stephen cowin | The City College of New York (original) (raw)

Papers by stephen cowin

Research paper thumbnail of A theory for static loads in bins

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Research paper thumbnail of Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid... more An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types
exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall
shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a
dimensionless ratio h=lv; in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled
by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to
be met: (1) h=lvo2; where h is the distance between the plates and lv is the viscous penetration depth; and (2) f0ofc=m; where the
critical frequency fc is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f0 is the fundamental
frequency of fluid flow.

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Research paper thumbnail of A new proof that the number of linear elastic symmetries is eight

Journal of the Mechanics and Physics of Solids, 2001

... anisotropic symmetries began to receive attention. (For references to the literature and a di... more ... anisotropic symmetries began to receive attention. (For references to the literature and a discussion of this development see Forte and Vianello (1996, Section 6) and Cowin and Mehrabadi (1989)). A modern approach which makes ...

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Research paper thumbnail of A continuum theory for granular materials

Archive for Rational Mechanics and Analysis, 1972

Page 1. A Continuum Theory for Granular Materials MA GOODMAN • SC COWIN Communicated by JL ERICKS... more Page 1. A Continuum Theory for Granular Materials MA GOODMAN • SC COWIN Communicated by JL ERICKSEN ... Page 3. Continuum Theory for Granular Materials 251 ...

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Research paper thumbnail of Inaugural Article by a Recently Elected Academy Member

Proceedings of The National Academy of Sciences, 2003

In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycoca... more In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycocalyx in several roles: as a transport barrier, as a porous hydrodynamic interface in the motion of red and white cells in microvessels, and as a mechanotransducer of fluid shearing stresses to the actin cortical cytoskeleton of the endothelial cell. These functions will be examined from a new perspective, the quasiperiodic ultrastructural model proposed in Squire et al. [Squire, J. M., Chew, M., Nneji, G., Neal, C., Barry, J. & Michel, C. (2001) J. Struct. Biol. 136, 239-255] for the 3D organization of the endothelial surface layer and its linkage to the submembranous scaffold. We shall show that the core proteins in the bush-like structures comprising the matrix have a flexural rigidity, EI, that is sufficiently stiff to serve as a molecular filter for plasma proteins and as an exquisitely designed transducer of fluid shearing stresses. However, EI is inadequate to prevent the buckling of these protein structures during the intermittent motion of red cells or the penetration of white cell microvilli. In these cellular interactions, the viscous draining resistance of the matrix is essential for preventing adhesive molecular interactions between proteins in the endothelial membrane and circulating cellular components.

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Research paper thumbnail of Ramp loading in Russian doll poroelasticity

Journal of The Mechanics and Physics of Solids, 2011

Aporoelastic model for porous materials with a nested pore space structure is developed to repres... more Aporoelastic model for porous materials with a nested pore space structure is developed to represent the interstitial fluid flow in bone tissue. The nested porosity model is applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar–canalicular porosity (PLC) in bone tissue in a ramp loading in the case where the fluid and solid constituents are assumed to be compressible. The compressibility assumption is appropriate for hard tissues while the incompressibility assumption is appropriate for soft tissues. The influence of blood pressure in the PV is included in the analysis. A formula for the fluid that moves between the two porosities is developed. The analysis showed the coupling of the two porosities and their influence on each other and concluded that the PV pore pressure has an influence less than 3% on the PLC pore pressure while the absence of the PV pore pressure will affect the fluid exchange between the PV and PLC by less than 6% (the blood pressure range is 40–60 mmHg). Also the analysis has shown that the draining time of the PLC is inversely proportional to its permeability. The significance of the result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells.

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Research paper thumbnail of The Anisotropic Elastic Constants of Cancellous Bone

Key Engineering Materials, 2001

... van Rietbergen, A. Odgaard, R. Huiskes, R. and S. С Cowin: The Anisotropic Hooke's Law f... more ... van Rietbergen, A. Odgaard, R. Huiskes, R. and S. С Cowin: The Anisotropic Hooke's Law for Cancellous Bone and Wood, J. Elasticity, 53, (1999) 125-146. ... [4] WK Thomson (Lord Kelvin), Elasticity, In: Encyclopaedia Britannica, Adam and Charles Black, Edinburgh (1878). ...

