Influence of slip-yield stress model on the oscillatory squeeze flow of a viscoelastic fluid confined between two spheres

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.

Recently fluid flow has been shown to be a potent physical stimulus in the regulation of bone cell metabolism. However, most investigators have applied steady or pulsing flow profiles rather than oscillatory fluid flow, which occurs in vivo because of mechanical loading. Here oscillatory fluid flow was demonstrated to be a potentially important physical signal for loading-induced changes in bone cell metabolism. We selected three well known biological response variables including intracellular calcium (Ca(2+)i), mitogen-activated protein kinase (MAPK) activity, and osteopontin (OPN) mRNA levels to examine the response of MC3T3-E1 osteoblastic cells to oscillatory fluid flow with shear stresses ranging from 2 to -2 Newtons/m(2) at 1 Hz, which is in the range expected to occur during routine physical activities. Our results showed that within 1 min, oscillatory flow induced cell Ca(2+)i mobilization, whereas two MAPKs (ERK and p38) were activated over a 2-h time frame. However, there was no activation of JNK. Furthermore 2 h of oscillatory fluid flow increased steady-state OPN mRNA expression levels by approximately 4-fold, 24 h after exposure to fluid flow. The presence of both ERK and p38 inhibitors and thapsigargin completely abolished the effect of oscillatory flow on steady-state OPN mRNA levels. In addition, experiments using a variety of pharmacological agents suggest that oscillatory flow induces Ca(2+)i mobilization via the L-type voltage-operated calcium channel and the inositol 1,4,5-trisphosphate pathway.

It was found that preosteoblast MC3T3-E1 cells were less responsive in calcium signaling than mature osteocyte MLO-Y4 cells when a steady fluid flow was exerted on a micropatterned cell network. However, the effect of fluid flow on the calcium response in preosteocyte MLO-A5 was seldom investigated. In the present study, MLO-A5 as well as MC3T3-E1 and MLO-Y4 cells were cultured on a regular substrate with high or low density under unidirectional or oscillatory fluid flow. The results showed that calcium oscillation in the cells during late osteogenesis was significantly stronger than during early osteogenesis regardless of the fluid flow type or the presence of a physical cell-cell connection. Calcium oscillation produced by the oscillatory flow in the three types of cells was stronger than that produced by the unidirectional flow, but MC3T3-E1 and MLO-A5 cells exhibited limited potential for calcium oscillation compared with MLO-Y4 cells. After suramin was used to block the binding of extracellular adenosine triphosphate (ATP) to the membrane P2 receptor, the calcium oscillation in the three types of bone cells with or without physical connections was significantly suppressed as a single responsive peak under unidirectional flow. For the ATP-blocking group of low-density cells under oscillatory flow, the number of oscillation peaks in three types of cells was still more than two. It indicates that besides the ATP pathway, other mechanosensitive calcium pathways may exist under oscillatory flow. The present study provided further evidence for the osteogenic stage-dependent calcium response of bone cells under unidirectional or oscillatory fluid flow.

Primary Cilia is appendage that extrudes from cell surface into the extracellular matrix .These organelles play a sensor role for mechanical stimulation in the cell and due to stretch ion channels in its base, play critical role in induce osteogenic differentiation of stem cells. Primary cilia deflected under fluid flow passing through the surface of the cell, which deflection causes tensile ion channels to be opened. In this study, cilia is assumed as linear elastic. The innovative aspect of this research is exerting of oscillatory fluid flow to the primary cilia and evaluating the response of cilia to the fluid flow. The results show that under conditions of exerting the oscillatory fluid flow, maximum strain occur in the base of the cilia which is experienced by tensile ion channels, is 0.5 and in the condition of steady flow is 0.3, Accordingly, mechanical stimuli are sensed by the tensile ionic channels during oscillatory flow higher than steady flow. osteogenic differentiation of stem cells, in addition, the result showed that by using the oscillatory fluid flow the mechanical stimulation better senses by cilia and It is anticipated that exerting oscillatory fluid flow facilitate osteogenic differentiation of stem cell.

