Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions.

We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation-dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible - an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.

A hybrid approach for the simulation of a nearly neutrally buoyant nanoparticle thermal motion in an incompressible Newtonian fluid medium.

A hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed in simulating the thermal motion of the particle suspended in the fluid contained in a cylindrical vessel. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery.

Temporal Multiscale Approach for Nanocarrier Motion with Simultaneous Adhesion and Hydrodynamic Interactions in Targeted Drug Delivery.

We present a fluctuating hydrodynamics approach and a hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics to resolve the motion of a nanocarrier when subject to both hydrodynamic interactions and adhesive interactions. Specifically, using these approaches, we compute equilibrium probability distributions at constant temperature as well as velocity autocorrelation functions of the nanocarrier subject to thermal motion in a quiescent Newtonian fluid medium, when tethered by a harmonic spring force mimicking a tether due to a single receptor-ligand bond. We demonstrate that the thermal equipartition of translation, rotation, and spring degrees of freedom are preserved by our formalism while simultaneously resolving the nature of the hydrodynamic correlations. Additionally, we evaluate the potential of mean force (or free energy density) along a specified reaction coordinate to faciltate extensive conformational sampling of the nanocarrier motion. We show that our results are in excellent agreement with analytical results and Monte Carlo simulations, thereby validating our methodologies. The frameworks we have presented provide a comprehensive platform for temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion in vascular targeted drug delivery.

A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium.

A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor-ligand interactions) at the vessel wall at a specified finite temperature.

MODELING OF A NANOPARTICLE MOTION IN A NEWTONIAN FLUID: A COMPARISON BETWEEN FLUCTUATING HYDRODYNAMICS AND GENERALIZED LANGEVIN PROCEDURES.

A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered.

Nanocarrier-Cell Surface Adhesive and Hydrodynamic Interactions: Ligand-Receptor Bond Sensitivity Study.

A hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics is employed to study the motion of a neutrally buoyant nanocarrier in an incompressible Newtonian stationary fluid medium. Both hydrodynamic interactions and adhesive interactions are included, as are different receptor-ligand bond constants relevant to medical applications. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed for the simulation. The flow around the particle and its motion are fully resolved. The temperatures of the particle associated with the various degrees of freedom satisfy the equipartition theorem. The potential of mean force (or free energy density) along a specified reaction coordinate for the harmonic (spring) interactions between the antibody and antigen is evaluated for two different bond constants. The numerical evaluations show excellent comparison with analytical results. This temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion has important implications for designing nanocarriers for vascular targeted drug delivery.

Fluctuating Hydrodynamics Approach for the Simulation of Nanoparticle Brownian Motion in a Newtonian Fluid.

The Brownian motion of a nanoparticle in an incompressible Newtonian fluid (quiescent or fully developed Poiseuille flow) has been investigated with an arbitrary Lagrangian-Eulerian based finite element method. Results for the motion in a compressible fluid medium are estimated. Thermal fluctuations from the fluid are implemented using a fluctuating hydrodynamics approach. The instantaneous flow around the particle and the particle motion are fully resolved. Carriers of two different sizes with three different densities have been investigated (nearly neutrally buoyant). The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively. Larger the particle, longer the time taken to attain this limit; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available.

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields.

We consider the Brownian motion of a nanoparticle in an incompressible Newtonian fluid medium (quiescent or fully developed Poiseuille flow) with the fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion and the hydrodynamic interactions are important. The flow results have been modified to account for compressibility effects. Different nanoparticle sizes and nearly neutrally buoyant particle densities are also considered. Tracked particles are initially located at various distances from the bounding wall to delineate wall effects. The results for thermal equilibrium are validated by comparing the predictions for the temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical and experimental results where available. The equipartition theorem for a Brownian particle in Poiseuille flow is verified for a range of low Reynolds numbers. Numerical predictions of wall interactions with the particle in terms of particle diffusivities are consistent with results, where available.

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise.

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

Surfactant properties differentially influence intravascular gas embolism mechanics.

