Bone canaliculus endings in the area of the osteocyte lacuna. Electron-microscopic studies.

Light- and electron-microscopic studies were carried out on the bone canaliculi and their endings in the wall fo the osteocyte lacuna. Two types of canalicular endings were distinguished in the lacuna wall. Those of the first type, fairly numerous, are the endings of small diameter, which do not branch off in the immediate proximity of the lacuna. The other type, occurring in twos or threes, are large in diameter and branch off in the close vicinity of the lacuna, invariably possessing two or three processes which run up to the point of branching of the canaliculus. The images obtained made it possible to demonstrate that the collagen fibrils in both types of endings in the lacuna wall are, in principle, arranged in a similar manner. Nonethless, the type of end formation found where the fibrils run along the axis of the lacuna differs from that for the fibrils in a plexus.     

Metabolic pathways of the fossil dinosaur bones Part II. Vascular canal in the communication system

Examination was made on the fossil dinosaur bone 80 million years old. Samples to be examined were prepared by specially elaborated methods. The vascular canal of the dinosaur bone was the object of study. The microscopic and ultrastructural images of the canal revealed three zones therein: proper, perivascular, and vascular. The zone proper was formed by the mineralized wall of the canal, the perivascular zone was a space between the proper and the vascular zone, and the vascular zone was made up of the canal contents identified with blood vessels. The perivascular zone contained collagen fibres; moreover, histochemical examinations revealed in it mucopolysaccharides and lipids. In the wall of the vascular canal (zone proper) the outlets of the bone canaliculi departing from the osteocyte lacunae were detected. The endings of these canaliculi were of two kinds: they were either of the same diameter as the rest of the canaliculus (more numerous) or assumed a widening funnel form as the canaliculi reached the vascular canal (less numerous). By analogy with modern bone appropriate functions may be ascribed to particular zones distinguished in the vascular canal and to the varied endings of the bone canaliculi in the system of conveyance of nutrient and conservative elements as well as metabolites.     

Decrease in the osteocyte lacunar density accompanied by hypermineralized lacunar occlusion reveals failure and delay of remodeling in aged human bone

Aging decreases the human femur’s fatigue resistance, impact energy absorption, and the ability to withstand load. Changes in the osteocyte distribution and in their elemental composition might be involved in age‐related bone impairment. To address this question, we carried out a histomorphometric assessment of the osteocyte lacunar distribution in the periosteal and endosteal human femoral cortexes of 16 female and 16 male donors with regard to age‐ and sex‐related bone remodeling. Measurements of the bone mineral density distribution by quantitative backscattered electron imaging and energy dispersive X‐ray analysis were taken to evaluate the osteocyte lacunar mineral composition and characteristics. Age‐dependent decreases in the total osteocyte lacunar number were measured in all of the cases. This change signifies a risk for the bone’s safety. Cortical subdivision into periosteal and endosteal regions of interest emphasized that, in both sexes, primarily the endosteal cortex is affected by age‐dependent reduction in number of osteocyte lacunae, whereas the periosteal compartment showed a less pronounced osteocyte lacunar deficiency. In aged bone, osteocyte lacunae showed an increased amount of hypermineralized calcium phosphate occlusions in comparison with younger cases. With respect to Frost’s early delineation of micropetrosis, our microanalyses revealed that the osteocyte lacunae are subject to hypermineralization. Intralacunar hypermineralization accompanied by a decrease in total osteocyte lacunar density may contribute to failure or delayed bone repair in aging bone. A decreased osteocyte lacunar density may cause deteriorations in the canalicular fluid flow and reduce the detection of microdamage, which counteracts the bone’s structural integrity, while hypermineralized osteocyte lacunae may increase bone brittleness and render the bone fragile.     

Orientation of collagen at the osteocyte lacunae in human secondary osteons

This work characterizes an aspect of human bone micro-structure, pertinent to fracture initiation and arrest. It addresses how the orientation of elementary components proximate to osteocyte lacunae influences secondary osteon micro-biomechanics. New data at the perilacunar region concerning orientation of collagen-apatite, and prior data on collagen orientation outside the perilacunar region, are incorporated in a novel simulation of osteons to investigate how orientation relates to strains and stresses during mechanical testing. The perilacunar region was observed by confocal microscopy within single lamellar specimens, isolated from osteons. The specimens were separated by extinct or bright appearance in transverse section under circularly polarizing light. This is because synchrotron diffraction and confocal microscopy had established that each type, away from the perilacunar region, corresponds to specific dominant collagen orientation (extinct lamellae's dominant collagen forming small angles with the original osteon axis, while the bright lamellae's forms larger angles). Morphometry of serial confocal images of each perilacunar region showed collagen orientation generally following the orientation of canaliculi, circumambiently-perpendicular to the lacuna. The lacunae tilted relative to the lamellar walls were more numerous in extinct than in bright lamella. Their apices were less likely in extinct than bright lamella to show collagen following the canalicular orientation. The simulation of osteocyte lacunae in osteons, under tension or compression loading, supports the hypothesis that collagen orientation affects strains and stresses at the equatorial perilacunar region in conjunction with the presence of the lacuna. We further conjecture that collagen orientation diverts propagation of micro-cracks initiating from apices.     

