A new view of mechanotransduction and strain amplification in cells with microvilli and cell processes

In this paper we shall describe new mechanical models for the deformation of the actin filament bundles in kidney microvilli and osteocytic cell processes to see whether these cellular extensions, like the stereocilia on hair cells in the inner ear, can function as mechanotransducers when subject to physiological flow. In the case of kidney microvilli we show that the hydrodynamic drag forces at the microvilli tip are <0.01 pN, but there is a 38-fold force amplification on the actin filaments at the base of the microvilli due to the resisting moment in its terminal web. This leads to forces that are more than sufficient to deform the terminal web complex of the microvillus where ezrin has been shown to couple the actin cytoskeleton to the Na(+)/H(+) exchanger. In the case of bone cell processes we show that the actin filament bundles have an effective Young's modulus that is 200 times > the measured modulus for the actin gel in the cell body. It is, therefore, unlikely that bone cell processes respond in vivo to fluid shear stress, as proposed in [59]. However, we show that the fluid drag forces on the pericellular matrix which tethers the cell processes to the canalicular wall can produce a 20-100 fold amplification of bone tissue strains in the actin filament bundle of the cell process.     

Effects of short-term recovery periods on fluid-induced signaling in osteoblastic cells

It is well known that cyclic mechanical loading can produce an anabolic response in bone. In vivo studies have shown that the insertion of short-term recovery periods (10-15 s) into mechanical loading profiles led to an increased osteogenic response compared to continuous cyclic loading of bone. Although this is suggestive of temporal processing at the bone cell level, there is little evidence to support such a hypothesis. Therefore, the current study investigated the cellular mechanism of bone's response to rest inserted vs. continuous mechanical loading. Cell responses to rest inserted mechanical loading were quantified by applying oscillatory fluid flow (OFF) to osteoblastic cells and quantifying real-time intracellular calcium [Ca2+]i, prostaglandin E2 (PGE2) release, and osteopontin (OPN) mRNA levels. Cells were exposed to OFF (1 Hz) at shear stresses of 1 and 2 Pa with rest periods of 5, 10, and 15s inserted every 10 loading cycles. The insertion of 10 and 15s rest periods into the flow profile resulted in multiple [Ca2+]i responses by individual cells, increased [Ca2+]i response magnitudes, and increased overall percent of cells responding compared to continuously loaded control groups. We determined the source of the multiple calcium responses to be from intracellular stores. In addition, rest inserted OFF led to similar levels of PGE2 release and increased levels of relative OPN mRNA compared to cells exposed to continuous OFF. Our study suggests that the cellular mechanism of bone adaptation to rest inserted mechanical loading may involve modulation of intracellular levels of calcium (frequency, magnitude, percent of cells responding).     

Correlation of cell strain in single osteocytes with intracellular calcium,but not intracellular nitric oxide,in response to fluid flow

Osteocytes compose 90–95% of all bone cells and are the mechanosensors of bone. In this study, the strain experienced by individual osteocytes resulting from an applied fluid flow shear stress was quantified and correlated to two biological responses measured in real-time within the same individual osteocytes: (1) the upregulation of intracellular calcium and (2) changes in intracellular nitric oxide. Osteocyte-like MLO-Y4 cells were loaded with Fluo-4 AM and DAR-4M and exposed to uniform laminar fluid flow shear stresses of 2, 8, or 16 dyn/cm². Intracellular calcium and nitric oxide changes were determined by measuring the difference in fluorescence intensity from the cell’s basal level prior to fluid flow and the level immediately following exposure. Individual cell strains were calculated using digital image correlation. MLO-Y4 cells showed a linear increase in cell strain, intracellular calcium concentration, and nitric oxide concentration with an increase in applied fluid flow rate. The increase in intracellular calcium was well correlated to the strain that each cell experienced. This study shows that osteocytes exposed to the same fluid flow experienced a range of individual strains and changes in intracellular calcium and nitric oxide concentrations, and the changes in intracellular calcium were correlated with cell strain. These results are among the first to establish a relationship between the strain experienced by osteocytes in response to fluid flow shear and a biological response at the single cell level. Mechanosensing and chemical signaling in osteocytes has been hypothesized to occur at the single cell level, making it imperative to understand the biological response of the individual cell.     

