Flow in the well: computational fluid dynamics is essential in flow chamber construction

A perfusion system was developed to generate well defined flow conditions within a well of a standard multidish. Human vein endothelial cells were cultured under flow conditions and cell response was analyzed by microscopy. Endothelial cells became elongated and spindle shaped. As demonstrated by computational fluid dynamics (CFD), cells were cultured under well defined but time varying shear stress conditions. A damper system was introduced which reduced pulsatile flow when using volumetric pumps. The flow and the wall shear stress distribution were analyzed by CFD for the steady and unsteady flow field. Usage of the volumetric pump caused variations of the wall shear stresses despite the controlled fluid environment and introduction of a damper system. Therefore the use of CFD analysis and experimental validation is critical in developing flow chambers and studying cell response to shear stress. The system presented gives an effortless flow chamber setup within a 6-well standard multidish.     

In Situ Spatiotemporal Mapping of Flow Fields around Seeded Stem Cells at the Subcellular Length Scale

A major hurdle to understanding and exploiting interactions between the stem cell and its environment is the lack of a tool for precise delivery of mechanical cues concomitant to observing sub-cellular adaptation of structure. These studies demonstrate the use of microscale particle image velocimetry (μ-PIV) for in situ spatiotemporal mapping of flow fields around mesenchymal stem cells, i.e. murine embryonic multipotent cell line C3H10T1/2, at the subcellular length scale, providing a tool for real time observation and analysis of stem cell adaptation to the prevailing mechanical milieu. In the absence of cells, computational fluid dynamics (CFD) predicts flow regimes within 12% of μ-PIV measures, achieving the technical specifications of the chamber and the flow rates necessary to deliver target shear stresses at a particular height from the base of the flow chamber. However, our μ-PIV studies show that the presence of cells per se as well as the density at which cells are seeded significantly influences local flow fields. Furthermore, for any given cell or cell seeding density, flow regimes vary significantly along the vertical profile of the cell. Hence, the mechanical milieu of the stem cell exposed to shape changing shear stresses, induced by fluid drag, varies with respect to proximity of surrounding cells as well as with respect to apical height. The current study addresses a previously unmet need to predict and observe both flow regimes as well as mechanoadaptation of cells in flow chambers designed to deliver precisely controlled mechanical signals to live cells. An understanding of interactions and adaptation in response to forces at the interface between the surface of the cell and its immediate local environment may be key for de novo engineering of functional tissues from stem cell templates as well as for unraveling the mechanisms underlying multiscale development, growth and adaptation of organisms.     

Flow around cells adhered to a microvessel wall. I. Fluid stresses and forces acting on the cells

To evaluate the fluid forces acting on cells adhered to a microvessel wall, we numerically studied the flow field around adherent cells and the distribution of the stresses on their surfaces. For simplicity, the cells were modeled as rigid particles attached to a wall of a circular cylindrical tube regularly in the flow direction, in a row or two rows. It was found that not the detailed shape of the model cells but their height from the vessel wall is a key determinant of the fluid forces and torque acting on them. In both arrangements of one row and two rows, the axial spacing between neighboring adherent cells significantly affects the distributions of the stresses on them, which results in drastic variations of the fluid forces with the axial spacing and the relative positions with respect to their neighboring cells. The drag force acting on an adherent cell in the vessel was evaluated to be larger than the value in the 2D chamber flow at the same wall shear stress, mainly due to much larger variations of the pressure distribution on the cell surface in the vessel flow.     

Flow-induced Wall Shear Stress in Abdominal Aortic Aneurysms: Part II - Pulsatile Flow Hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 h Re m h 300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure ( p w ), wall shear stress ( w ), Wall Shear Stress Gradient (WSSG), time-average wall shear stress ( w *), and time-average Wall Shear Stress Gradient WSSG *. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

T型分叉流槽中前列环素和内皮素分泌的研究

动脉粥样硬化（atherosclerosis）的非随机分布与当地的血流动力环境有关。借助平行平板式平直流槽和以T型分叉流槽为代表的平行平板式异型流槽,可以模拟血管的主要形状特征,首先,在数值模拟的基础上分析了流型特征参数,确定了流槽的设计尺寸。然后,通过实验研究,探讨流型改变对内皮细胞血管活性物质分泌的影响,发现扩张效应流线偏转和驻点效应使得异型流槽前列环素和内皮素的分泌水平与相同入口雷诺数（Re）条件下的平直流槽分别有降低趋势和显著差异。为进一步研究流型对血管内皮细胞的影响提供了实验数据。     

