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A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed.

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. 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.A lthough the endothelial surface glycocalyx was first identified by special electron microscopic staining techniques nearly 40 years ago (1), it is only relatively recently that this surface layer has been observed in vivo (2) and the importance of its multifaceted physiological functions recognized. Key among these functions are its role as a molecular sieve in determining the oncotic forces that are established across microvessel endothelium (3-6), its role as a hydrodynamic exclusion layer preventing the interaction of proteins in the red cell and endothelial cell membranes (7-9), its function in modulating leukocyte attachment and rolling (10) and as a transducer of mechanical forces to the intracellular cytoskeleton in the initiation of intracellular signaling, as proposed herein.It is widely recognized that fluid shearing forces acting on endothelial cells (ECs) have a profound effect on EC morphology, structure, and function (11,12). It is now also clear from theoretical considerations (7,9,13,14) that the shear stress at the edge of the endothelial surface layer is greatly attenuated by the extracellular matrix of proteoglycans and glycoproteins in the glycocalyx, with the result that fluid velocities, except near the edge of the layer, are vanishingly small. Thus, the shear stress due to the fluid flow acting on the apical membrane of the EC itself is negligible. This paradoxical prediction has raised a fundamental question as to how hydrodynamic and mechanical forces, more generally, are transmitted across the structural components of the glycocalyx. How do these components deform under the action of these forces, and how are these forces and deformations communicated to the underlying cortical cytoskeleton (CC)?Little was known about the specific proteins or generalized structure...

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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 Ͻ0.2%, yet an extensive range of in vitro experiments show that dynamic substrate strains must be at least an order of magnitude larger in order for intracellular biochemical responses to occur. Recently, a theoretical model was developed (You et al. J. Biomech., 2001; 34:1375-1386) that provides a possible mechanism by which mechanical loading-induced fluid flow in the lacuno-canalicular system, under routine physical activity, can produce cellular-level strains on the osteocyte processes that are at least one order of magnitude larger than bone tissue deformations. This would resolve the fundamental paradox mentioned above. In this work we experimentally confirm and quantify the essential ultrastructural elements in this model: 1) the presence of the transverse elements that bridge the pericellular space surrounding the osteocyte process, which interact with the fluid flow and lead to an outward hoop tension on the process; and 2) the presence of bundled F-actin in the osteocyte processes, which resists the outward hoop tension and limits the cell process membrane deformation. Morphological data to support these assumptions are scant. Special staining techniques employing ruthenium III hexamine trichloride (RHT) were developed to elucidate these structures in the humeri of adult mice.

A thermomechanical continuum theory involving a chemical reaction and mass transfer between two constituents is developed here as a model for bone remodeling. Bone remodeling is a collective term for the continual processes of growth, reinforcement and resorbtion which occur in living bone. The resulting theory describes an elastic material which adapts its structure to applied loading. ZUSAMMENFASSUNGEine Thermo-mechanische kontinuum Theorie als Modell fiir die Knochenrekonstrucktion wird entwickelt, die eine chemische Reaktion und einen Massentransport zwischen zwei Komponenten behandelt. Knochenrekonstruktion ist ein Sammelbegriff fiJr die kontinuierlichen Prozesse des Wachsens, der Verstiirkung und des Abbaus wie sie im lebenden Knochen auftreten. Die Theorie beschreibt ein elastisches Material, das sich in der Form der Belastung anpasst.

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