Improvement and validation of a computational model of flow in the swirling well cell culture model

Effects of fluid dynamics on cells are often studied by growing the cells on the base of cylindrical wells or dishes that are swirled on the horizontal platform of an orbital shaker. The swirling culture medium applies a shear stress to the cells that varies in magnitude and directionality from the center to the edge of the vessel. Computational fluid dynamics methods are used to simulate the flow and hence calculate shear stresses at the base of the well. The shear characteristics at each radial location are then compared with cell behavior at the same position. Previous simulations have generally ignored effects of surface tension and wetting, and results have only occasionally been experimentally validated. We investigated whether such idealized simulations are sufficiently accurate, examining a commonly-used swirling well configuration. The breaking wave predicted by earlier simulations was not seen, and the edge-to-center difference in shear magnitude (but not directionality) almost disappeared, when surface tension and wetting were included. Optical measurements of fluid height and velocity agreed well only with the computational model that incorporated surface tension and wetting. These results demonstrate the importance of including accurate fluid properties in computational models of the swirling well method.     

Osteoblasts and osteocytes respond differently to oscillatory and unidirectional fluid flow profiles

Bone cells subjected to mechanical loading by fluid shear stress undergo significant architectural and biochemical changes. The models of shear stress used to analyze the effects of loading bone cells in vitro include both oscillatory and unidirectional fluid shear profiles. Although the fluid flow profile experienced by cells within bone is most likely oscillatory in nature, to date there have been few direct comparisons of how bone cells respond to these two fluid flow profiles. In this study we evaluated morphologic and biochemical responses to a time course of unidirectional and oscillatory fluid flow in two commonly used bone cell lines, MC3T3-E1 osteoblasts and MLO-Y4 osteocytes. We determined that stress fibers formed and aligned within osteoblasts after 1 h of unidirectional fluid flow, but this response was not observed until greater than 5 h of oscillatory fluid flow. Despite the delay in stress fiber formation, oscillatory and unidirectional fluid flow profiles elicited similar temporal effects on the induction of both cyclooxygenase-2 (Cox-2) and osteopontin protein expression in osteoblasts. Interestingly, MLO-Y4 osteocytes formed organized stress fibers after exposure to 24 h of unidirectional shear stress, while the number of dendritic processes per cell increased along with Cox-2 protein levels after 24 h of oscillatory shear stress. Despite these differences, both flow profiles significantly altered osteopontin levels in MLO-Y4 osteocytes. Together these results demonstrate that the profile of fluid shear can induce significantly different responses from osteoblasts and osteocytes.     

Computation in the rabbit aorta of a new metric – the transverse wall shear stress – to quantify the multidirectional character of disturbed blood flow

Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric – the transverse wall shear stress (transWSS) – calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.     

The biased lamellipodium development and microtubule organizing center position in vascular endothelial cells migrating under the influence of fluid flow*

Summary— To analytically study the morphological responses of vascular endothelial cells (ECs) to fluid flow, we designed a parallel plate flow culture chamber in which cells were cultured under fluid shear stress ranging from 0.01 to 2.0 Pa for several days. Via a viewing window of the chamber, EC responses to known levels of fluid shear stress were monitored either by direct observations or by a video-enhanced time-lapse microscopy. Among the responses of cultured ECs to flow, morphological responses take from hours to days to be fully expressed, except for the fluid shear stress-dependent motility pattern change we reported earlier which could be detected within 30 min of flow changes. We report here that ECs exposed to more than 1.0 Pa of fluid shear shear stress have developed lamellipodia in the direction of flow in 10 min. This is the fastest structurally identifiable EC response to fluid shear stress. This was a reversible response. When the flow was stopped or reduced to the level which exerted less than 0.1 Pa of fluid shear stress, the biased lamellipodium development was lost within several minutes. The microtubule organizing center was located posterior to the nucleus in ECs under the influence of flow. However, this position was established only in ECs responding to fluid shear stress for longer than 1 h, indicating that positioning of the microtubule organizing center was not the reason for, but rather the result of, the biased lamellipodium response. Colcemid-treated ECs responded normally to flow, indicating that microtubules were not involved in both flow sensing and the flow-induced, biased lamellipodium development.     