Pseudomonas aeruginosa and Saccharomyces cerevisiae Biofilm in Flow Cells

Many microbial cells have the ability to form sessile microbial communities defined as biofilms that have altered physiological and pathological properties compared to free living microorganisms. Biofilms in nature are often difficult to investigate and reside under poorly defined conditions¹. Using a transparent substratum it is possible to device a system where simple biofilms can be examined in a non-destructive way in real-time: here we demonstrate the assembly and operation of a flow cell model system, for in vitro 3D studies of microbial biofilms generating high reproducibility under well-defined conditions^2,3.The system consists of a flow cell that serves as growth chamber for the biofilm. The flow cell is supplied with nutrients and oxygen from a medium flask via a peristaltic pump and spent medium is collected in a waste container. This construction of the flow system allows a continuous supply of nutrients and administration of e.g. antibiotics with minimal disturbance of the cells grown in the flow chamber. Moreover, the flow conditions within the flow cell allow studies of biofilm exposed to shear stress. A bubble trapping device confines air bubbles from the tubing which otherwise could disrupt the biofilm structure in the flow cell.The flow cell system is compatible with Confocal Laser Scanning Microscopy (CLSM) and can thereby provide highly detailed 3D information about developing microbial biofilms. Cells in the biofilm can be labeled with fluorescent probes or proteins compatible with CLSM analysis. This enables online visualization and allows investigation of niches in the developing biofilm. Microbial interrelationship, investigation of antimicrobial agents or the expression of specific genes, are of the many experimental setups that can be investigated in the flow cell system.     

Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a dimensionless ratio h / lambda(v), in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to be met: (1) h / lambda(v) < 2, where h is the distance between the plates and lambda(v) is the viscous penetration depth; and (2) f(0) < f(c) / m, where the critical frequency f(c) is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f(0) is the fundamental frequency of fluid flow.     

Flow within models of the vertebrate embryonic heart

Vertebrate cardiogenesis is believed to be partially regulated by fluid forces imposed by blood flow in addition to myocardial activity and other epigenetic factors. To understand the flow field within the embryonic heart, numerical simulations using the immersed boundary method were performed on a series of models that represent simplified versions of some of the early morphological stages of heart development. The results of the numerical study were validated using flow visualization experiments conducted on equivalent dynamically scaled physical models. The chamber and cardiac cushion (or valve) depths in the models were varied, and Reynolds numbers ranging from 0.01 to 1000 corresponding to the scale of the early heart tube to the adult heart were considered. The observed results showed that vortex formation within the chambers occurred for Reynolds numbers on the order of 1-10. This transition to vortical flow appears to be highly sensitive to the chamber and cushion depths within the model. These fluid dynamic events could be important to induce shear sensing at the endothelial surface layer which is thought to be a part of regulating the proper morphological development and functionality of the valves.     

A low shear stress modular bioreactor for connected cell culture under high flow rates

A generic “system on a plate” modular multicompartmental bioreactor array which enables microwell protocols to be transferred directly to the bioreactor modules, without redesign of cell culture experiments or protocols is described. The modular bioreactors are simple to assemble and use and can be easily compared with standard controls since cell numbers and medium volumes are quite similar. Starting from fluid dynamic and mass transport considerations, a modular bioreactor chamber was first modeled and then fabricated using “milli‐molding,” a technique adapted from soft lithography. After confirming that the shear stress was extremely low in the system in the range of useful flow rates, the bioreactor chambers were tested using hepatocytes. The results show that the bioreactor chambers can increase or maintain cell viability and function when the flow rates are below 500 µL/min, corresponding to wall shear stresses of 10^?5 Pa or less at the cell culture surface. Biotechnol. Bioeng. 2010; 106: 127–137. © 2010 Wiley Periodicals, Inc.     

突然扩张流槽中血管内皮细胞表面粘附蛋白表达的研究

动脉粥样硬化的非随机分布与当地的血流动力环境有关,为了研究复杂的流体动力学条件对血和皮细胞生理功能的影响,构建了平行板式平直流槽和突然扩张流槽,通过数值模拟分析了流型的特征,并探讨流型改变对人脐静脉血管内皮细胞表面粘附蛋白表达的影响,发现突然扩张流槽中流动的空间变化使得总体细胞表面粘附蛋白ICAM－1的表达显著高于平直流槽中的均匀定常剪切作用,表明局部流动空间变化的性质可以影响血管内皮细胞的功能。     

Receptor-mediated binding of IgE-sensitized rat basophilic leukemia cells to antigen-coated substrates under hydrodynamic flow.

