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S C Cowin

Publications and source records attributed to S C Cowin.

At least 19 recordsLinked to original sources
PubMed2002

Estimation of the effective transversely isotropic elastic constants of a material from known values of the material's orthotropic elastic constants.

A method is illustrated for determining the effective transversely isotropic (or isotropic) elastic constants from measured orthotropic elastic constants. This method consists of constructing upper and lower bounds on the effective transversely isotropic (or isotropic) elastic constants using the known orthotropic values. This method is illustrated using three sets of elastic constants for bone. Fortunately, the upper and lower bounds are very close. Thus very good approximations for the effective transversely isotropic (or isotropic) elastic constants for cortical and cancellous bone are obtained from previously published data on the orthotropic elastic constants for those tissue types. This work is undertaken to build a greater database for the transversely isotropic elastic constants of bone with the intention of employing them in a transversely isotropic model of bone poroelasticity. An interesting aspect of the present result is that the Voigt and Reuss bounds are very tight for these anisotropic materials. This is not always the case for these bounds.

Animals↗
PubMed2002

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.

Journal Article↗
PubMed2001

A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix.

A model is presented that provides a resolution to a fundamental paradox in bone physiology, namely, that the strains applied to whole bone (i.e., tissue level strains) are much smaller (0.04-0.3 percent) than the strains (1-10 percent) that are necessary to cause bone signaling in deformed cell cultures (Rubin and Lanyon, J. Bone Joint Surg. 66A (1984) 397-410; Fritton et al., J. Biomech. 33 (2000) 317-325). The effect of fluid drag forces on the pericellular matrix (PM), its coupling to the intracellular actin cytoskeleton (IAC) and the strain amplification that results from this coupling are examined for the first time. The model leads to two predictions, which could fundamentally change existing views. First, for the loading range 1-20MPa and frequency range 1-20Hz, it is, indeed, possible to produce cellular level strains in bone that are up to 100 fold greater than normal tissue level strains (0.04-0.3 percent). Thus, the strain in the cell process membrane due to the loading can be of the same order as the in vitro strains measured in cell culture studies where intracellular biochemical responses are observed for cells on stretched elastic substrates. Second, it demonstrates that in any cellular system, where cells are subject to fluid flow and tethered to more rigid supporting structures, the tensile forces on the cell due to the drag forces on the tethering fibers may be many times greater than the fluid shear force on the cell membrane.

Actins↗
PubMed2000

Modeling tracer transport in an osteon under cyclic loading.

A mathematical model is developed to explain the fundamental conundrum as to how during cyclic mechanical loading there can be net solute (e.g., nutrient, tracer) transport in bone via the lacunar-canalicular porosity when there is no net fluid movement in the canaliculi over a loading cycle. Our hypothesis is that the fluid space in an osteocytic lacuna facilitates a nearly instantaneous mixing process of bone fluid that creates a difference in tracer concentration between the inward and outward canalicular flow and thus ensures net tracer transport to the osteocytes during cyclic loading, as has been shown experimentally. The sequential spread of the tracer from the osteonal canal to the lacunae is investigated for an osteon experiencing sinusoidal loading. The fluid pressure in the canaliculi is calculated using poroelasticity theory and the mixing process in the lacunae is then simulated computationally. The tracer concentration in lacunae extending radially from the osteonal canal to the cement line is calculated as a function of the loading frequency, loading magnitude, and number of loading cycles as well as the permeability of the lacunar-canalicular porosity. Our results show that net tracer transport to the lacunae does occur for cyclic loading. Tracer transport is found to increase with higher loading magnitude and higher permeability and to decrease with increasing loading frequency. This work will be helpful in designing experimental studies of tracer movement and bone fluid flow, which will enhance our understanding of bone metabolism as well as bone adaptation.

Animals↗
PubMed2000

How is a tissue built?