A novel in vitro loading system to produce supraphysiologic oscillatory fluid shear stress

A multi-well fluid loading (MFL) system was developed to deliver oscillatory subphysiologic to supraphysiologic fluid shear stresses to cell monolayers in vitro using standard multi-well culture plates. Computational fluid dynamics modeling with fluid-structure interactions was used to quantify the squeeze film fluid flow between an axially displaced piston and the well plate surface. Adjusting the cone angle of the piston base modulated the fluid pressure, velocity, and shear stress magnitudes. Modeling results showed that there was near uniform fluid shear stress across the well with a linear drop in pressure across the radius of the well. Using the MFL system, RAW 264.7 osteoclastic cells were exposed to oscillatory fluid shear stresses of 0, 0.5, 1.5, 4, 6, and 17 Pa. Cells were loaded 1 h per day at 1 Hz for two days. Compared to sub-physiologic and physiologic levels, supraphysiologic oscillatory fluid shear induced upregulation of osteoclastic activity as measured by tartrate-resistant acid phosphatase activity and formation of mineral resorption pits. Cell number remained constant across all treatment groups.     

血浆层对血管壁剪应力和剪应力梯度的影响

在细小血管中,由于血细胞明显的趋轴效应,管中的血液分为两个不同的区域,即具有血细胞的核心区和邻近管壁和血浆层。应用两相分层流模型,研究在相同的流量和管径下,当核心区中的血液分别为牛顿流体和Casson流体时,不同的血浆层厚度对细小血管壁剪应力和剪应力梯度的影响。结果表明,血浆层的存在对壁剪应力和壁剪应力梯度有较大影响,当血浆层厚度仅为血管半径的1％和3％时,壁剪应力梯度分别下降约10％和20％。     

离体血流循环切应力水平控制方法的研究

本文应用流体力学及血流动力学理论和分析方法,建立了离体心血管循环系统的切应力水平控制方法。并采用该方法研制可精确控制切应变水平的模拟在体血流动力学环境的层流流动装置,用于研究动力学因素对人工培养的内皮细胞生物学特性影响。     

Flow rates in perfusion bioreactors to maximise mineralisation in bone tissue engineering in vitro

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5–5 mL/min (or in terms of fluid velocity: 0.166–1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments.     

Numerical investigations of the haemodynamic changes associated with stent malapposition in an idealised coronary artery

The deployment of a coronary stent near complex lesions can sometimes lead to incomplete stent apposition (ISA), an undesirable side effect of coronary stent implantation. Three-dimensional computational fluid dynamics (CFD) calculations are performed on simplified stent models (with either square or circular cross-section struts) inside an idealised coronary artery to analyse the effect of different levels of ISA to the change in haemodynamics inside the artery. The clinical significance of ISA is reported using haemodynamic metrics like wall shear stress (WSS) and wall shear stress gradient (WSSG). A coronary stent with square cross-sectional strut shows different levels of reverse flow for malapposition distance (MD) between 0 mm and 0.12 mm. Chaotic blood flow is usually observed at late diastole and early systole for MD=0 mm and 0.12 mm but are suppressed for MD=0.06 mm. The struts with circular cross section delay the flow chaotic process as compared to square cross-sectional struts at the same MD and also reduce the level of fluctuations found in the flow field. However, further increase in MD can lead to chaotic flow not only at late diastole and early systole, but it also leads to chaotic flow at the end of systole. In all cases, WSS increases above the threshold value (0.5 Pa) as MD increases due to the diminishing reverse flow near the artery wall. Increasing MD also results in an elevated WSSG as flow becomes more chaotic, except for square struts at MD=0.06 mm.     