Gas bubble motion in a blood vessel causes temporal and spatial gradients of shear stress at the cell surface lining the vessel wall as the bubble approaches the cell, moves over it and passes it by. Rapid reversals occur in the sign of the shear stress imparted to the cell surface during this motion. These may result in injury to the cell. The presence of a soluble surfactant in the bulk medium reduces the level of the shear stress gradients imparted to the cell surface as compared to an equivalent surfactant-free system and is an important therapeutic aid. This is particularly true for a very small vessel. In this study, we analyze various physical and chemical properties of any given soluble surfactant to ascertain the relative significance of the property of the surfactant on the reduction in the level of the shear stress gradients imparted to the cell surface in such a vessel. While adsorption, desorption, and maximum possible monolayer interface surfactant concentration significantly impact the shear stress levels, physical properties such as the bulk or surface diffusivity do not appear to have large effects. At a given diameter, surfactants with k(a)/(k(d)d>O(10)⁻5 and Γ(∞)/C(0)d>9.5 x 10⁻4 are noted to be preferable from the point of view of an increased gap size between the bubble and vessel wall, and a corresponding reduction in the shear stress level imparted to an endothelial cell. The shear stress characteristics of nearly occluding bubbles, in contrast with smaller sized bubbles under identical conditions, are most affected by the introduction of a surfactant in regard to shear stress levels. These observations could form a basis for choosing surfactants in treating gas embolism related illnesses.

Effect of a soluble surfactant on a finite sized bubble motion in a blood vessel.

We present detailed results for the motion of a finite sized gas bubble in a blood vessel. The bubble (dispersed phase) size is taken to be such as to nearly occlude the vessel. The bulk medium is treated as a shear thinning Casson fluid and contains a soluble surfactant that adsorbs and desorbs from the interface. Three different vessel sizes, corresponding to a small artery, a large arteriole, and a small arteriole, in normal humans, are considered. The hematocrit (volume fraction of RBCs) has been taken to be 0.45. For arteriolar flow, where relevant, the Fahraeus-Lindqvist effect is taken into account. Bubble motion cause temporal and spatial gradients of shear stress at the cell surface lining the vessel wall as the bubble approaches the cell, moves over it and passes it by. Rapid reversals occur in the sign of the shear stress imparted to the cell surface during this motion. Shear stress gradients together with sign reversals are associated with a recirculation vortex at the rear of the moving bubble. The presence of the surfactant reduces the level of the shear stress gradients imparted to the cell surface as compared to an equivalent surfactant-free system. Our numerical results for bubble shapes and wall shear stresses may help explain phenomena observed in experimental studies related to gas embolism, a significant problem in cardiac surgery and decompression sickness.

Bubble motion in a blood vessel: shear stress induced endothelial cell injury.

Mechanisms governing endothelial cell (EC) injury during arterial gas embolism have been investigated. Such mechanisms involve multiple scales. We have numerically investigated the macroscale flow dynamics due to the motion of a nearly occluding finite-sized air bubble in blood vessels of various sizes. Non-Newtonian behavior due to both the shear-thinning rheology of the blood and the Fahraeus-Lindqvist effect has been considered. The occluding bubble dynamics lends itself for an axisymmetric treatment. The numerical solutions have revealed several hydrodynamic features in the vicinity of the bubble. Large temporal and spatial shear stress gradients occur on the EC surface. The stress variations manifest in the form of a traveling wave. The gradients are accompanied by rapid sign changes. These features are ascribable to the development of a region of recirculation (vortex ring) in the proximity of the bubble. The shear stress gradients together with sign reversals may partially act as potential causes in the disruption of endothelial cell membrane integrity and functionality.

Bubble motion through a generalized power-law fluid flowing in a vertical tube.

Intravascular gas embolism may occur with decompression in space flight, as well as during cardiac and vascular surgery. Intravascular bubbles may be deposited into any end organ, such as the heart or the brain. Surface interactions between the bubble and the endothelial cells lining the vasculature result in serious impairment of blood flow and can lead to heart attack, stroke, or even death. To develop effective therapeutic strategies, there is a need for understanding the dynamics of bubble motion through blood and its interaction with the vessel wall through which it moves. Toward this goal, we numerically investigate the axisymmetric motion of a bubble moving through a vertical circular tube in a shear-thinning generalized power-law fluid, using a front-tracking method. The formulation is characterized by the inlet Reynolds number, capillary number, Weber number, and Froude number. The flow dynamics and the associated wall shear stresses are documented for a combination of two different inlet flow conditions (inlet Reynolds numbers) and three different effective bubble radii (ratio of the undeformed bubble radii to the tube radii). The results of the non-Newtonian model are then compared with that of the model assuming a Newtonian blood viscosity. Specifically, for an almost occluding bubble (effective bubble radius = 0.9), the wall shear stress and the bubble residence time are compared for both Newtonian and non-Newtonian cases. Results show that at low shear rates, for a given pressure gradient the residence time for a non-Newtonian flow is higher than that for a Newtonian flow.

The effect of simulated microgravity on osteoblasts is independent of the induction of apoptosis.