Microstructural strain near osteocyte lacuna in cortical bone in vitro

Mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Two proposed mechanical signals are stress-generated fluid flow forces acting on cells and bone matrix deformation itself. A prominent current theory is that bone cells are more responsive to fluid flow than to mechanical strain. Recent experiments support this conclusion: bone cells increase their production of osteopontin (OPN) mRNA, prostaglandin (PGE(2)), and nitric oxide (NO) in response to fluid flow in contrast to cells stimulated by mechanical strain levels similar to those measured in vivo. However, when cells are subjected to substrate strains levels many times greater than those measured in vivo, increased biological activity again results. We assert that it is neither fluid flow nor matrix deformation per se, but rather the resulting cell deformation that causes cell biological response. Machined specimens of undamaged bovine cortical bone were subjected to increasing levels of macroscopic strain while observed under an optical microscope at 220X. Continuum level strain was measured using a standard foil strain gauge attached to the back of the specimen and ranged from 500 to 6,000 microstrain. Images of the specimen surface at each strain level were captured. To determine the level of osteocyte deformation that results from fluid flow in vitro, MLO-Y4 cells were cultured on collagen coated 190 cm2 plastic sheets and subjected to steady fluid flow at 16 dynes/cm(2). Images representing the initial undisturbed cell configuration and the configuration of the cells after ten minutes of fluid flow were acquired from a videotape of the flow experiment. The captured unloaded vs. loaded image pairs were analyzed to determine the local deformation and strain fields using a digital stereoimaging system. When subjected to a nominal continuum strain level approximately equal to that measured in humans in vivo during rigorous activity (2,000 microstrain), the local, osteocyte level strains can be as high as 12,000 to 15,000 microstrain (1.2% to 1.5%). Average osteocyte strains due to fluid flow in vitro increase from 7,972 microstrains after 16 seconds of flow to 22,856 microstrains after 64 seconds of flow. In contrast, maximum strains measured in vivo are approximately 1,800 microstrain in humans and up to 3,000 microstrain in other species. These data may help to explain why bone cells are more sensitive to fluid flow than substrate strain; fluid forces result in cell deformations much higher than those considered to be "physiological".     

Analysis of avian bone response to mechanical loading, Part Two: Development of a computational connected cellular network to study bone intercellular communication

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by connected bone cells before reaching the bone surfaces where adaptation occurs. A computational connected cellular network (CCCN) model is developed to explore how bone cells perceive and transmit the signals through intercellular communication. This is part two of a two-part study in which a CCCN is developed to study the intercellular communication within a grid of bone cells. The excitation signal was computed as the loading-induced bone fluid shear stress in part one. Experimentally determined bone adaptation responses (Gross et al. in J Bone Miner Res 12:982-988, 1997 and Judex et al. in J Bone Miner Res 12:1737-1745, 1997) are correlated with the fluid shear stress by the CCCN, which adjusts cell sensitivities (loading and signal thresholds) and connection weights. Intercellular communication patterns extracted by the CCCN indicate the cell population responsible for perceiving the loading-induced signal, and loading threshold is shown to play an important role in regulating the bone response.     

Microrheology of human lung epithelial cells measured by atomic force microscopy

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.     

Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Nonlinear behavior of trabecular bone at small strains

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.     

Inelastic strain accumulation in cortical bone during rapid transient tensile loading

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of +/- 420 MPa/s. Loads were reversed at pre selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.     

Different responsiveness of cells from adult and neonatal mouse bone to mechanical and biochemical challenge

Neonatal rodent calvarial bone cell cultures are often used to study bone cell responsiveness to biochemical and mechanical signals. However, mechanical strains in the skull are low compared to the axial and appendicular skeleton, while neonatal, rapidly growing bone has a more immature cell composition than adult bone. In the present study, we tested the hypothesis that bone cell cultures from neonatal and adult mouse calvariae, as well as adult mouse long bones, respond similarly to treatment with mechanical stress or 1,25-dihydroxyvitamin D3 (1,25(OH)2 D3). Treatment with pulsating fluid shear stress (0.6 +/- 0.3 Pa, 5 Hz) caused a rapid (within 5 min) 2-4-fold increase in NO production in all cases, without significant differences between the three cell preparations. However, basal NO release was significantly higher in neonatal calvarial cells than adult calvarial and long bone cells. The response to 1,25(OH)2 D3), measured as increased alkaline phosphatase activity, was about three times higher in the neonatal cells than the adult cell cultures. We conclude that all three types of primary bone cell cultures responded similarly to fluid shear stress, by rapid production of NO. However, the neonatal cell cultures were different in basal metabolism and vitamin D3 responsiveness, suggesting that cell cultures from adult bone are best used for in vitro studies on bone cell biology.     