Hemodynamic force dictates endothelial angiogenesis through MIEN1-ERK/MAPK-signaling axis

It is well-recognized that blood flow at branches and bends of arteries generates disturbed shear stress, which plays a crucial in driving atherosclerosis. Flow-generated fluid shear stress (FSS), as one of the key hemodynamic factors, is appreciated for its critical involvement in regulating angiogenesis to facilitate wound healing and tissue repair. Endothelial cells can directly sense FSS but the mechanobiological mechanism by which they decode different patterns of FSS to trigger angiogenesis remains unclear. In the current study, laminar shear stress (LSS, 15 dyn/cm²) was employed to mimic physiological blood flow, while disturbed shear stress (DSS, ranging from 0.5 ± 4 dyn/cm²) was applied to simulate pathological conditions. The aim was to investigate how these distinct types of blood flow regulated endothelial angiogenesis. Initially, we observed that DSS impaired angiogenesis and downregulated endogenous vascular endothelial growth factor B (VEGFB) expression compared to LSS. We further found that the changes in membrane protein, migration and invasion enhancer 1 (MIEN1) play a role in regulating ERK/MAPK signaling, thereby contributing to endothelial angiogenesis in response to FSS. We also showed the involvement of MIEN1-directed cytoskeleton organization. These findings suggest the significance of shear stress in endothelial angiogenesis, thereby enhancing our understanding of the alterations in angiogenesis that occur during the transition from physiological to pathological blood flow.     

Computational modeling of shear forces and experimental validation of endothelial cell responses in an orbital well shaker system

Vascular endothelial cells are continuously exposed to hemodynamic shear stress. Intensity and type of shear stress are highly relevant to vascular physiology and pathology. Here, we modeled shear stress distribution in a tissue culture well (R = 17.5 mm, fill volume 2 ml) under orbital translation using computational fluid dynamics with the finite element method. Free surface distribution, wall shear stress, inclination angle, drag force, and oscillatory index on the bottom surface were modeled. Obtained results predict nonuniform shear stress distribution during cycle, with higher oscillatory shear index, higher drag force values, higher circular component, and larger inclination angle of the shear stress at the periphery of the well compared with the center of the well. The oscillatory index, inclination angle, and drag force are new quantitative parameters modeled in this system, which provide a better understanding of the hydrodynamic conditions experienced and reflect the pulsatile character of blood flow in vivo. Validation experiments revealed that endothelial cells at the well periphery aligned under flow and increased Kruppel-like Factor 4 (KLF-4), cyclooxygenase-2 (COX-2) expression and endothelial nitric oxide synthase (eNOS) phosphorylation. In contrast, endothelial cells at the center of the well did not show clear directional alignment, did not induce the expression of KLF-4 and COX-2 nor increased eNOS phosphorylation. In conclusion, this improved computational modeling predicts that the orbital shaker model generates different hydrodynamic conditions at the periphery versus the center of the well eliciting divergent endothelial cell responses. The possibility of generating different hydrodynamic conditions in the same well makes this model highly attractive to study responses of distinct regions of the same endothelial monolayer to different types of shear stresses thereby better reflecting in vivo conditions.     

Computational simulations predict a key role for oscillatory fluid shear stress in de novo valvular tissue formation