Bone loss during spaceflight has been attributed, in part, to a reduction in osteoblast number, altered gene expression, and an increase in cell death. To test the hypothesis that microgravity induces osteoblast apoptosis and suppresses the mature phenotype, we created a novel system to simulate spaceflight microgravity combining control and experimental cells within the same in vitro environment. Cells were encapsulated into two types of alginate carriers: non-rotationally stabilized (simulated microgravity) and rotationally stabilized (normal gravity). Using these specialized carriers, we were able to culture MC3T3-E1 osteoblast-like cells for 1-14 days in simulated microgravity and normal gravity in the same rotating wall vessel (RWV). The viability of cells was not affected by simulated microgravity, nor was the reductive reserve. To determine if simulated microgravity sensitized the osteoblasts to apoptogens, cells were challenged with staurosporine or sodium nitroprusside and the cell death was measured. Simulated microgravity did not alter the sensitivity of C3H10T-1/2 stem cells, MC3T3-E1 osteoblast-like cells, or MLO-A5 osteocyte-like cells to the action of these agents. RT-PCR analysis indicated that MC3T3-E1 osteoblasts maintained expression of RUNX2, osteocalcin, and collagen type I, but alkaline phosphatase expression was decreased in cells subjected to simulated microgravity for 5 days. We conclude that osteoblast apoptosis is not induced by vector-averaged gravity, thus suggesting that microgravity does not directly induce osteoblast death.

Escherichia coli biofilms formed under low-shear modeled microgravity in a ground-based system.

Bacterial biofilms cause chronic diseases that are difficult to control. Since biofilm formation in space is well documented and planktonic cells become more resistant and virulent under modeled microgravity, it is important to determine the effect of this gravity condition on biofilms. Inclusion of glass microcarrier beads of appropriate dimensions and density with medium and inoculum, in vessels specially designed to permit ground-based investigations into aspects of low-shear modeled microgravity (LSMMG), facilitated these studies. Mathematical modeling of microcarrier behavior based on experimental conditions demonstrated that they satisfied the criteria for LSMMG conditions. Experimental observations confirmed that the microcarrier trajectory in the LSMMG vessel concurred with the predicted model. At 24 h, the LSMMG Escherichia coli biofilms were thicker than their normal-gravity counterparts and exhibited increased resistance to the general stressors salt and ethanol and to two antibiotics (penicillin and chloramphenicol). Biofilms of a mutant of E. coli, deficient in sigma(s), were impaired in developing LSMMG-conferred resistance to the general stressors but not to the antibiotics, indicating two separate pathways of LSMMG-conferred resistance.

Surface transformation of bioactive glass in bioreactors simulating microgravity conditions. Part I: experimental study.

Surface modified bioactive glass with surface properties akin to those of the bone mineral phase is an attractive candidate for use as a microcarrier material for 3-D growth of bone-like tissue in rotating wall vessel bioreactors (RWVs). The critical surface properties of this material are the result of reaction in solution. Because an RWV environment is completely different from conditions previously employed for bioactive glass testing, a detailed study of the surface reactions is warranted. Under properly chosen conditions, RWVs can also provide a simulated microgravity environment for the bioactive glass (BG) particles. In this sense, this study is also a report on the behavior of a bioactive material under microgravity conditions simulated on earth. A high aspect ratio vessel (HARV) and carefully selected experimental conditions enabled the simulation of microgravity in our laboratory. A complimentary numerical study was simultaneously conducted to ascertain the appropriateness of the experimental parameters (particle size, particle density, medium density, medium viscosity, and rotational speed) that ensure simulated microgravity conditions for the glass particles in the HARV. Physiological solutions (pH 7.4) with and without electrolytes, and also with serum proteins, were used to study the change in surface character resulting from simulated microgravity. Control tests at normal gravity, both static and dynamic, were also conducted. Solution and surface analyses revealed major effects of simulated microgravity. The rates of leaching of constituent ions (Si-, Ca-, and P-ions) were greatly increased in all solutions tested. The enhanced dissolution was followed by the enhanced formation of bone-like minerals at the BG surface. This enhancement is expected to affect adsorption of serum proteins and attachment molecules, which, in turn, may favorably affect bone cell adhesion and function. The findings of the study are important for the use of bioactive materials as microcarriers to generate and analyze 3-D bone-like tissue structures in bioreactors under microgravity conditions or otherwise.

Surface transformation of bioactive glass in bioreactors simulating microgravity conditions. Part II: numerical simulations.

The effects of simulated microgravity on the surface modification of bioactive glass (BG) in solution were studied using a numerical method. Models were developed for estimating the mass transfers of different chemical species from the surface of bioactive glass particles (microcarriers) suspended in the rotating liquid medium of a NASA-designed high aspect ratio vessel (HARV) bioreactor and on the bottom surface of a static vial. The concentration profiles resulting from chemical reactions and ionic transports were ascertained. Numerical results for the transport under simulated microgravity in the HARV and at normal gravity in the static vial were compared. These results were also compared with those of experiments to verify the enhancement of the reaction kinetics under simulated microgravity conditions. The experimental and numerical studies confirm that simulated microgravity conditions lead to the quick achievement of bioactive glass surface modification.

