours after shockwave exposure.