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Research paper thumbnail of Structural Change in Living Tissues

Meccanica, 1999

Tissues change in many ways in the period that they are part of a living organism. Tissues are cr... more Tissues change in many ways in the period that they are part of a living organism. Tissues are created in fairly repeatable structural patterns, and 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 also the methods of tissue construction. When the tissue structure is altered to accommodate a new loading, it is not known how the decision is made for the structural reconstruction. We 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. Beyond the objective is the hope that the work will stimulate new ideas and new observations in developmental biology.

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

Biomechanics and Modeling in Mechanobiology, 2005

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by connected... more 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.

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Research paper thumbnail of Fabric dependence of wave propagation in anisotropic porous media

Biomechanics and Modeling in Mechanobiology, 2011

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral d... more Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric—a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

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Research paper thumbnail of In Response to “Mixing Mechanisms and Net Solute Transport in Bone” by M. L. Knothe Tate

Annals of Biomedical Engineering, 2001

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Research paper thumbnail of Experimental Determination of the Permeability in the Lacunar-Canalicular Porosity of Bone

Journal of Biomechanical Engineering-transactions of The Asme, 2009

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Research paper thumbnail of Preface on Physicochemical and Electromechanical Interactions in Porous Media

Transport in Porous Media, 2003

The focus of science and engineering shifts towards smaller length scales. Porous media mechanics... more The focus of science and engineering shifts towards smaller length scales. Porous media mechanics has a vital role to play in the translation of microstructural data into macroscopic models of multicomponent systems. As the length scales shrink, more fundamental levels of understanding of natural laws, cause the boundaries between disciplines to blur. In particular, geosciences, polymer sciences and biosciences find a common ground of interest in high specific surface mixtures.

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Research paper thumbnail of Study of Site-Specific Bone Formation Using a Neural Network Model

ABSTRACT

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Research paper thumbnail of The elastic moduli estimation of the solid-water mixture

International Journal of Solids and Structures, 2009

Conceptually, the undrained elastic constants estimated by the poroelasticity theory should be id... more Conceptually, the undrained elastic constants estimated by the poroelasticity theory should be identical to the effective moduli of the two-phase composite of a porous material saturated with pore water. Here we show numerically that the undrained elastic constants determined by an effective moduli estimate are almost identical with those calculated by poroelasticity theory, and if pore shapes are not exactly known and the porosity is around 50%, estimating the elastic constant as the average value of its Voigt and Reuss bounds is reasonably accurate. This is the situation in bone and dentin, the materials that are our primary intended application. This result will hold for situations in which the totally enclosed water phase is constrained to small deformations by virtue of its confinement. Importantly, in this work we assume that water is an isotropic elastic solid with a shear modulus that is 10−4 times the bulk modulus of the water. Note that it is compressible, but almost incompressible with a Poisson’s ratio of 0.4999.

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Research paper thumbnail of Remarks on Coaxiality of Strain and Stress in Anisotropic Elasticity

Journal of Elasticity, 1997

Two different consequences of the problem of the extremization of the strain energy by varying th... more Two different consequences of the problem of the extremization of the strain energy by varying the orientation of the material symmetry axes relative to the principal axes of stress are discussed. These two different consequences depend upon whether the stress state is considered as arbitrary and general or as fixed and specific.

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Research paper thumbnail of Analysis of avian bone response to mechanical loading—Part One: Distribution of bone fluid shear stress induced by bending and axial loading

Biomechanics and Modeling in Mechanobiology, 2005

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by a bone-co... more Mechanical loading-induced signals are hypothesized to be transmitted and integrated by a bone-connected cellular network (CCN) before reaching the bone surfaces where adaptation occurs. Our objective is to establish a computational model to explore how bone cells transmit the signals through intercellular communication. In this first part of the study the bone fluid shear stress acting on every bone cell in a CCN is acquired as the excitation signal for the computational model. Bending and axial loading-induced fluid shear stress is computed in transverse sections of avian long bones for two adaptation experiments (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). The computed fluid shear stress is found to be correlated with the radial strain gradient but not with bone formation. These results suggest that the radial strain gradient is the driving force for bone fluid flow in the radially distributed lacunar-canalicular system and that bone formation is not linearly related to the loading-induced local stimulus.