The physiological function of many cells is dependent on their ability to adhere via receptors to ligand-coated surfaces under fluid flow. We have developed a model experimental system to measure cell adhesion as a function of cell and surface chemistry and fluid flow. Using a parallel-plate flow chamber, we measured the binding of rat basophilic leukemia cells preincubated with anti-dinitrophenol IgE antibody to polyacrylamide gels covalently derivatized with 2,4-dinitrophenol. The rat basophilic leukemia cells' binding behavior is binary: cells are either adherent or continue to travel at their hydrodynamic velocity, and the transition between these two states is abrupt. The spatial location of adherent cells shows cells can adhere many cell diameters down the length of the gel, suggesting that adhesion is a probabilistic process. The majority of experiments were performed in the excess ligand limit in which adhesion depends strongly on the number of receptors but weakly on ligand density. Only 5-fold changes in IgE surface density or in shear rate were necessary to change adhesion from complete to indistinguishable from negative control. Adhesion showed a hyperbolic dependence on shear rate. By performing experiments with two IgE-antigen configurations in which the kinetic rates of receptor-ligand binding are different, we demonstrate that the forward rate of reaction of the receptor-ligand pair is more important than its thermodynamic affinity in the regulation of binding under hydrodynamic flow. In fact, adhesion increases with increasing receptor-ligand reaction rate or decreasing shear rate, and scales with a single dimensionless parameter which compares the relative rates of reaction to fluid shear.     

The use of a conventional tissue culture plate as an optically accessible perfusion chamber for in situ assays and for long-term cultivation of mammalian cells

An alternative culture system has been developed based on a conventional tissue culture plate (3.5 cm diameter) which is changed into a closed perfusion chamber. The system can easily be scaled up from one to several chambers. The shape and the size of the area of cell growth may be designed to individual experimental demands. The whole culture chamber is optically accessible, so cell growth and morphology can be evaluated by light microscopy. Furthermore the cellular physiology can be characterised by any fluorimetric assay using a bottom type fluorescence reader. A peristaltic pump sustains a constant medium flow through the chamber thus creating true homeostasis. The use of HPLC-valves and connectors allows the switching between different media or assay solutions. Thus it is possible to perform in situ assays also measuring transient effects. A protocol for vitality tests using calcein-AM is worked out for an adherent cell line and for a suspension cell line. The lower detection limits are 7 × 10² cells cm^-2 for the adherent cells and 5 × 10⁴ cells mL^-1 for the suspension cells. The upper limits are 1–2 × 10⁵ cells cm^-2 respectively 8 × 10⁶ cells mL^-1.     

MECHANISMS OF FLUID SHEAR‐INDUCED INHIBITION OF POPULATION GROWTH IN A RED‐TIDE DINOFLAGELLATE1

Net population growth of some dinoflagellates is inhibited by fluid shear at shear stresses comparable with those generated during oceanic turbulence. Decreased net growth may occur through lowered cell division, increased mortality, or both. The dominant mechanism under various flow conditions was determined for the red‐tide dinoflagellate Lingulodinium polyedrum (Stein) Dodge. Cell division and mortality were determined by direct observation of isolated cells in 0.5‐mL cultures that were shaken to generate unquantified fluid shear. Larger volume cultures were exposed to quantified laminar shear in Couette‐flow chambers (0.004–0.019 N·m ^{? 2} shear stress) and to unquantified flow in shaken flasks. In these larger cultures, cell division frequency was calculated from flow cytometric measurements of DNA·cell^?1. The mechanism by which shear inhibits net growth of L. polyedrum depends on shear stress level and growth conditions. Observations on the isolated cells showed that shaking inhibited growth by lowering cell division without increased mortality. Similar results were found for early exponential‐phase cultures exposed to the lowest experimental shear stress in Couette‐flow chambers. However, mortality occurred when a late exponential‐phase culture was exposed to the same low shear stress and was inferred to occur in cultures exposed to higher shear stresses. Elevated mortality in those treatments was confirmed using behavioral, morphological, and physiological assays. The results predict that cell division in L. polyedrum populations will be inhibited by levels of oceanic turbulence common for near‐surface waters. Shear‐induced mortality is not expected unless shear‐stress levels are unusually high or when cellular condition resembles late exponential/stationary phase cultures.     