Mechanosensation and fluid transport in living bone

The mechanosensory mechanisms in bone include (i) the cell system that is stimulated by external mechanical loading applied to the bone; (ii) the system that transduces that mechanical loading to a communicable signal; and (iii) the systems that transmit that signal to the effector cells for the maintenance of bone homeostasis and for strain adaptation of the bone structure. The effector cells are the osteoblasts and the osteoclasts. These systems and the mechanisms that they employ have not yet been unambiguously identified. The candidate systems will be reviewed. It will be argued that the current theoretical and experimental evidence suggests that osteocytes are the principal mechanosensory cells of bone, that they are activated by shear stress from fluid flowing through the osteocyte canaliculi, and that the electrically coupled three-dimensional network of osteocytes and lining cells is a communications system for the control of bone homeostasis and structural strain adaptation. The movement of bone fluid from the region of the bone vasculature through the canaliculi and the lacunae of the surrounding mineralized tissue accomplishes three important tasks. First, it transports nutrients to the osteocytes in the lacunae buried in the mineralized matrix. Second, it carries away the cell waste. Third, the bone fluid exerts a force on the cell process, a force that is large enough for the cell to sense. This is probably the basic mechanotransduction mechanism in bone, the way in which bone senses the mechanical load to which it is subjected. The mechanisms of bone fluid flow are described with particular emphasis on mechanotransduction. Also described is the cell to cell communication by which higher frequency signals might be transferred, a potential mechanism in bone by which the small whole tissue strain is amplified so the bone cells can respond to it. One of the conclusions is that higher frequency low amplitude strains can maintain bone as effectively as low frequency high amplitude strains. This conclusion leads to a paradigm shift in how to treat osteoporosis and how to cope with microgravity.     

The modified super-ellipsoid yield criterion for human trabecular bone

Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micromechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through microcomputed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error +/-SD less than -0.04 +/- 5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error +/- SD < 2.5 +/- 6.5%). We conclude that the four-parameter "Modified Super-Ellipsoid" yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.     

Simulated and experimental estimates of hydrodynamic drag from bio-logging tags

Drag force acting on swimming marine mammals is difficult to measure directly. Researchers often use simple modeling and kinematic measurements from animals, or computational fluid dynamics (CFD) simulations to estimate drag. However, studies that compare these methods are lacking. Here, computational simulation and physical experiments were used to estimate drag forces on gliding bottlenose dolphins (Tursiops truncatus). To facilitate comparison, variable drag loading (no-tag, tag, tag + 4, tag + 8) was used to increase force in both simulations and experiments. During the experiments, two dolphins were trained to perform controlled glides with variable loading. CFD simulations of dolphin/tag geometry in steady flow (1–6 m/s) were used to model drag forces. We expect both techniques will capture relative changes created by experimental conditions, but absolute forces predicted by the methods will differ. CFD estimates were within a calculated 90% confidence interval of the experimental results for all but the tag condition. Relative drag increase predicted by the simulation vs. experiment, respectively, differed by between 21% and 31%: tag, 4% vs. 33%; tag + 4, 47% vs. 68%; and tag + 8, 108% vs. 77%. The results from this work provide a direct comparison of computational and experimental estimates of drag, and provide a framework to quantify uncertainty.     

In vivo bone strain and bone functional adaptation

Mechanistic interpretations of bone cross-sectional shapes are based on the paradigm of shape optimization such that bone offers maximum mechanical resistance with a minimum of material. Recent in vivo strain studies (Demes et al., Am J Phys Anthropol 106 (1998) 87-100, Am J Phys Anthropol 116 (2001) 257-265; Lieberman et al., Am J Phys Anthropol 123 (2004) 156-171) have questioned these interpretations by demonstrating that long bones diaphyses are not necessarily bent in planes in which they offer maximum resistance to bending. Potential limitations of these in vivo studies have been pointed out by Ruff et al. (Am J Phys Anthropol 129 (2006) 484-498). It is demonstrated here that two loading scenarios, asymmetric bending and buckling, would indeed not lead to correct predictions of loads from strain. It is also shown that buckling is of limited relevance for many primate long bones. This challenges a widely held view that circular bone cross sections make loading directions unpredictable for bones which is based on a buckling load model. Asymmetric bending is a potentially confounding factor for bones with directional differences in principal area moments (I(max) > I(min)). Mathematical corrections are available and should be applied to determine the bending axis in such cases. It is concluded that loads can be reliably extrapolated from strains. More strain studies are needed to improve our understanding of the relationships between activities, bone loading regimes associated with them, and the cross-sectional geometry of bones.     

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.     