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Research paper thumbnail of The unconfined compression of a poroelastic annular cylindrical disk

Mechanics of Materials, 2008

The analytical solution to the problem of a saturated annular poroelastic disk subjected to uncon... more The analytical solution to the problem of a saturated annular poroelastic disk subjected to unconfined compression in the case when the fluid and solid constituents of the poroelastic medium are both compressible is recorded. Infinitesimal deformations and transverse isotropy are assumed. The algebraic complexity of the problem stems from the need to have the solution to the problem for three different sets of boundary drainage conditions on fluid flow or no flow through the inner and outer boundaries of the annular disk. The analytical solution demonstrates the effects of the assumptions of isotropy versus transverse isotropy and compressibility versus incompressibility of the poroelastic constituents. The advantages of this solution are that they provide insight into the nature of the elastic response and fluid flow of soft tissues versus hard tissues and saturated swampy soils versus saturated rocks and as an analytical tool to analyze unconfined compression experiments performed on these materials.

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Research paper thumbnail of The significance of bone microstructure in mechanotransduction

Journal of Biomechanics, 2007

Recent developments in modeling the relationship between bone microstructure and mechanotransduct... more Recent developments in modeling the relationship between bone microstructure and mechanotransduction are reviewed. The focus is on the relationship between the bone microstructure and the mechanosensation mechanism by which osteocytes sense the bone fluid motion propelled by the mechanical loading of the whole bone.

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Research paper thumbnail of An estimate of anisotropic poroelastic constants of an osteon

Biomechanics and Modeling in Mechanobiology, 2008

The anisotropic poroelastic constants of an osteon are estimated by micromechanical analysis. Two... more The anisotropic poroelastic constants of an osteon are estimated by micromechanical analysis. Two extreme cases are examined, the drained and the undrained elastic constants. The drained elastic constants are the porous medium’s effective elastic constants when the fluid in the pores easily escapes and the pore fluid can sustain no pore pressure. The undrained elastic constants are the porous medium’s effective elastic constants when the medium is fully saturated with pore fluid and the fluid cannot escape. The drained and undrained elastic constants at the lacunar and canalicular porosity tissue levels are estimated by using an effective moduli model consisting of the periodic distribution of ellipsoidal cavities. These estimated anisotropic poroelastic constants provide a database for the development of an accurate anisotropic poroelastic model of an osteon.

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Research paper thumbnail of A theory for static loads in bins

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Research paper thumbnail of Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid... more An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types
exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall
shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a
dimensionless ratio h=lv; in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled
by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to
be met: (1) h=lvo2; where h is the distance between the plates and lv is the viscous penetration depth; and (2) f0ofc=m; where the
critical frequency fc is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f0 is the fundamental
frequency of fluid flow.

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Research paper thumbnail of A new proof that the number of linear elastic symmetries is eight

Journal of the Mechanics and Physics of Solids, 2001

... anisotropic symmetries began to receive attention. (For references to the literature and a di... more ... anisotropic symmetries began to receive attention. (For references to the literature and a discussion of this development see Forte and Vianello (1996, Section 6) and Cowin and Mehrabadi (1989)). A modern approach which makes ...

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Research paper thumbnail of A continuum theory for granular materials

Archive for Rational Mechanics and Analysis, 1972

Page 1. A Continuum Theory for Granular Materials MA GOODMAN • SC COWIN Communicated by JL ERICKS... more Page 1. A Continuum Theory for Granular Materials MA GOODMAN • SC COWIN Communicated by JL ERICKSEN ... Page 3. Continuum Theory for Granular Materials 251 ...

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Research paper thumbnail of Inaugural Article by a Recently Elected Academy Member

Proceedings of The National Academy of Sciences, 2003

In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycoca... more In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycocalyx in several roles: as a transport barrier, as a porous hydrodynamic interface in the motion of red and white cells in microvessels, and as a mechanotransducer of fluid shearing stresses to the actin cortical cytoskeleton of the endothelial cell. These functions will be examined from a new perspective, the quasiperiodic ultrastructural model proposed in Squire et al. [Squire, J. M., Chew, M., Nneji, G., Neal, C., Barry, J. & Michel, C. (2001) J. Struct. Biol. 136, 239-255] for the 3D organization of the endothelial surface layer and its linkage to the submembranous scaffold. We shall show that the core proteins in the bush-like structures comprising the matrix have a flexural rigidity, EI, that is sufficiently stiff to serve as a molecular filter for plasma proteins and as an exquisitely designed transducer of fluid shearing stresses. However, EI is inadequate to prevent the buckling of these protein structures during the intermittent motion of red cells or the penetration of white cell microvilli. In these cellular interactions, the viscous draining resistance of the matrix is essential for preventing adhesive molecular interactions between proteins in the endothelial membrane and circulating cellular components.