Study of local hydrodynamic environment in cell-substrate adhesion using side-view μPIV technology

Tumor cell adhesion to the endothelium under shear flow conditions is a critical step that results in circulation-mediated tumor metastasis. This study presents experimental and computational techniques for studying the local hydrodynamic environment around adherent cells and how local shear conditions affect cell-cell interactions on the endothelium in tumor cell adhesion. To study the local hydrodynamic profile around heterotypic adherent cells, a side-view flow chamber assay coupled with micro particle imaging velocimetry (μPIV) technique was developed, where interactions between leukocytes and tumor cells in the near-endothelial wall region and the local shear flow environment were characterized. Computational fluid dynamics (CFD) simulations were also used to obtain quantitative flow properties around those adherent cells. Results showed that cell dimension and relative cell-cell positions had strong influence on local shear rates. The velocity profile above leukocytes and tumor cells displayed very different patterns. Larger cell deformations led to less disturbance to the flow. Local shear rates above smaller cells were observed to be more affected by relative positions between two cells.     

Loss of Syndecan-1 Induces a Pro-inflammatory Phenotype in Endothelial Cells with a Dysregulated Response to Atheroprotective Flow

Fluid shear stresses are potent regulators of vascular homeostasis and powerful determinants of vascular disease progression. The glycocalyx is a layer of glycoaminoglycans, proteoglycans, and glycoproteins that lines the luminal surface of arteries. The glycocalyx interacts directly with hemodynamic forces from blood flow and, consequently, is a prime candidate for the mechanosensing of fluidic shear stresses. Here, we investigated the role of the glycocalyx component syndecan-1 (sdc-1) in controlling the shear stress-induced signaling and flow-mediated phenotypic modulation in endothelial cells. We found that knock-out of sdc-1 abolished several key early signaling events of endothelial cells in response to shear stress including the phosphorylation of Akt, the formation of a spatial gradient in paxillin phosphorylation, and the activation of RhoA. After exposure to atheroprotective flow, we found that sdc-1 knock-out endothelial cells had a phenotypic shift to an inflammatory/pro-atherosclerotic phenotype in contrast to the atheroprotective phenotype of wild type cells. Consistent with these findings, we found increased leukocyte adhesion to sdc-1 knock-out endothelial cells in vitro that was reduced by re-expression of sdc-1. In vivo, we found increased leukocyte recruitment and vascular permeability/inflammation in sdc-1 knock-out mice. Taken together, our studies support a key role for sdc-1 in endothelial mechanosensing and regulation of endothelial phenotype.     

A multishear microfluidic device for quantitative analysis of calcium dynamics in osteoblasts

Microfluidics is a convenient platform to study the influences of fluid shear stress on calcium dynamics. Fluidic shear stress has been proven to affect bone cell functions and remodelling. We have developed a microfluidic system which can generate four shear flows in one device as a means to study cytosolic calcium concentration ([Ca²⁺]_c) dynamics of osteoblasts. Four shear forces were achieved by having four cell culture chambers with different widths while resistance correction channels compensated for the overall resistance to allow equal flow distribution towards the chambers. Computational simulation of the local shear stress distribution highlighted the preferred section in the cell chamber to measure the calcium dynamics. Osteoblasts showed an [Ca²⁺]_c increment proportional to the intensity of the shear stress from 0.03 to 0.30 Pa. A delay in response was observed with an activation threshold between 0.03 and 0.06 Pa. With computational modelling, our microfluidic device can offer controllable multishear stresses and perform quantitative comparisons of shear stress-induced intensity change of calcium in osteoblasts.     

A theoretical model study of the influence of fluid stresses on a cell adhering to a microchannel wall.

We predict the amplification of mechanical stress, force, and torque on an adherent cell due to flow within a narrow microchannel. We model this system as a semicircular bulge on a microchannel wall, with pressure-driven flow. This two-dimensional model is solved computationally by the boundary element method. Algebraic expressions are developed by using forms suggested by lubrication theory that can be used simply and accurately to predict the fluid stress, force, and torque based upon the fluid viscosity, muoffhannel height, H, cell size, R, and flow rate per unit width, Q2-d. This study shows that even for the smallest cells (gamma = R/H << 1), the stress, force, and torque can be significantly greater than that predicted based on flow in a cell-free system. Increased flow resistance and fluid stress amplification occur with bigger cells (gamma > 0.25), because of constraints by the channel wall. In these cases we find that the shear stress amplification is proportional to Q2-d(1-gamma)-2, and the force and torque are proportional to Q2-d(1-gamma2)-5/2. Finally, we predict the fluid mechanical influence on three-dimensional immersed objects. These algebraic expressions have an accuracy of approximately 10% for flow in channels and thus are useful for the analysis of cells in flow chambers. For cell adhesion in tubes, the approximations are accurate to approximately 25% when gamma > 0.5. These calculations may thus be used to simply predict fluid mechanical interactions with cells in these constrained settings. Furthermore, the modeling approach may be useful in understanding more complex systems that include cell deformability and cell-cell interactions.     