Tissues change in many ways in the period that they are part of a living organism. They are created in fairly repeatable structural patterns, and we know that the patterns are due to both the genes and the (mechanical) environment, but we do not know exactly what part or percentage of a particular pattern to consider the genes, or the environment, responsible for. We do not know much about the beginning of tissue construction (morphogenesis) and we do not know the methods of tissue construction. When the tissue structure is altered to accommodate a new loading, we do not know how the decision is made for the structural reconstruction. We do know that tissues grow or reconstruct themselves without ceasing to continue with their structural function, but we do not understand the processes that permit them to accomplish this. Tissues change their structures to altered mechanical environments, but we are not sure how. Tissues heal themselves and we understand little of the structural mechanics of the process. With the objective of describing the interesting unsolved mechanics problems associated with these biological processes, some aspects of the formation, growth, and adaptation of living tissues are reviewed. The emphasis is on ideas and models. Beyond the objective is the hope that the work will stimulate new ideas and new observations in the mechanical and chemical aspects of developmental biology.

Adaptation, Physiological↗
PubMed1999

Bone poroelasticity.

Poroelasticity is a well-developed theory for the interaction of fluid and solid phases of a fluid-saturated porous medium. It is widely used in geomechanics and has been applied to bone by many authors in the last 30 years. The purpose of this work is, first, to review the literature related to the application of poroelasticity to the interstitial bone fluid and, second, to describe the specific physical and modeling considerations that establish poroelasticity as an effective and useful model for deformation-driven bone fluid movement in bone tissue. The application of poroelasticity to bone differs from its application to soft tissues in two important ways. First, the deformations of bone are small while those of soft tissues are generally large. Second, the bulk modulus of the mineralized bone matrix is about six times stiffer than that of the fluid in the pores while the bulk moduli of the soft tissue matrix and the pore water are almost the same. Poroelasticity and electrokinetics can be used to explain strain-generated potentials in wet bone. It is noted that strain-generated potentials can be used as an effective tool in the experimental study of local bone fluid flow, and that the knowledge of this technique will contribute to the answers of a number of questions concerning bone mineralization, osteocyte nutrition and the bone mechanosensory system.

Body Fluids↗
PubMed1999

The effect of surface roughness on the stress adaptation of trabecular architecture around a cylindrical implant.

The effect of implant-bone bonding and the effect of implant surface roughness on bone remodeling near the bone-implant interface were studied by using a surface remodeling theory and the boundary element method. The study has shown that implant attachment plays an important role in bone remodeling near the implant. It has been observed in animal experiments and in clinical situations that the remodeled trabecular bone architecture around a cylindrical implant could vary, on one hand, from a hub surrounding the implant with a set of external spokes to, on the other hand, a hubless situation in which a set of spokes attach directly to the implant. It is shown here that the difference in these structures may be attributed to differences in implant attachment. The results show that the bone with perfect bonding or roller boundary condition without a gap remodeled to a hubless spoke trabecular bone architecture. On the other hand, the roller boundary condition with a specified gap yielded a spoke trabecular architecture with a hub or ring surrounding the implant. These quantitative results mirror the experimental and clinical observations. It is concluded that the hub is a consequence of the gap and not a consequence of the lack of friction between the implant and the bone.

Humans↗
PubMed1999

Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment.

When bone is mechanically loaded, bone fluid flow induces shear stresses on bone cells that have been proposed to be involved in bone's mechanosensory system. To investigate bone fluid flow and strain-generated potentials, several theoretical models have been proposed to mimic oscillatory four-point bending experiments performed on thin bone specimens. While these previous models assume that the bone fluid relaxes across the specimen thickness, we hypothesize that the bone fluid relaxes primarily through the vascular porosity (osteonal canals) instead and develop a new poroelastic model that integrates the microstructural details of the lacunar-canalicular porosity, osteonal canals, and the osteonal cement lines. Local fluid pressure profiles are obtained from the model, and we find two different fluid relaxation behaviors in the bone specimen, depending on its microstructure: one associated with the connected osteonal canal system, through which bone fluid relaxes to the nearby osteonal canals; and one associated with the thickness of a homogeneous porous bone specimen (approximately 1 mm in our model), through which bone fluid relaxes between the external surfaces of the bone specimen at relatively lower loading frequencies. Our results suggest that in osteonal bone specimens the fluid pressure response to cyclic loading is not sensitive to the permeability of the osteonal cement lines, while it is sensitive to the applied loading frequency. Our results also reveal that the fluid pressure gradients near the osteonal canals (and thus the fluid shear stresses acting on the nearby osteocytes) are significantly amplified at higher loading frequencies.

Body Fluids↗
PubMed1998

Imposing thermodynamic restrictions on the elastic constant-fabric tensor relationship.