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Research paper thumbnail of Ramp loading in Russian doll poroelasticity

Journal of The Mechanics and Physics of Solids, 2011

Aporoelastic model for porous materials with a nested pore space structure is developed to repres... more Aporoelastic model for porous materials with a nested pore space structure is developed to represent the interstitial fluid flow in bone tissue. The nested porosity model is applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar–canalicular porosity (PLC) in bone tissue in a ramp loading in the case where the fluid and solid constituents are assumed to be compressible. The compressibility assumption is appropriate for hard tissues while the incompressibility assumption is appropriate for soft tissues. The influence of blood pressure in the PV is included in the analysis. A formula for the fluid that moves between the two porosities is developed. The analysis showed the coupling of the two porosities and their influence on each other and concluded that the PV pore pressure has an influence less than 3% on the PLC pore pressure while the absence of the PV pore pressure will affect the fluid exchange between the PV and PLC by less than 6% (the blood pressure range is 40–60 mmHg). Also the analysis has shown that the draining time of the PLC is inversely proportional to its permeability. The significance of the result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells.

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Research paper thumbnail of The Anisotropic Elastic Constants of Cancellous Bone

Key Engineering Materials, 2001

... van Rietbergen, A. Odgaard, R. Huiskes, R. and S. С Cowin: The Anisotropic Hooke's Law f... more ... van Rietbergen, A. Odgaard, R. Huiskes, R. and S. С Cowin: The Anisotropic Hooke's Law for Cancellous Bone and Wood, J. Elasticity, 53, (1999) 125-146. ... [4] WK Thomson (Lord Kelvin), Elasticity, In: Encyclopaedia Britannica, Adam and Charles Black, Edinburgh (1878). ...

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Research paper thumbnail of Structural Change in Living Tissues

Meccanica, 1999

Tissues change in many ways in the period that they are part of a living organism. Tissues are cr... more Tissues change in many ways in the period that they are part of a living organism. Tissues are created in fairly repeatable structural patterns, and 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 also the methods of tissue construction. When the tissue structure is altered to accommodate a new loading, it is not known how the decision is made for the structural reconstruction. We 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. Beyond the objective is the hope that the work will stimulate new ideas and new observations in developmental biology.

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

Biomechanics and Modeling in Mechanobiology, 2005

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by connected... more 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.

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Research paper thumbnail of Fabric dependence of wave propagation in anisotropic porous media

Biomechanics and Modeling in Mechanobiology, 2011

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral d... more Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric—a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

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Research paper thumbnail of In Response to “Mixing Mechanisms and Net Solute Transport in Bone” by M. L. Knothe Tate

Annals of Biomedical Engineering, 2001

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Research paper thumbnail of Experimental Determination of the Permeability in the Lacunar-Canalicular Porosity of Bone

Journal of Biomechanical Engineering-transactions of The Asme, 2009

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Research paper thumbnail of Preface on Physicochemical and Electromechanical Interactions in Porous Media

Transport in Porous Media, 2003

The focus of science and engineering shifts towards smaller length scales. Porous media mechanics... more The focus of science and engineering shifts towards smaller length scales. Porous media mechanics has a vital role to play in the translation of microstructural data into macroscopic models of multicomponent systems. As the length scales shrink, more fundamental levels of understanding of natural laws, cause the boundaries between disciplines to blur. In particular, geosciences, polymer sciences and biosciences find a common ground of interest in high specific surface mixtures.