3D bone tissue engineered with bioactive microspheres in simulated microgravity.

Three-dimensional (3D) osteoblast cell cultures were obtained in rotating-wall vessels (RWV), simulating microgravity. Three types of bioactive microcarriers, specifically modified bioactive glass particles, bioceramic hollow microspheres, and biodegradable bioactive glass-polymer composite microspheres, were developed and used with osteoblasts. The surfaces of composite microspheres fully transformed into bone apatite after 2-wk immersion in simulated physiological fluid, which demonstrated their bone-bonding ability. The motion of microcarriers in RWVs was photographically recorded and numerically analyzed. The trajectories of hollow microspheres showed that they migrated and eventually stayed around at the central region of the RWV. At their surfaces, shear stresses were low. In contrast, solid glass or polymer particles moved toward and finally bounced off the outer wall of the RWVs. Cell culture studies in the RWV using bone marrow stromal cells showed that the cells attached to and formed 3D aggregates with the hollow microspheres. Extracellular matrix and mineralization were observed in the aggregates. Cell culture studies also confirmed the ability of the composite microspheres to support 3D bone-like tissue formation. These data suggest that the new hollow bioceramic microspheres and degradable composite microspheres can be used as microcarriers for 3D bone tissue engineering in microgravity. They also have potential applications as drug delivery systems.

New bioactive, degradable composite microspheres as tissue engineering substrates.

Novel bioactive, degradable polymer/glass/ceramic composite microspheres were developed using a solid-in-oil-in-water (s/o/w) emulsion solvent removal method. Modified bioactive glass (MBG) powders were encapsulated into the polylactic acid (PLA) matrix. Scanning electron microscopy and energy-dispersive X-ray analyses revealed that the MBG powders were mostly embedded in the polymer matrix, and submicron-size pores were present at the surface. Immersion in simulated physiological fluid (SPF) was used to evaluate the surface reactivity of the microspheres. The polymeric surface was fully transformed into carbonated calcium hydroxyapatite (c-HA) after 3 weeks of immersion. In contrast, PLA microspheres showed no evidence of any calcium phosphate deposition. Ion concentration analyses revealed a decrease in Ca and P concentrations and an increase in Si concentration in the SPF immersed with composite microspheres during the 3-week period. The Ca and P uptake rates decreased after 2 days of incubation. This coincided with the decrease of the Si release rate. These data lend support to the suggestion that the Si released from the MBG powders present in the polymer matrix is involved in the formation of the Ca-P layer. Our results support the concept that these new bioactive, degradable composite microspheres may serve as microcarriers for synthesis of bone and other tissues in vitro and in vivo.

Fabrication, characterization and evaluation of bioceramic hollow microspheres used as microcarriers for 3-D bone tissue formation in rotating bioreactors.

Novel bioactive ceramic hollow microspheres with an apparent density in the range 0.8-1.0 g cm(-3) have been developed as microcarriers for 3-D bone tissue formation in rotating-wall vessels (RWV). Hollow ceramic microspheres with a composition of 58-72% SiO2, 28-42% Al2O3 (wt%) and an apparent density 0.8-1.0 g cm(-3) were pretreated in 1.0 N NaOH for 2 h before being coated with synthesized calcium hydroxyapatite (HA) particulate sol. The HA-coated hollow microspheres were sintered for 1 h at 600, 800 and 1000 degrees C. SEM analysis revealed that the grain size and pore size of the calcium phosphate coating increased with the sintering temperature. FTIR analysis showed that crystalline calcium hydroxyapatite was present in the coatings sintered at 600 and 800 degrees C. When sintered at 1000 degrees C, the coating consisted of alpha-tricalcium phosphate. All the coatings adhered well, independent of sintering temperature. The trajectory analysis revealed that the hollow microsphere remained suspended in a rotating-wall vessel (RWV), and experienced a low shear stress (approximately 0.6 dyn cm(-2)). Cell culture studies using rat bone marrow stromal cells and osteosarcoma cells (ROS 17/2.8) showed that the cells attached to and formed 3-D aggregates with the hollow microspheres in a RWV. Extracellular matrix was observed in the aggregates. These data suggest that these hollow bioactive ceramic microspheres can be used as microcarriers for 3-D bone tissue formation in vitro, as well as for the study of the effects of microgravity on bone cell functions.