We investigate the Taylor-Aris dispersion resulting from oscillatory squeeze flow (OSF) of an Oldroyd-B viscoelastic fluid in the gap between two hydrophobic disks. The slippage between the fluid and the surfaces of both disks is modeled using a dynamic slip boundary condition, which accounts for periodic motion and the fluid's rheological properties. The fluid motion is induced by the periodic vertical movement of one of the disks. Using the lubrication approximation, we simplify and solve the governing equationsto determine the flow field. We then derive key variables, including the velocity field, pressure distribution, and the force and power associated with OSF. To analyze mass transport, we used the convection-diffusion equation, which we solved using the multiple-timescale homogenization method. This study highlights the influence of various dimensionless parameters that govern hydrodynamics and Taylor dispersion, specifically the Womersley number, two Deborah numbers related to the fluid's relaxation and retardation times, and a slip parameter. Our research focuses on how the slip boundary condition and the fluid's rheology affect the dispersion process and other related variables. A key aspect of our work is to identify conditions that maximize the effective dispersion coefficient under the given assumptions. Our findings indicate that the slip condition generally reduces the dispersion coefficient in an OSF. Furthermore, when comparing the effect on the effective dispersion coefficient using the Oldroyd-B and Maxwell models, we observe that the Maxwell model tends to overestimate the effective dispersion coefficient.

Calcium response in osteocytic networks under steady and oscillatory fluid flow

Oscillatory fluid flow-induced shear stress decreases osteoclastogenesis through RANKL and OPG signaling

We previously found that oscillatory fluid flow activated MC3T3-E1 osteoblastic cell Ca(2+)(i) mobilization via the inositol 1,4,5-trisphosphate pathway in the presence of 2% fetal bovine serum (FBS). However, the molecular mechanism of fluid flow-induced Ca(2+)(i) mobilization is unknown. In this study, we first demonstrated that oscillatory fluid flow in the absence of FBS failed to increase [Ca(2+)](i) in MC3T3-E1 cells. Apyrase (10 units/ml), which rapidly hydrolyzes 5' nucleotide triphosphates to monosphophates, prevented the fluid flow induced increases in [Ca(2+)](i) in the presence of FBS. Adding ATP or UTP to flow medium without FBS restored the ability of fluid flow to increase [Ca(2+)](i), suggesting that ATP or UTP may mediate the effect of fluid flow on [Ca(2+)](i). Furthermore, adenosine, ADP, UDP, or adenosine 5'-O-(3-thiotriphosphate) did not induce Ca(2+)(i) mobilization under oscillatory fluid flow without FBS. Pyridoxal phosphate 6-azophenyl-2,4'-disulfonic acid, an antagonist of P2X purinoceptors, did not alter the effect of fluid flow on the Ca(2+)(i) response, whereas pertussis toxin, a G(i/o)-protein inhibitor, inhibited fluid flow-induced increases in [Ca(2+)](i) in the presence of 2% FBS. Thus, by the process of elimination, our data suggest that P2Y purinoceptors (P2Y2 or P2Y4) are involved in the Ca(2+)(i) response to fluid flow. Finally, a decreased percentage of MC3T3-E1 osteoblastic cells treated with P2Y2 antisense oligodeoxynucleotides responded to fluid flow with an increase in [Ca(2+)](i), and an increased percentage of ROS 17/2.8 cells, which do not normally express P2Y2 purinoceptors, transfected with P2Y2 purinoceptors responded to fluid flow in the presence of 2% FBS, confirming that P2Y2 purinoceptors are responsible for oscillatory fluid flow-induced Ca(2+)(i) mobilization. Our findings shed new light of the molecular mechanisms responsible for oscillatory fluid flow-induced Ca(2+)(i) mobilization in osteoblastic cells.

Flow-Induced DNA Synthesis Requires Signaling to a Translational Control Pathway

Fluid flow-induced prostaglandin E 2 response of osteoblastic ROS 17/2.8 cells is gap junction-mediated and independent of cytosolic calcium

