In memory of

# Stephen CowinSan Diego State University | SDSU · Department of Mechanical Engineering

Stephen Cowin

PhD

## About

299

Publications

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Introduction

Stephen Cowin currently works at the Department of Mechanical Engineering, San Diego State University. Stephen does research in Bioengineering and Mechanical Engineering. Their most recent publication is 'Trabecular Microarchicture Predicts Fabric Tensor and Anisotropic Mechanical Behavior of Trabecular Bone in Compression and Shear..'

## Publications

Publications (299)

This work focuses on the Lacunar–Canalicular Porosity (PLC) of cortical bone which includes the osteons. Osteons are semicylindrical porous structures saturated with fluid within the bone and are approximately 250[Formula: see text][Formula: see text]m in diameter. The outer boundary of the osteon is called the cement line. Some studies suggested t...

The multiple definitions of permeability and tortuosity employed by investigators modifying the basic equations of dynamic poroelasticity pose a problem as some resulting analyses produce results conflicting with those of other investigators. When the same words are used to describe different definitions of different concepts, the problem is compou...

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar-canalicular permeability [Formula: see text] in bone. The interest in the permeability of the lacunar-canalicular pore system (LCS) is due t...

“The perfectly elastic material is a particular kind of ideal material. It has a single preferred or natural configuration. We think a portion of this material in a certain configuration with material coordinates X, which we choose as specifying the reference configuration. However this material is deformed, into whatever configuration it is brough...

The theme for this chapter is contained in a quote from the 1941 paper of M. A. Biot that clearly describes an RVE: “Consider a small cubic element of soil, its sides being parallel with the coordinate axes. This element is taken to be large enough compared to the size of the pores so that it may be treated as homogeneous, and at the same time smal...

The theme for this chapter is contained in a quote from Truesdell and Noll’s volume on the Non-Linear Field Theories of Mechanics: “The general physical laws in themselves do not suffice to determine the deformation or motion of. an object. subject to given loading. Before a determinate problem can be formulated, it is usually necessary to specify...

Continuum mechanics deals with idealized materials consisting of material points and material neighborhoods. It assumes that the material distribution, the stresses, and the strains within an infinitesimal material neighborhood of a typical particle (or a material element) can be regarded as essentially uniform. On the microscale, however, the infi...

The variation of material properties with respect to direction at a fixed point in a material is called material symmetry.

The modern theory of the motion of the water in the soil based on Darcy’s law does not take into account the fact that the particles of the soil can be elastically compressed and extended, assuming that the external forces and the hydrostatic pressure act on the liquid filling these pores only. This simplifying assumption necessitates a correction...

This work focuses on the Lacunar Canalicular Porosity (PLC) of cortical bone which includes the osteons. Osteons are semi-cylindrical, porous structures saturated with fluid within the bone and are approximately 250 micrometers in diameter. Their outer boundary is called the cement line. The first objective of this work is to introduce an experimen...

In this study, the local variability of microarchitecture of human trabecular calcaneus bone is investigated using high-resolution microCT scanning. Our results show that strong correlation exists between most scalar architectural parameters and volumetric bone mineral density (vBMD). However, no statistical correlation was found between vBMD and t...

The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are to be applied to the problem of determining the exchange of pore fluid between the vascular porosity and the lacunar-canalicular porosity in bone tis...

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-dependen...

Propagation of two waves (fast and slow) in trabecular bone has been reported by several laboratories around the world. This is an unequivocal signature of poroelastic wave propagation accordingly to Biot's theory. Velocity and attenuation of fast and slow waves in Biot's poroelasticity theory depend on the porosity, physical properties of the soli...

Current theoretical and experimental evidence suggests that the sensory bone cells are activated by the induced drag from fluid flowing through the lacunar-canalicular porosity (PLC). One of the most important parameters of the interstitial fluid flow is the PLC permeability. However, the reported measurements of this permeability span over eight o...

Biot's theory of wave propagation in porous media predicts the genesis of two waves (fast and slow) due to the in-phase and out-of-phase motion of the solid and fluid constituents of the porous medium. In Biot's theory, the loss of energy (attenuation) of both fast and slow waves is modeled to occur due to absorption and dispersion processes. Howev...

The relationship between the macro- and microvelocity fields in a poroelastic representative volume element (RVE) has not being fully investigated. This relationship is considered to be a function of the tortuosity: a quantitative measure of the effect of the deviation of the pore fluid streamlines from straight (not tortuous) paths in fluid-satura...