Zysset and Curnier (1995) rederive the general representation for the fourth rank elasticity tensor in terms of the fabric tensor given originally by Cowin (1985). Zysset and Curnier (1995) then obtain a form of the representation that is sufficiently restricted to satisfy the thermodynamic constraint that the compliance tensor be positive definite. Zysset and Curnier (1995, 1996) argue that their representation has an advantage over that of Cowin (1985) because it has, a priori, been sufficiently restricted to satisfy the thermodynamic constraint that the compliance tensor be positive definite. The purpose of this note is to point out that the limitations of the Zysset and Curnier (1995, 1996) sufficiency representation are quite severe, restricting the flexibility of the model by allowing only five of the nine normally independent orthotropic elastic coefficients to be independent. Potential users should consider employing the Cowin (1985) representation and subsequently imposing the condition that the elasticity tensor be positive definite.

Algorithms↗
PubMed1998

On mechanosensation in bone under microgravity.

Recent research has illuminated the biological response of bone to mechanical loading at the cellular level, but the precise mechanosensory system that signals bone cells to deposit or resorb tissue has not been identified. The purpose of this paper is to describe the current status of this research and to suggest some possible mechanosensory systems by which bone cells might sense environmental loads. The question of whether the mechanosensory system in bone tissue is at the level of the cell or whether it is at the tissue level and involving the cells is considered here. More precisely, the following question is addressed: can an osteocyte or an osteoblast read the gravitational field changes directly (and independent of changes in its environment), or does it detect those changes indirectly from its environment by contact stresses as it must detect other changes in mechanical loading on the surface of the earth? Our strategies for coping with the decay of the musculoskeletal system in long term space flight are somewhat dependent upon the answer to this question.

Animals↗
PubMed1998

Strain amplification in the bone mechanosensory system.

This article discusses the potential mechanisms by which the strain induced at the membrane of an osteocyte may be amplified from the strain experienced by the whole bone due to mechanical loading. These mechanisms address the question of how these mechanical load-induced small strains of (typically) about 0.1% (but up to 0.5%) applied to a whole bone are amplified to strains of 1% or larger at the membrane of the osteocyte buried in its lacuna in the bone matrix. The answer to this question is an important link in the mechanosensory system in bone and in relating in vitro cell studies to in vivo cellular response.

Bone and Bones↗
PubMed1998

Estimates of the peak pressures in bone pore water.

The maximum pore fluid pressures due to uniaxial compression are determined for both the vascular porosity (Haversian and Volkmann's canals) and the lacunar-canalicular porosity of live cortical bone. It is estimated that the peak pore water pressure will be 19 percent of the applied axial stress in the vascular porosity and 12 percent of the applied axial stress in the lacunar-canalicular porosity for an impulsive step loading. However, the estimated relaxation time for the vascular porosity (1.36 microseconds) is three orders of magnitude faster than that estimated for the lacunar-canalicular porosity (4.9 ms). Thus, under physiological loading, which has a stress rise time generally larger than 1 ms, pressures higher than the vascular pressure cannot be sustained in the vascular porosity due to the swift pressure relaxation in this porosity (unless the fluid drainage through the boundary is obstructed). The model also predicts a slight hydraulic stiffening of the bulk modulus due to longer draining time of the lacunar-canalicular porosity. The undrained bulk modulus is 6 percent higher than the drained bulk modulus in this case.

Cell Membrane Permeability↗
PubMed1996

Strain or deformation rate dependent finite growth in soft tissues.

The particular portion of the mechanical loading history of a tissue that serves as stimulus for growth or remodeling of that tissue is presently unknown. A kinematic basis for the implementation of strain or rate of deformation as a growth stimulus is presented. It is shown here that a recently proposed continuum theory for finite volumetric growth in soft tissue may be extended to include strain and rate of deformation as growth stimuli. The basis of the presentation is the recognition of two different time scales in the remodeling process, one on the order of seconds associated with the loading, and one on the order of weeks or months associated with the growth.

Algorithms↗
PubMed1996

Dynamic relationships of trabecular bone density, architecture, and strength in a computational model of osteopenia.