Previous efforts in heart valve tissue engineering demonstrated that the combined effect of cyclic flexure and steady flow on bone marrow derived stem cell-seeded scaffolds resulted in significant increases in engineered collagen formation [Engelmayr et al. Cyclic flexure and laminar flow synergistically accelerate mesenchymal stem cell-mediated engineered tissue formation: Implications for engineered heart valve tissues. Biomaterials 2006; 27(36): 6083–95]. Here, we provide a new interpretation for the underlying reason for this observed effect. In addition, another related investigation demonstrated the impact of fluid flow on DNA content and quantified the fluid-induced shear stresses on the engineered heart valve tissue specimens [Engelmayr et al. A Novel Flex-Stretch-Flow Bioreactor for the Study of Engineered Heart Valve Tissue Mechanobiology]. Annals of Biomedical Engineering 2008, 36, 1–13]. In this study, we performed more advanced CFD analysis with an emphasis on oscillatory wall shear stresses imparted on specimens when mechanically conditioned by a combination of cyclic flexure and steady flow. Specifically, we hypothesized that the dominant stimulatory regulator of the bone marrow stem cells is fluid-induced and depends on both the magnitude and temporal directionality of surface stresses, i.e., oscillatory shear stresses (OSS) acting on the developing tissues. Therefore, we computationally quantified the (i) magnitude of fluid-induced shear stresses as well as (ii) the extent of temporal fluid oscillations in the flow field using the oscillatory shear index (OSI) parameter. Noting that sample cyclic flexure induces a high degree of OSS, we incorporated moving boundary computational fluid dynamic simulations of samples housed within a bioreactor to consider the effects of: (1) No Flow, No Flexure (control group), (2) Steady Flow-alone, (3) Cyclic Flexure-alone and (4) Combined Steady flow and Cyclic Flexure environments. Indeed we found that the coexistence of both OSS and appreciable shear stress magnitudes explained the high levels of engineered collagen previously observed from combining cyclic flexure and steady flow states. On the other hand, each of these metrics on its own showed no association. This finding suggests that cyclic flexure and steady flow synergistically promote engineered heart valve tissue production via OSS, so long as the oscillations are accompanied by a critical magnitude of shear stress.     

Determining possible thrombus sites in an extracorporeal device,using computational fluid dynamics-derived relative residence time

The prediction of conditions that may result in thrombus formation is a useful application of computational fluid dynamics. A number of techniques exist, based on the consideration of wall shear stress and regions of low blood flow; however, no clear guideline exists for the best practice of their use. In this paper, the sensitivity of each parameter and the specific mechanical forces are explained, before the optimal indicator of thrombosis risk is outlined. An extracorporeal access device cavity provides a suitable geometry to test the methodology. The recommended method for thrombus prediction considers areas with a calculated residence time (RT) and shear strain rate (SSR) thresholds, here set to RT>1 and SSR < 10 s^? 1. Evidence of thrombosis was found for physiological waveforms with an absence of reverse flow, which is expected to ‘wash out’ the cavity. The predicted thrombosis sites compare well with evidence collected from explanted devices.     

Modeling of flow‐induced shear stress applied on 3D cellular scaffolds: Implications for vascular tissue engineering

Novel tissue‐culture bioreactors employ flow‐induced shear stress as a means of mechanical stimulation of cells. We developed a computational fluid dynamics model of the complex three‐dimensional (3D) microstructure of a porous scaffold incubated in a direct perfusion bioreactor. Our model was designed to predict high shear‐stress values within the physiological range of those naturally sensed by vascular cells (1–10 dyne/cm²), and will thereby provide suitable conditions for vascular tissue‐engineering experiments. The model also accounts for cellular growth, which was designed as an added cell layer grown on all scaffold walls. Five model variants were designed, with geometric differences corresponding to cell‐layer thicknesses of 0, 50, 75, 100, and 125 µm. Four inlet velocities (0.5, 1, 1.5, and 2 cm/s) were applied to each model. Wall shear‐stress distribution and overall pressure drop calculations were then used to characterize the relation between flow rate, shear stress, cell‐layer thickness, and pressure drop. The simulations showed that cellular growth within 3D scaffolds exposes cells to elevated shear stress, with considerably increasing average values in correlation to cell growth and inflow velocity. Our results provide in‐depth analysis of the microdynamic environment of cells cultured within 3D environments, and thus provide advanced control over tissue development in vitro. Biotechnol. Bioeng. 2010; 105: 645–654. © 2009 Wiley Periodicals, Inc.     

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.     