Continuum Mechanics of Anisotropic Materials(CMAM) presents an entirely new and unique development of material anisotropy in the context of an appropriate selection and organization of continuum mechanics topics. These features will distinguish this continuum mechanics book from other books on this subject. Textbooks on continuum mechanics are wide...

This contribution presents an alternative approach to mixture theory-based poroelasticity by transferring some poroelastic concepts developed by Biot to mixture theory. These concepts are a larger RVE and the subRVE-RVE velocity average tensor, which Biot called the micro-macro velocity average tensor. This velocity average tensor is assumed here t...

The theme of this chapter was stated with exuberance and in an idealistic deterministic extreme by Marquis Pierre-Simon de Laplace (1759–1827): “Thus, we must consider the present state of the universe as the effect of its previous state and as the cause of those states to follow. An intelligent being which, for a given point in time, knows all the...

The typical types of models that have been employed in the analysis of the mechanical behavior of material objects are described in this chapter. Specifically, descriptions of the various model types employed in mechanics, namely the particle model, the rigid object model, the deformable continuum model, and the lumped parameter model are described...

The theme for this chapter is captured by a quote from Herbert Callen’s book (Callen 1960) on thermodynamics. Callen introduces the conservation of energy and the concept of internal energy in the following paragraph: “The development of the principle of conservation of energy has been one of the most significant achievements in the evolution of ph...

The decisive word in this postulate is the quantifier all it makes the postulate a restrictive condition on the internal constitutive assumptions that can be imposed on systems of the type under consideration.

Four linear theories are considered in this chapter. Each has a distinctive and interesting history. Each one of the theories was originally formulated between 1820 and 1860. Representative of the theme of this chapter are the opening lines of the Historical Introduction in A. E. H. Love’s Theory of Elasticity (original edition, 1892): “The Mathema...

The local variability of microarchitecture of human trabecular calcaneus bone is investigated using high resolution microCT scanning. The fabric tensor is employed as the measure of the microarchitecture of the pore structure of a porous medium. It is hypothesized that a fabric tensor-dependent poroelastic ultrasound approach will more effectively...

The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of th...

Skeletal muscle is widely perceived as nearly incompressible despite the fact that blood and lymphatic vessels within the endomysial and perimysial spaces undergo significant changes in diameter and length during stretch and contraction. These fluid shifts between fascicle and interstitial compartments have proved extremely difficult to measure. In...

Ultrasound waves have a broad range of clinical applications as a non-destructive testing approach in imaging and in the diagnoses of medical conditions. Generally, biological tissues are modeled as an homogenized equivalent medium with an apparent density through which a single wave propagates. Only the first wave arriving at the ultrasound probe...

This contribution presents an alternative approach to mixture theory-based poroelasticity by transferring some poroelastic concepts developed by Maurice Biot to mixture theory. These concepts are a larger RVE and the subRVE-RVE velocity average tensor, which Biot called the micro-macro velocity average tensor. This velocity average tensor is assume...

An analytical model for the determination of the permeability in the lacunar-canalicular porosity of bone using cyclic loading is described in this contribution. The objective of the analysis presented is to relate the lacunar-canalicular permeability to a particular phase angle that is measurable when the bone is subjected to infinitesimal cyclic...

The objective of this paper is to show that the different forms of the elasticity or compliance tensors that represent the different linear elastic material symmetries may be obtained by assuming that the strain energy depends on a set of vectors, a different specific set for each of the eight linear elastic material symmetries. This connection per...

This work presents a graphically illustrated version of the Nur-Byerlee-Carroll proof of the formula for the Biot effective
stress coefficient in poroelasticity. The original elegant proof was provided by Nur and Byerlee (J.Geophys. Res. 76:6414,
1971) for isotropic materials and extended by Carroll (J.Geophys. Res. 84:7510–7512, 1979) to anisotrop...

Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to...

The first objective of this review and re-evaluation is to present a brief history of efforts to mathematically model the growth of tissues. The second objective is to place this historical material in a current perspective where it may be of help in future research. The overall objective is to look backward in order to see ways forward. It is note...

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review th...

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...

IntroductionArterial SupplyMicrovascular Network of the Medullary CanalMicrovascular Network of Cortical BoneVenous Drainage of BoneBone Lymphatics and Blood Vessel Trans-Wall TransportThe Levels of Bone Porosity and their Bone InterfacesInterstitial Fluid FlowReferences

Constructing continuum kinematical models of mass increasing biological growth has been the objective of many studies in the last 100 years. The significant features of the successful studies are briefly described, critically reviewed and organized in the contemporary notation of continuum kinematics. While success has been achieved in many kinemat...

