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NASA NTRS1995

Stokes problems for moving half-planes

New exact solutions of the Navier-Stokes equations are obtained for the unbounded and bounded oscillatory and impulsive tangential edgewise motion of touching half-infinite plates in their own plane. In contrast to Stokes classical solutions for the harmonic and impulsive motion of an infinite plane wall, where the solutions are separable or have a simple similarity form, the present solutions have a two-dimensional structure in the near region of the contact between the half-infinite plates. Nevertheless, it is possible to obtain relatively simple closed-form solutions for the flow field in each case by defining new variables which greatly simplify the r- and theta- dependence of the solutions in the vicinity of the contact region. These solutions for flow in a half-infinite space are then extended to bounded flows in a channel using an image superposition technique. The impulsive motion has application to the motion near geophysical faults, whereas the oscillatory motion has arisen in the design of a novel oscillating half-plate flow chamber for examining the effect of fluid shear stress on cultured cell monolayers.

NASA Discipline Musculoskeletal↗

NASA NTRS1998

Electrical signal transmission in a bone cell network: the influence of a discrete gap junction

A refined electrical cable model is formulated to investigate the role of a discrete gap junction in the intracellular transmission of electrical signals in an electrically coupled system of osteocytes and osteoblasts in an osteon. The model also examines the influence of the ratio q between the membrane's electrical time constant and the characteristic time of pore fluid pressure, the circular, cylindrical geometry of the osteon, and key simplifying assumptions in our earlier continuous cable model (see Zhang, D., S. C. Cowin, and S. Weinbaum. Electrical signal transmission and gap junction regulation in a bone cell network: A cable model for an osteon. Ann. Biomed. Eng. 25:379-396, 1997). Using this refined model, it is shown that (1) the intracellular potential amplitude at the osteoblastic end of the osteonal cable retains the character of a combination of a low-pass and a high-pass filter as the corner frequency varies in the physiological range; (2) the presence of a discrete gap junction near a resting osteoblast can lead to significant modulation of the intracellular potential and current in the osteoblast for measured values of the gap junction coupling strength; and (3) the circular, cylindrical geometry of the osteon is well simulated by the beam analogy used in Zhang et al.

Non-NASA Center↗

NASA NTRS1994

A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon

A theoretical model is developed to predict the fluid shear stress and streaming potential at the surface of osteocytic processes in the lacunar-canalicular porosity of an osteon when the osteon is subject to mechanical loads that are parallel or perpendicular to its axis. The theory developed in Weinbaum et al. (31) for the flow through a proteoglycan matrix in a canaliculus is employed in a poroelastic model for the osteon. Our formulation is a generalization of that of Petrov et al. (17). Our model predicts that, in order to satisfy the measured frequency dependence of the phase and magnitude of the SGP in macroscopic bone samples, the fiber spacing in the fluid annulus must lie in the narrow range 6-7 nm typical of the spacing of GAG sidechains along a protein monomer. The model predictions for the local SGP profiles in the osteon agree with the experimental observations of Starkebaum et al. (24). The theory predicts that the pore pressure relaxation time, tau d, for a 150-300 microns diameter osteon with the foregoing matrix structure is approximately 0.03-0.13 sec, and that the amplitude of the mean fluid shear stress on the membrane of the osteocytic process at the mean areal radius of the osteon has a maximum at 28 Hz if tau d = 0.06 sec. This maximum, which is independent of the magnitude of the loading, could be important in vivo since the recent experiments of Turner et al. (28) and McLeod et al. (15) have a peak in the strain frequency spectrum between 20 and 30 Hz that also appears to be independent of the type (magnitude) of loading. Numerical predictions for the amplitude of the average fluid shear stress on the osteocytic membrane at the mean areal radius of the osteon show that the fluid shear stress associated with the low amplitude 20-30 Hz spectral strain component is at least as large as the average fluid shear stress associated with the high amplitude 1 Hz stride component, although the latter loading is an order of magnitude larger, and has a magnitude that lies within the middle of the range, 6-30 dynes/cm2, where fluid shear stresses in tissue culture studies with osteoblast monolayers have elicited an intracellular Ca++ response (31). The implications of these results for intracellular electrical communication are discussed.

Non-NASA Center↗