Oscillatory fluid flow induced the vesicular release of ATP from human BMSCs that directly contributes to the induction of BMSC proliferation. Degrading extracellular nucleotides prevents fluid flow-induced increases in intracellular calcium concentration, the activation of calcineurin, and the nuclear translocation of NFAT. Regulation of bone cell activity by autocrine/paracrine factors is a well-established mechanism by which skeletal homeostasis is regulated by mechanical signals. The release of extracellular nucleotides in particular has been shown to induce many of the responses thought to be necessary for load-induced bone formation. In these studies, we examined the effect of oscillatory fluid flow on the release of ATP from bone marrow stromal cells (BMSCs) and the effect of ATP release on BMSC proliferation and intracellular calcium signaling pathways. BMSCs were exposed to oscillatory fluid flow, and the concentration of ATP in conditioned media samples was determined using a luciferin:luciferase-based reaction. Western blot analysis was used to examine the expression of purinergic receptors. Using pharmacological antagonists of gap junction hemichannels and vesicular trafficking, we studied the mechanism of ATP release from BMSCs. Apyrase was used to study the effect of extracellular nucleotides on intracellular calcium concentration, calcineurin activity, and nuclear factor of activated T cells (NFAT) nuclear translocation. Fluid flow exposure induced the flow rate-dependent release of ATP from BMSCs that was attenuated by treatment with monensin and N-ethylmaleimide, suggesting a vesicular mechanism. Treating BMSCs with ATP, but not other nucleotides, increased cellular proliferation. Moreover, extracellular ATP was a prerequisite for fluid flow-induced increases in intracellular calcium concentration, activation of calcineurin, the nuclear translocation of NFATc1, and proliferation. These data indicate that ATP regulates not only osteoblastic and osteocytic cell behavior but also that of mesenchymal precursors and support our hypothesis that similar mechanotransduction mechanisms are activated by fluid flow in these cell types.

Oscillating fluid flow regulates cytosolic calcium concentration in bovine articular chondrocytes

Fluid flow plays an important role in load-induced bone remodeling. However, the molecular mechanism of flow-induced signal transduction in osteoblasts remains unclear. In endothelial cells, fluid flow alters activation of NF-kappaB resulting in changes in expression of cell adhesion molecules. To test the hypothesis that fluid flow alters NF-kappaB activation and expression of cell adhesion molecules in osteoblastic cells, we examined the effect of oscillating fluid flow (OFF) on tumor necrosis factor (TNF)-alpha-induced NF-kappaB activation in rat osteoblast-like UMR106 cells. We found that OFF inhibits NF-kappaB-DNA binding activities, especially TNF-alpha-induced p50-p65 heterodimer NF-kappaB activation and TNF-alpha-induced intercellular adhesion molecule-1 mRNA expression. The inhibitory effects of OFF on both TNF-alpha-induced NF-kappaB activation and intercellular adhesion molecule-1 mRNA expression were shear stress-dependent and also increased with OFF exposure duration, indicating that OFF has potent effects on mechanotransduction pathways. OFF also inhibited TNF-alpha-induced IkappaBalpha degradation and TNF-alpha-induced IkappaB kinase (IKK) activity in a shear stress-dependent manner. These results demonstrate that IKK is an initial target molecule for OFF effects on osteoblastic cells. Thus, OFF inhibits TNF-alpha-induced IKK activation, leading to a decrease in phosphorylation and degradation of inhibitory IkappaBalpha, which in turn results in the decrease of TNF-alpha-induced NF-kappaB activation and potentially the transcription of target genes.

An analysis has been carried out to obtain the effect of the non-Newtonian parameter on the problem of magnetohydrodynamic (MHD) mixed convective oscillat- ory flow of an electrically conducting optically thin viscoelastic fluid through a planer channel filled with saturated porous medium in the presence of a first-order chemical reaction. The effect of buoyancy, heat source, thermal radiation, and chemical reaction are taken into account embedded with slip boundary condition, varying temperature and concentration. The closed form analytical solutions are constructed for the prob- lem. The effects of the magnetic field, porous parameter, solutal and thermal Grashof numbers on velocity profile for different values of the non-Newtonian parameter are illustrated with the help of figures. A table containing the numerical data for skin friction is also provided. Keywords : viscoelastic fluid; chemical reaction; MHD; oscillatory flow. 2010 Mathematics Subject Classification 76A10; 76W05.

We investigated the nonlinear and nonsymmetric responses of viscoelastic fluids under large amplitude oscillatory squeeze (LAOSQ) flow. The nonlinear and nonsymmetric stress response is a unique feature of oscillatory squeeze (OSQ) flow under larger deformation, but has rarely been investigated. The goal of this study is to systematically characterize the responses of viscoelastic fluids at larger deformation under oscillatory squeeze flow and to provide a platform for the analysis of nonsymmetric stress signals. We report a framework for the analysis of nonlinear-and-nonsymmetric stress signals at larger strain amplitude under oscillatory squeeze flow. The storage and loss modulus showed strain thinning behavior as the strain amplitude increases in both oscillatory shear and oscillatory squeeze flow. However the normal stress under LAOSQ was found to be nonsymmetric in both magnitude and shape unlike the shear stress under oscillatory shear flow. In addition the energy dissipation was found to be larger in extension than in compression. This study is expected to provide a platform to understand the nonlinear and nonsymmetric characteristics of complex fluids under LAOSQ flow.