With particular interest on total hip arthroplasty (THA), optimization of orthopedic prostheses is employed in this work to minimize the probability of implant failure or maximize prosthesis reliability. This goal is often identified with the reduction of stress concentrations at the interface between bone and these devices. However, aseptic loosen...

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) t...

The governing equations for wave motion in the linear theory of anisotropic poroelastic materials have been developed and extended to include the dependence of the constitutive relations on fabric. Fabric is a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. With the addition of...

The governing equations for wave motion in the linear theory of anisotropic poroelastic materials have been developed and extended to include the dependence of the constitutive relations upon fabric. Fabric is a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This anisotropic po...

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) t...

The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar-canalicular porosity (PLC) in bon...

Permeability of the mineralized bone tissue is a critical element in understanding fluid flow occurring in the lacunar-canalicular porosity (PLC) compartment of bone and its role in bone nutrition and mechanotransduction. However, the estimation of bone permeability at the tissue level is affected by the influence of the vascular porosity in macros...

Determining the poroelastic properties of osteons is critical to better understand the role of fluid flow in the nutrition, mechanotransduction, remodeling, homeostasis and loss of bone. The permeability of single osteons is among the key properties that may influence these phenomena. The measurement of permeability of a single osteon remains one o...

The current gold standard to assess bone loss is the bone mineral density (BMD) test, performed with a dual x-ray absorptiometry system. BMD measurements are highly correlated to bone mass when measured in spine, wrist, and femoral neck. However, the BMD cannot fully explain the decrease in bone strength and the associated risk of fracture because...

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. Fabric is a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. With the addition of the...

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 calculate...

Measurement of the permeability of a single osteon is important to understand the role of interstitial fluid flow and mechanotransduction in osteocytes, the sensory bone cells. The challenges in the measurement of the permeability of a single osteon are the size of the osteon (approximately 250 microns in diameter) and the limitations or absence of...

A poroelastic model for porous materials with nested pore space structures is developed to represent the interstitial fluid flow in bone tissue. It is applied here to solve the unconfined compression problem for an annular, transversely isotropic, poroelastic disk with compressible constituents. Unlike previous computational models, this model prop...

The current gold standard to assess bone loss is the Bone Mineral Density (BMD) test, which is performed with a Dual X-ray Absorptiometry system. BMD measurements are highly correlated to bone mass when measured in spine, wrist and femoral neck. However, the BMD cannot fully explain the decrease in bone strength and the associated risk of fracture...

This contribution is a review of the application of poroelasticity theory to the modeling of the mechanical behavior of bone fluid in living bone tissue. The models reviewed, while seeking to present an accurate representation of the porous architecture of bone tissue, extend classical Biot theory in two distinct new directions associated with the...

Measurement of a permeability of a single osteon is still one of the most demanding tasks in bone mechanics to be solved. The challenges are the size of the osteon and the limitations or absence of the tools that can take a direct measurement. Determining the permeability in an osteon may help to best understand the fluid flow occurring in cortical...

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...

Micromechanical estimates of the elastic constants for a single bone osteonal lamella and its substructures are reported. These estimates of elastic constants are accomplished at three distinct and organized hierarchical levels, that of a mineralized collagen fibril, a collagen fiber, and a single lamella. The smallest collagen structure is the col...

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. T...

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.

The governing equations for the theory of anisotropic poroelastic materials with incompressible constituents undergoing small deformations are developed from the theory of anisotropic poroelastic materials without the constituent incompressibility constraint. The development of the constituent specific incompressibility constraint is accomplished b...

“During the daily activities of life the bones of the skeleton, individually and collectively, are subjected to a variety of force systems. The response of the bones to these systems is a function, to a large extent, of the mechanical properties of the bones. Of course, the type, magnitude, direction, and point of application of the force as well a...

This work is a review of recent advances in the understanding of strain adaptive bone remodeling. The phenomenological theories of surface bone strain adaptation and internal bone strain adaptation are summarized as well as the possible cellular mechanisms for mechanotransduction that occurs in bone tissue adaptation. The phenomenological bone stra...

While interstitial fluid flow is necessary for the viability of osteocytes, it is also believed to play a role in bone's mechanosensory system by shearing bone cell membranes or causing cytoskeleton deformation and thus activating biochemical responses that lead to the process of bone adaptation. However, the fluid flow properties that regulate bon...

In the last decades, new experimental and numerical techniques have taken many advanced features of porous media mechanics down to practical engineering applications. This happened in areas that sometimes were not even suspected to be open to engineering ideas at all. The challenge that often faces engineers in the field of geomechanics, biomechani...

