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S C Cowin

Publications and source records attributed to S C Cowin.

At least 55 records · Page 3Linked to original sources
PubMed1987

Bone remodeling of diaphyseal surfaces by torsional loads: theoretical predictions.

A theory of surface bone remodeling is extended to include the effects of shearing strains as well as normal strains. It is shown that the surface velocity can only depend upon the square of shearing strains, but that it can be linear as well as quadratic in the normal strains. The theory is applied to predict the surface bone remodeling in the diaphysis of a long bone under combined axial and torsional loading. In the general case the diaphysis of the long bone is modeled as a hollow thin-walled cylinder of arbitrary cross-section and, in a special case, as a right circular thin-walled tube. It is shown here that if a thin-walled right circular cylinder capable of surface remodeling is subjected to an axial compressive load and a twisting torque, then the effect of increasing the torque is the same as the effect of decreasing the axial compressive load, namely the mean radius of the cross-section increases and the wall width thins. Conversely, the effect of reducing the torque is the same as the effect of increasing the axial compressive load, namely the mean radius of the cross-section decreases and the wall width thickens.

Animals↗
PubMed1986

Thermodynamic restrictions on the elastic constants of bone.

The thermodynamic restrictions on the elastic coefficients of linear orthotropic elasticity and linear transversely isotropy elasticity are recorded and it is shown that previously reported data for the elastic orthotropic constants of bone satisfy these thermodynamic restrictions.

Bone and Bones↗
PubMed1986

Wolff's law of trabecular architecture at remodeling equilibrium.

An elastic constitutive relation for cancellous bone tissue is developed. This relationship involves the stress tensor T, the strain tensor E and the fabric tensor H for cancellous bone. The fabric tensor is a symmetric second rank tensor that is a quantitative stereological measure of the microstructural arrangement of trabeculae and pores in the cancellous bone tissue. The constitutive relation obtained is part of an algebraic formulation of Wolff's law of trabecular architecture in remodeling equilibrium. In particular, with the general constitutive relationship between T, H and E, the statement of Wolff's law at remodeling equilibrium is simply the requirement of the commutativity of the matrix multiplication of the stress tensor and the fabric tensor at remodeling equilibrium, T*H* = H*T*. The asterisk on the stress and fabric tensor indicates their values in remodeling equilibrium. It is shown that the constitutive relation also requires that E*H* = H*E*. Thus, the principal axes of the stress, strain and fabric tensors all coincide at remodeling equilibrium.

Bone and Bones↗
PubMed1985

The mechanical properties of immature osteopetrotic bone.

The elastic properties of the longer bones of the fore and hind limbs of an osteopetrotic Angus calf were measured using an ultrasonic technique. The same bones of a second Angus calf with unaffected bone tissue were also studied. The osteopetrotic bones were found to exhibit statistically significant lower values of density and mineral content than did the unaffected bones (P = .0054 and P = .0492, respectively). This result is contrary to what has been reported in the literature. The variations of the elastic properties and the density around the circumference of both the immature osteopetrotic femur and the unaffected femur were found to be similar to those previously measured on normal adult bovine femora.

Animals↗
PubMed1985

Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients.

In this paper we describe a computational means, based on beam theory, for application of the theory of adaptive elasticity to examples of real bone geometries. The results of the animal experiments were taken from the literature, and each documented the temporal evolution of a change in bone shape after a significant change in the mechanical loading environment of the bone. For each of these studies, we establish preliminary estimates of the in vivo values of the surface remodeling rate coefficients--the key parameters in the theory of surface remodeling. Our preliminary parameter estimates are established by comparison of published animal experimental results with surface remodeling theory predictions generated by the computational method.

Adaptation, Physiological↗
PubMed1985

The bone tissue of the canine mandible is elastically isotropic.

This paper reports experimental measurements which show that canine mandibular bone tissue is elastically isotropic. Earlier work has established that human, canine and bovine cortical bone tissue of the femur, tibia and skull are elastically anisotropic and therefore the reported isotropy of mandibular tissue was unexpected. The isotropic elastic moduli of the canine mandible are represented by a Young's modulus of 7.5 GPa and a Poisson's ratio of 0.4. Earlier work gave the three orthotropic Young's moduli of the cortical one of the canine femur as 12.8 GPa, 15.6 GPa and 20.1 GPa. The experimental technique employed is elastic wave propagation at ultrasonic frequencies.

Animals↗
PubMed1984

Bone remodeling due to continuously applied loads.

It has long been known that the stress history of bone tissue influences its structure; however, the nature of this relationship remains largely uncharacterized. The objective of this work was to induce a quantifiable change in the stress history of in vivo bone tissue and examine subsequent changes in structural and material properties that might occur. Continuous compressive loads were applied to the diaphysis of adult mongrel dogs for 2 months. The loads, ranging from 12-130 N, were superposed on the normal activity of the animals by implanting spring loading devices on the diaphysis of the femur. After the animals were sacrificed, mid-diaphysial specimens were subjected to compression testing to determine a structural bulk stiffness. The cross-sectional areas of original bone tissue and new bone deposition were then determined. The ash weights of selected specimens were also determined. The results indicate that a positive correlation between the increase in cross-sectional area and the superposed stress does exist. The new bone apposition was found almost entirely on the periosteal surface. Very little evidence of internal remodeling or endosteal movement was observed. The new tissue was found to have a lower ash weight and appeared to have a disorganized microstructure. Mechanical testing also suggests that the newly deposited tissue is far less stiff than the mature original bone.