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Research paper thumbnail of Study of Site-Specific Bone Formation Using a Neural Network Model

ABSTRACT

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Research paper thumbnail of The elastic moduli estimation of the solid-water mixture

International Journal of Solids and Structures, 2009

Conceptually, the undrained elastic constants estimated by the poroelasticity theory should be id... more Conceptually, the undrained elastic constants estimated by the poroelasticity theory should be identical to the effective moduli of the two-phase composite of a porous material saturated with pore water. Here we show numerically that the undrained elastic constants determined by an effective moduli estimate are almost identical with those calculated by poroelasticity theory, and if pore shapes are not exactly known and the porosity is around 50%, estimating the elastic constant as the average value of its Voigt and Reuss bounds is reasonably accurate. This is the situation in bone and dentin, the materials that are our primary intended application. This result will hold for situations in which the totally enclosed water phase is constrained to small deformations by virtue of its confinement. Importantly, in this work we assume that water is an isotropic elastic solid with a shear modulus that is 10−4 times the bulk modulus of the water. Note that it is compressible, but almost incompressible with a Poisson’s ratio of 0.4999.

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Research paper thumbnail of Remarks on Coaxiality of Strain and Stress in Anisotropic Elasticity

Journal of Elasticity, 1997

Two different consequences of the problem of the extremization of the strain energy by varying th... more Two different consequences of the problem of the extremization of the strain energy by varying the orientation of the material symmetry axes relative to the principal axes of stress are discussed. These two different consequences depend upon whether the stress state is considered as arbitrary and general or as fixed and specific.

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Research paper thumbnail of Analysis of avian bone response to mechanical loading—Part One: Distribution of bone fluid shear stress induced by bending and axial loading

Biomechanics and Modeling in Mechanobiology, 2005

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by a bone-co... more Mechanical loading-induced signals are hypothesized to be transmitted and integrated by a bone-connected cellular network (CCN) before reaching the bone surfaces where adaptation occurs. Our objective is to establish a computational model to explore how bone cells transmit the signals through intercellular communication. In this first part of the study the bone fluid shear stress acting on every bone cell in a CCN is acquired as the excitation signal for the computational model. Bending and axial loading-induced fluid shear stress is computed in transverse sections of avian long bones for two adaptation experiments (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). The computed fluid shear stress is found to be correlated with the radial strain gradient but not with bone formation. These results suggest that the radial strain gradient is the driving force for bone fluid flow in the radially distributed lacunar-canalicular system and that bone formation is not linearly related to the loading-induced local stimulus.

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Research paper thumbnail of The unconfined compression of a poroelastic annular cylindrical disk

Mechanics of Materials, 2008

The analytical solution to the problem of a saturated annular poroelastic disk subjected to uncon... more The analytical solution to the problem of a saturated annular poroelastic disk subjected to unconfined compression in the case when the fluid and solid constituents of the poroelastic medium are both compressible is recorded. Infinitesimal deformations and transverse isotropy are assumed. The algebraic complexity of the problem stems from the need to have the solution to the problem for three different sets of boundary drainage conditions on fluid flow or no flow through the inner and outer boundaries of the annular disk. The analytical solution demonstrates the effects of the assumptions of isotropy versus transverse isotropy and compressibility versus incompressibility of the poroelastic constituents. The advantages of this solution are that they provide insight into the nature of the elastic response and fluid flow of soft tissues versus hard tissues and saturated swampy soils versus saturated rocks and as an analytical tool to analyze unconfined compression experiments performed on these materials.

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Research paper thumbnail of The significance of bone microstructure in mechanotransduction

Journal of Biomechanics, 2007

Recent developments in modeling the relationship between bone microstructure and mechanotransduct... more Recent developments in modeling the relationship between bone microstructure and mechanotransduction are reviewed. The focus is on the relationship between the bone microstructure and the mechanosensation mechanism by which osteocytes sense the bone fluid motion propelled by the mechanical loading of the whole bone.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An estimate of anisotropic poroelastic constants of an osteon

Biomechanics and Modeling in Mechanobiology, 2008

The anisotropic poroelastic constants of an osteon are estimated by micromechanical analysis. Two... more The anisotropic poroelastic constants of an osteon are estimated by micromechanical analysis. Two extreme cases are examined, the drained and the undrained elastic constants. The drained elastic constants are the porous medium’s effective elastic constants when the fluid in the pores easily escapes and the pore fluid can sustain no pore pressure. The undrained elastic constants are the porous medium’s effective elastic constants when the medium is fully saturated with pore fluid and the fluid cannot escape. The drained and undrained elastic constants at the lacunar and canalicular porosity tissue levels are estimated by using an effective moduli model consisting of the periodic distribution of ellipsoidal cavities. These estimated anisotropic poroelastic constants provide a database for the development of an accurate anisotropic poroelastic model of an osteon.

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