Micromechanically based poroelastic modeling of fluid flow in Haversian bone

To explore the hypothesis that load-induced fluid flow in bone is a mechano-transduction mechanism in bone adaptation, unit cell micro-mechanical techniques are used to relate the microstructure of Haversian cortical bone to its effective poroelastic properties. Computational poroelastic models are then applied to compute in vitro Haversian fluid flows in a prismatic specimen of cortical bone during harmonic bending excitations over the frequency range of 10(0) to 10(6) Hz. At each frequency considered, the steady state harmonic response of the poroelastic bone specimen is computed using complex frequency-domain finite element analysis. At the higher frequencies considered, the breakdown of Poisueille flow in Haversian canals is modeled by introduction of a complex fluid viscosity. Peak bone fluid pressures are found to increase linearly with loading frequency in proportion to peak bone stress up to frequencies of approximately 10 kHz. Haversian fluid shear stresses are found to increase linearly with excitation frequency and loading magnitude up until the breakdown of Poisueille flow. Tan delta values associated with the energy dissipated by load-induced fluid flow are also compared with values measured experimentally in a concurrent broadband spectral analysis of bone. The computational models indicate that fluid shear stresses and fluid pressures in the Haversian system could, under physiologically realistic loading, easily reach the level of a few Pascals, which have been shown in other works to elicit cell responses in vitro.     

Bone strain magnitude is correlated with bone strain rate in tetrapods: implications for models of mechanotransduction

Hypotheses suggest that structural integrity of vertebrate bones is maintained by controlling bone strain magnitude via adaptive modelling in response to mechanical stimuli. Increased tissue-level strain magnitude and rate have both been identified as potent stimuli leading to increased bone formation. Mechanotransduction models hypothesize that osteocytes sense bone deformation by detecting fluid flow-induced drag in the bone''s lacunar–canalicular porosity. This model suggests that the osteocyte''s intracellular response depends on fluid-flow rate, a product of bone strain rate and gradient, but does not provide a mechanism for detection of strain magnitude. Such a mechanism is necessary for bone modelling to adapt to loads, because strain magnitude is an important determinant of skeletal fracture. Using strain gauge data from the limb bones of amphibians, reptiles, birds and mammals, we identified strong correlations between strain rate and magnitude across clades employing diverse locomotor styles and degrees of rhythmicity. The breadth of our sample suggests that this pattern is likely to be a common feature of tetrapod bone loading. Moreover, finding that bone strain magnitude is encoded in strain rate at the tissue level is consistent with the hypothesis that it might be encoded in fluid-flow rate at the cellular level, facilitating bone adaptation via mechanotransduction.     

Membrane-based actuation for high-speed single molecule force spectroscopy studies using AFM

Atomic force microscopy (AFM)-based dynamic force spectroscopy of single molecular interactions involves characterizing unbinding/unfolding force distributions over a range of pulling speeds. Owing to their size and stiffness, AFM cantilevers are adversely affected by hydrodynamic forces, especially at pulling speeds >10 μm/s, when the viscous drag becomes comparable to the unbinding/unfolding forces. To circumvent these adverse effects, we have fabricated polymer-based membranes capable of actuating commercial AFM cantilevers at speeds ≥100 μm/s with minimal viscous drag effects. We have used FLUENT^®, a computational fluid dynamics (CFD) software, to simulate high-speed pulling and fast actuation of AFM cantilevers and membranes in different experimental configurations. The simulation results support the experimental findings on a variety of commercial AFM cantilevers and predict significant reduction in drag forces when membrane actuators are used. Unbinding force experiments involving human antibodies using these membranes demonstrate that it is possible to achieve bond loading rates ≥10⁶ pN/s, an order of magnitude greater than that reported with commercial AFM cantilevers and systems.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Nitric oxide production by bone cells is fluid shear stress rate dependent

Shear stress due to mechanical loading-induced flow of interstitial fluid through the lacuno-canalicular network is a likely signal for bone cell adaptive responses. Moreover, the rate (determined by frequency and magnitude) of mechanical loading determines the amount of bone formation. Whether the bone cells' response to fluid shear stress is rate dependent is unknown. Here we investigated whether bone cell activation by fluid shear stress is rate dependent. MC3T3-E1 osteoblastic cells were subjected for 15 min to fluid shear stress of varying frequencies and amplitudes, resulting in peak fluid shear stress rates ranging from 0 to 39.6 Pa-Hz. Nitric oxide production, a parameter for bone cell activation, was found to be linearly dependent on the fluid shear stress rate; the slope was steepest at 5 min (0.11 Pa-Hz(-1)) and decreased to 0.03 Pa-Hz(-1) at 15 min. We conclude that the fluid shear stress rate is an important parameter for bone cell activation.