Shear-induced intracellular loading of cells with molecules by controlled microfluidics

This study tested the hypothesis that controlled flow through microchannels can cause shear-induced intracellular loading of cells with molecules. The overall goal was to design a simple device to expose cells to fluid shear stress and thereby increase plasma membrane permeability. DU145 prostate cancer cells were exposed to fluid shear stress in the presence of fluorescent cell-impermeant molecules by using a cone-and-plate shearing device or high-velocity flow through microchannels. Using a syringe pump, cell suspensions were flowed through microchannels of 50-300 microm diameter drilled through Mylar sheets using an excimer laser. As quantified by flow cytometry, intracellular uptake and loss of viability correlated with the average shear stress. Optimal results were observed when exposing the cells to high shear stress for short durations in conical channels, which yielded uptake to over one-third of cells while maintaining viability at approximately 80%. This method was capable of loading cells with molecules including calcein (0.62 kDa), large molecule weight dextrans (150-2,000 kDa), and bovine serum albumin (66 kDa). These results supported the hypothesis that shear-induced intracellular uptake could be generated by flow of cell suspensions through microchannels and further led to the design of a simple, inexpensive, and effective device to deliver molecules into cells. Such a device could benefit biological research and the biotechnology industry.     

Design of cellular porous biomaterials for wall shear stress criterion

The microfluidic environment provided by implanted prostheses has a decisive influence on the viability, proliferation and differentiation of cells. In bone tissue engineering, for instance, experiments have confirmed that a certain level of wall shear stress (WSS) is more advantageous to osteoblastic differentiation. This paper proposes a level‐set‐based topology optimization method to regulate fluidic WSS distribution for design of cellular biomaterials. The topological boundary of fluid phase is represented by a level‐set model embedded in a higher‐dimensional scalar function. WSS is determined by the computational fluid dynamics analysis in the scale of cellular base cells. To achieve a uniform WSS distribution at the solid–fluid interface, the difference between local and target WSS is taken as the design criterion, which determines the speed of the boundary evolution in the level‐set model. The examples demonstrate the effectiveness of the presented method and exhibit a considerable potential in the design optimization and fabrication of new prosthetic cellular materials for bioengineering applications. Biotechnol. Bioeng. 2010;107:737–746. © 2010 Wiley Periodicals, Inc.     

The influence of fluid shear stress on the remodeling of the embryonic primary capillary plexus

The primary capillary plexus in early yolk sacs is remodeled into matured vitelline vessels aligned in the direction of blood flow at the onset of cardiac contraction. We hypothesized that the influence of fluid shear stress on cellular behaviors may be an underlying mechanism by which some existing capillary channels remain open while others are closed during remodeling. Using a recently developed E-Tmod knock-out/lacZ knock-in mouse model, we showed that erythroblasts exhibited rheological properties similar to those of a viscous cell suspension. In contrast, the non-erythroblast (NE) cells, which attach among themselves within the yolk sac, are capable of lamellipodia extension and cell migration. Isolated NE cells in a parallel-plate flow chamber exposed to fluid shear stress, however, ceased lamellipodia extension. Such response may minimize NE cell migration into domains exposed to fluid shear stress. A two-dimensional mathematical model incorporating these cellular behaviors demonstrated that shear stress created by the blood flow initiated by the embryonic heart contraction might be needed for the remodeling of primary capillary plexus.     

Response of osteoblasts to low fluid shear stress is time dependent

The process of mechanotransduction of bone, the conversion of a mechanical stimulus into a biochemical response, is known to occur in osteoblasts in response to fluid shear stress. In order to understand the reaction of osteoblasts to various times of flow perfusion, osteoblasts were seeded on three-dimensional scaffolds, and cultured in the following conditions: continuous flow perfusion, intermittent flow perfusion, and static condition. We collected samples on day 4, 8 and 12 for analysis. Osteoblast proliferation was demonstrated by cell proliferation and scanning electron microscopy assay. Additionally, the expression of known markers of differentiation, including alkaline phosphatase and osteocalcin, were tested by qRT-PCR and alkaline phosphatase activity assay, and the deposition of calcium was used as an indicator of mineralization demonstrated by calcium content assay. The results supported that low fluid shear stress plays an important role in the activation of osteoblasts: enhance cell proliferation, increase calcium deposition, and promote the expression of osteoblastic markers. Furthermore, the continuous flow perfusion is a more favorable environment for the initiation of osteoblast activity compared with intermittent flow perfusion. Therefore, the force and time of fluid shear stress are important parameters for osteoblast activation.