A computational model was developed to study the effects of short- and long-term periods of disuse osteopenia and repair to elucidate the interrelationships between bone mass, architecture, and strength. The model is one in which the sequence of structural change events is followed in time. This temporal feature contrasts with studies of real trabecular tissue which are necessarily cross-sectional in nature and do not lend themselves to insights into the dynamic nature of the structural changes with time. In the model it was assumed that the stimulus for bone adaptation to mechanical load is the local mechanical strain rate, according to which the trabecular surfaces are differentially formed and resorbed. The effects of mechanical loading and unloading (disuse) on the cancelous bone properties were studied. The bone mass, architecture, and elastic stiffness were shown to be strongly dependent upon the period of the unloading phase, as well as the period of the reloading phase. Mechanical stiffness is demonstrated computationally to be a multivalued function of bone mass, if architecture is not accounted for. The model shows how the same value of trabecular bone mass can be associated with two or more distinct values of biomechanical stiffness. This result is the first explicit demonstration of how bone mass, architecture, and strength are related under dynamical load-bearing conditions. The results explain the empirical observation that bone mass can account for about 65% of the observed variation in bone strength, but that by incorporating measures of bony architecture into the analysis, the predictability is increased to 94%. The computational model may be used to explore the effects of different loading regimes on mass, architecture, and strength, and potentially for assistance in designing both animal and clinical bone loss studies.

Adaptation, Physiological↗
PubMed1995

On the minimization and maximization of the strain energy density in cortical bone tissue.

Universal minimization and maximization of the strain energy density, while possible in materials with cubic symmetry, is not possible for cortical long bone with its orthotropic material symmetry. Illustrating this point, it is shown that the stress state obtained when an axial load is applied along the long axis of a long bone at the midshaft is a minimizer of the strain energy density, while the stress state obtained when a load is applied perpendicular to the long axis, and perpendicular to the surface, of the mid-diaphysis of a long bone is a maximizer of the strain energy density. Thus, the bone tissue at the midshaft of a long bone is designed by nature so that it has the greatest stiffness in the direction of its long axis and its greatest impact loading resistance in the transverse direction.

Algorithms↗
PubMed1995

A case for bone canaliculi as the anatomical site of strain generated potentials.

We address the question of determining the anatomical site that is the source of the experimentally observed strain generated potentials (SGPs) in bone tissue. There are two candidates for the anatomical site that is the SGP source, the collagen-hydroxyapatite porosity and the larger size lacunar-canalicular porosity. In the past it has been argued, on the basis of experimental data and a reasonable model, that the site of the SGPs in bone is the collagen-hydroxyapatite porosity. The theoretically predicted pore radius necessary for the SGPs to reside in this porosity is 16 nm, which is somewhat larger than the pore radii estimated from gas adsorption data where the preponderance of the pores were estimated to be in the range 5-12.5 nm. However, this pore size is significantly larger than the 2 nm size of the small tracer, microperoxidase, which appears to be excluded from the mineralized matrix. In this work a similar model, but one in which the effects of fluid dynamic drag of the cell surface matrix in the bone canaliculi are included, is used to show that it is possible for the generation of SGPs to be associated with the larger size lacunar-canalicular porosity when the hydraulic drag and electrokinetic contribution of the bone fluid passage through the cell coat (glycocalyx) is considered. The consistency of the SGP data with this model is demonstrated. A general boundary condition is introduced to allow for current leakage at the bone surface. The results suggest that the current leakage is small for the in vitro studies in which the strain generated potentials have been measured.

Biomechanical Phenomena↗
PubMed1995

Implementation of strain rate as a bone remodeling stimulus.

Strain rate is implemented as a stimulus for surface bone remodeling. Using idealized models for trabecular bone structures, the surface remodeling predictions using the strain rate as the stimulus are compared with the predictions using the peak strain magnitude as the stimulus. For a uniaxially loaded cruciform shape, the comparison shows that the two surface remodeling stimuli predict the same final shape under a periodic compressive load, but the two evolutionary paths to final shapes are different. Two biaxially loaded regular grid models of trabecular structure were considered, one a grid of square diamond shaped elements and the other a brick wall patterned grid. For both of these idealized trabecular structures, the comparison shows that the two surface remodeling stimuli predict the same final shape under a periodic compressive load, even from these distinctly different initial grid patterns, and the evolutionary paths to final shapes are quite different. In general the two stimuli do not predict the same remodeling and the conditions under which they do are derived. The models developed are also applied to the data from the animal experiments reported in Goldstein et al. (1991), and it is shown that the strain rate stimulus predicts bone remodeling similar to what was experimentally observed.

Animals↗