Numerical model of fluid flow and oxygen transport in a radial-flow microchannel containing hepatocytes

The incorporation of monolayers of cultured hepatocytes into an extracorporeal perfusion system has become a promising approach for the development of a temporary bioartificial liver (BAL) support system. In this paper we present a numerical investigation of the oxygen tension, shear stress, and pressure drop in a bioreactor for a BAL composed of plasma-perfused chambers containing monolayers of porcine hepatocytes. The chambers consist of microfabricated parallel disks with center-to-edge radial flow. The oxygen uptake rate (OUR), measured in vitro for porcine hepatocytes, was curve-fitted using Michaelis-Menten kinetics for simulation of the oxygen concentration profile. The effect of different parameters that may influence the oxygen transport inside the chambers, such as the plasma flow rate, the chamber height, the initial oxygen tension in the perfused plasma, the OUR, and K(m) was investigated. We found that both the plasma flow rate and the initial oxygen tension may have an important effect upon oxygen transport. Increasing the flow rate and/or the inlet oxygen tension resulted in improved oxygen transport to cells in the radial-flow microchannels, and allowed significantly greater diameter reactor without oxygen limitation to the hepatocytes. In the range investigated in this paper (10 microns < H < 100 microns), and for a constant plasma flow rate, the chamber height, H, had a negligible effect on the oxygen transport to hepatocytes. On the contrary, it strongly affected the mechanical stress on the cells that is also crucial for the successful design of the BAL reactors. A twofold decrease in chamber height from 50 to 25 microns produced approximately a fivefold increase in maximal shear stress at the inlet of the reactor from 2 to 10 dyn/cm2. Further decrease in chamber height resulted in shear stress values that are physiologically unrealistic. Therefore, the channel height needs to be carefully chosen in a BAL design to avoid deleterious hydrodynamic effects on hepatocytes.     

A Flow Sensing Model for Mesenchymal Stromal Cells Using Morphogen Dynamics

The differentiation of mesenchymal stromal cells has been shown to be affected by many parameters such as morphogens, flow rate, medium viscosity, and shear stress when exposed to fluid flow. The mechanism by which these cells sense their environment is still under intense discussion. In particular, during flow chamber experiments, it is difficult to interpret the interplay of the above-mentioned parameters in the process of cell differentiation. In this work, we tested the hypothesis that the competition between diffusion and advection of paracrine morphogens could explain the dependency of the cell differentiation to the above-mentioned parameters. To evaluate this hypothesis, we developed a numerical model simulating a simplified version of the advection-diffusion-reaction of morphogens secreted by the cells within a flow chamber. The model predicted a sharp transition in the fraction of receptors bound to the morphogen. This transition was characterized by a new, dimensionless number depending on flow rate, flow viscosity, flow chamber dimensions, and morphogen decay rate. We concluded that the competition between diffusion and advection of paracrine morphogens can act as a probe for the cells to sense their pericellular environment.     

Gradient fluid shear stress regulates migration of osteoclast precursors

Cell migration is highly sensitive to fluid shear stress (FSS) in blood flow or interstitial fluid flow. However, whether the FSS gradient can regulate the migration of cells remains unclear. In this work, we constructed a parallel-plate flow chamber with different FSS gradients and verified the gradient flow field by particle image velocimetry measurements and finite element analyses. We then investigated the effect of FSS magnitudes and gradients on the migration of osteoclast precursor RAW264.7 cells. Results showed that the cells sensed the FSS gradient and migrated toward the low-FSS region. This FSS gradient-induced migration tended to occur in low-FSS magnitudes and high gradients, e.g., the migration angle relative to flow direction was approximately 90° for 0.1 Pa FSS and 0.2 Pa mm^?1 FSS gradient. When chemically inhibiting the calcium signaling pathways of the mechanosensitive cation channel, endoplasmic reticulum, phospholipase C, and extracellular calcium, the cell migration toward the low-FSS region was significantly reduced. This study may provide insights into the mechanism of the recruitment of osteoclast precursors at the site of bone resorption and of mechanical stimulation-induced bone remodeling.