A tissue is a composite material whose constituents, and therefore structure, are continually changing due to growth and response of the tissue to its physical and chemical environment. A tissue's physiochemical environment includes the environment it is presently experiencing and the recent history of that environment. A tissue itself is a collect...

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...

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 s...

Conservation laws and constitutive relations for a density-gradient-dependent viscous fluid as a multipolar continuum obeying an entropy inequality with generalized entropy flux and supply density are considered in this paper. A decomposition of the rate of work of dipolar stress, which reveals the contribution of various parts of this stress to th...

The objective of this paper is to describe a different approach to modeling the material symmetry associated with singularities that can occur in curvilinear anisotropic elastic symmetries. In this analysis, the intrinsic non-linearity of a cylindrically anisotropic problem is demonstrated. We prove that a simple homogenization process applied to a...

Experimentally based isotropic tensile and compressive strain yield criteria for cancellous bone are shown to imply tensile and compressive stress yield criteria, respectively. In particular, it is deduced that the directional variation of uniaxial yield stress is proportional to the one of Young's modulus. The obtained tensile and compressive stre...

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...

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 adapta...

Introduction Interstitial fluid mechanical behavior in bone has received little attention by itself. Fluid flow phenomena occur at a smaller scale than pores. Physical phenomena that do not influence macroscopic flow could be of interest at the microscopic scale for their interaction with cells membrane. Thus, physical phenomena need to be describe...

In the last decades, new experimental and numerical techniques have taken many advanced features of porous media mechanics down to practical engineering applications. This happened in areas that sometimes were not even suspected to be open to engineering ideas at all. The challenge that often faces engineers in the field of geomechanics, biomechani...

A paradox in bone tissue is that tissue-level strains due to animal and human locomotion are too small to initiate intracellular chemical responses directly. A model recently was proposed to resolve this paradox, which predicts that the fluid flow through the pericellular matrix in the lacunar-canalicular porosity due to mechanical loading can indu...

In this paper, we present a theorem that provides solutions for anisotropic and inhomogeneous elastostatic problems by using the known solution of an associated anisotropic and homogeneous problem if the associated problem has a stress state with a zero eigenvalue everywhere in the domain of the problem. The fundamental property on which this stres...

A representation of anisotropic poroelasticity is derived in which the drained and undrained elastic compliance constants, as well as the permeability tensor, are expressed as functions of the fabric tensor. The fabric tensor employed is a quantitative stereological measure of the anisotropy of the structure of the pores in the porous medium. It is...

Osteocytes are believed to be the mechanical sensor cells in bone. One potential physical mechanism for the mechanosensing process is that osteocytes directly sense the deformation of the substrate to which they are attached. However, there is a fundamental paradox in this theory: tissue-level strains in whole bone are typically <0.2%, yet an exten...

The hypothesis that analogues to liquid crystal flow processes occur in the supramolecular self-assembly processes of living biological tissues is reviewed.

The growth and remodeling of a tissue depends on certain features in the history of its mechanical environment as well as its genetic makeup. The mechanical environment influences the tissue's developing morphology, the process of simply increasing the size of existing morphological structures, and the formation of the proteins of which the tissue...

This paper addresses the question of whether or not interstitial fluid flow due to the blood circulation accounts for the observed periosteal bone formation associated with comprised venous return (venous stasis). Increased interstitial fluid flow induced by increased intramedullary pressure has been proposed to account for the periosteal response...

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. Thes...

We tested the hypothesis that fluid shear stress (tau) modifies the expression, function, and distribution of junctional proteins [connexin (Cx)43, Cx45, and zona occludens (ZO)-1] in cultured bone cells. Cell lines with osteoblastic (MC3T3-E1 cells) and osteocytic (MLO-Y4 cells) phenotypes were exposed to tau-values of 5 or 20 dyn/cm(2) for 1-3 h....

While it is demonstrated here that the symmetry plane classification criteria and the symmetry group classification criteria are equivalent in the case of symmetric second order tensors, it is also demonstrated that the two classification criteria are not equivalent in the case of asymmetric second order tensors.

The equations associated with the theory of anisotropic poroelastic materials undergoing small deformations are recast in a matrix notation where the matrices are composed of proper tensor components. Using this notation the compatibility conditions on the components of the strain tensor are expressed in terms of the stress tensor, the pore pressur...

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 bl...

The topic considered is the close connection between computational bone adaptation -to mechanical loading and structural optimization. An open mathematical problem connecting computational bone adaptation based on local surface adaptation rules and global structural-optimization methods is described. Bone adaptation to mechanical loading The remode...