Adaptation, Physiological↗
PubMed1984

Mechanical modeling of the stress adaptation process in bone.

The philosophy, techniques, and concepts involved in the mechanical modeling of the process of stress adaptation in bone are described here. First, the idea of a control surface, across which all mechanical forces and fluid transport are monitored, is introduced and employed to totally enclose a living whole bone. Then the mechanical forces are related to local tissue stresses and the fluid transport to the local microcirculation. The concepts of strain, stress, and elasticity are introduced next and the applications of these concepts to biological tissue are discussed. It is argued that biological tissue can only sense strain and not stress; thus baroreceptors are, in fact, strain receptors. The concept of remodeling or stress adaptive equilibrium is then introduced and associated with a particular range of strain values called the band of remodeling equilibrium strains. The deposition or resorption of bone tissue is hypothesized to be a function of the amount of strain by which the actual strain at an anatomical site differs from values of strain in the band of remodeling equilibrium strains. The form of this functional dependence is discussed with regard to a number of points, including its variance from anatomical site to site and the particular features of the strain history which are the most significant in enhancing bone remodeling. In the closing section of the paper, the basic mechanistic ideas underlying our models of bone stress adaptation are presented. These are mechanical models for internal bone remodeling (remodeling) and surface bone remodeling (modeling).

Adaptation, Physiological↗
PubMed1984

A continuous wave technique for the measurement of the elastic properties of cortical bone.

A continuous wave technique is described for measuring the nine independent orthotropic elastic coefficients from a single cubic specimen. The side dimensions of this cubic specimen are on the order of 5 mm. Because of the small size of the specimen, the spatial resolution of material inhomogeneity using this technique is quite good. Although it is possible to apply this technique to any elastic material such as woods or metals, the elastic properties of human and canine cortical femora are presented here. The orthotropic elastic coefficients and the variation of these coefficients are presented as a function of anatomical position.

Animals↗
PubMed1983

The mechanical and stress adaptive properties of bone.

The properties of bone tissue as a material and bones as the structural elements of the skeleton are reviewed and summarized. The first half of this work describes bone tissue microstructure, the stress-strain relations, and the strength and fracture of bone. The second and slightly larger half concerns the adaptation of living bone tissue to its load environment. Some observations and experiments of bone remodeling due to applied stress are described and continuum models for this process are formulated. An example of bone remodeling leading to shape changes in the bone is described as well as an example of bone remodeling leading to changes in the bulk density of the bone tissue.

Biomechanical Phenomena↗
PubMed1981

Ultrasonic measurement of orthotropic elastic constants of bovine femoral bone.

Using a pulse transmission ultrasound method, we have determined the elastic properties of bone samples taken from along the length and around the periphery of a bovine femur. Twenty specimens, in the form of 5-mm cubes, were tested. All nine of the orthotropic elastic constants were determined for each specimen. Analysis of our data indicate that there are statistically significant variations from the usual assumption of transverse isotropy.

Animals↗
PubMed1981

An analytical model of Pauwels' functional adaptation mechanism in bone.

In this paper it is argued and partially demonstrated that the features of Pauwels' qualitative theory of functional adaptation of bone tissue are expressed mathematically by the cubic approximation to the theory of internal remodeling presented by Cowin and Hegedus. Complete solutions for the steady stress and steady strain situations in the cubic approximation to the theory of internal remodeling are presented. The cubic remodeling rate equation is shown to correspond closely to the remodeling equation suggested by Kummer for the qualitative theory of Pauwels.

Adaptation, Physiological↗
PubMed1980

Devolution of inhomogeneities in bone structure--predictions of adaptive elasticity theory.

In this paper we consider an initially inhomogeneous adaptive elastic body subjected to a steady homogeneous stress state. The adaptive elastic body, which is a model for living bone tissue, is inhomogeneous in both its anisotropic elastic properties and its density. The principal result of the paper is the determination of the devolution of the initially inhomogeneous body to a homogeneous body under the influence of the steady homogeneous stress state. A cylindrical body that is inhomogeneous along the axis of the cylinder, but homogeneous in each transverse plane of the cylinder, is used as an example. This cylindrical body is loaded by a steady uniform stress directed along the cylindrical axis. The temporal devolution of an inhomogeneity in the initial shape of a sine wave is illustrated. As time progresses the amplitude of the sine wave decreases, rapidly at first and then more slowly. As time becomes very large the sine wave becomes a straight line signifying that the cylinder has become homogeneous.

Biomechanical Phenomena↗
PubMedDate not supplied

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.

Biomechanical Phenomena↗