Multilevel finite element modeling for the prediction of local cellular deformation in bone

The underlying mechanisms by which bone cells respond to mechanical stimuli or how mechanical loads act on osteocytes housed in lacunae in bone are not well understood. In this study, a multilevel finite element (FE) approach is applied to predict local cell deformations in bone tissue. The local structure of the matrix dictates the local mechanical environment of an osteocyte. Cell deformations are predicted from detailed linear FE analysis of the microstructure, consisting of an arrangement of cells embedded in bone matrix material. This work has related the loads applied to a whole femur during the stance phase of the gait cycle to the strain of a single lacuna and of canaliculi. The predicted bone matrix strains around osteocyte lacunae and canaliculi were nonuniform and differed significantly from the macroscopically measured strains. Peak stresses and strains in the walls of the lacuna were up to six times those in the bulk extracellular matrix. Significant strain concentrations were observed at sites where the process meets the cell body.     

Tissue strain amplification at the osteocyte lacuna: a microstructural finite element analysis

A parametric finite element model of an osteocyte lacuna was developed to predict the microstructural response of the lacuna to imposed macroscopic strains. The model is composed of an osteocyte lacuna, a region of perilacunar tissue, canaliculi, and the surrounding bone tissue. A total of 45 different simulations were modeled with varying canalicular diameters, perilacunar tissue material moduli, and perilacunar tissue thicknesses. Maximum strain increased with a decrease in perilacunar tissue modulus and decreased with an increase in perilacunar tissue modulus, regardless of the thickness of the perilacunar region. An increase in the predicted maximum strain was observed with an increase in canalicular diameter from 0.362 to 0.421 microm. In response to the macroscopic application of strain, canalicular diameters increased 0.8% to over 1.0% depending on the perilacunar tissue modulus. Strain magnification factors of over 3 were predicted. However, varying the size of the perilacunar tissue region had no effect on the predicted perilacunar tissue strain. These results indicate that the application of average macroscopic strains similar to strain levels measured in vivo can result in significantly greater perilacunar tissue strains and canaliculi deformations. A decrease in the perilacunar tissue modulus amplifies the perilacunar tissue strain and canaliculi deformation while an increase in the local perilacunar tissue modulus attenuates this effect.     

Estimation of bone permeability using accurate microstructural measurements

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 bone's adaptive response are poorly understood. In this paper, we present an analytical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity in bone. First, we estimate the total number of canaliculi emanating from each osteocyte lacuna based on published measurements from parallel-fibered shaft bones of several species (chick, rabbit, bovine, horse, dog, and human). Next, we determine the local three-dimensional permeability of the lacunar-canalicular porosity for these species using recent microstructural measurements and adapting a previously developed model. Results demonstrated that the number of canaliculi per osteocyte lacuna ranged from 41 for human to 115 for horse. Permeability coefficients were found to be different in three local principal directions, indicating local orthotropic symmetry of bone permeability in parallel-fibered cortical bone for all species examined. For the range of parameters investigated, the local lacunar-canalicular permeability varied more than three orders of magnitude, with the osteocyte lacunar shape and size along with the 3-D canalicular distribution determining the degree of anisotropy of the local permeability. This two-step theoretical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity will be useful for accurate quantification of interstitial fluid movement in bone.     

High-resolution image-based simulation reveals membrane strain concentration on osteocyte processes caused by tethering elements

Osteocytes are vital for regulating bone remodeling by sensing the flow-induced mechanical stimuli applied to their cell processes. In this mechanosensing mechanism, tethering elements (TEs) connecting the osteocyte process with the canalicular wall potentially amplify the strain on the osteocyte processes. The ultrastructure of the osteocyte processes and canaliculi can be visualized at a nanometer scale using high-resolution imaging via ultra-high voltage electron microscopy (UHVEM). Moreover, the irregular shapes of the osteocyte processes and the canaliculi, including the TEs in the canalicular space, should considerably influence the mechanical stimuli applied to the osteocytes. This study aims to characterize the roles of the ultrastructure of osteocyte processes and canaliculi in the mechanism of osteocyte mechanosensing. Thus, we constructed a high-resolution image-based model of an osteocyte process and a canaliculus using UHVEM tomography and investigated the distribution and magnitude of flow-induced local strain on the osteocyte process by performing fluid–structure interaction simulation. The analysis results reveal that local strain concentration in the osteocyte process was induced by a small number of TEs with high tension, which were inclined depending on the irregular shapes of osteocyte processes and canaliculi. Therefore, this study could provide meaningful insights into the effect of ultrastructure of osteocyte processes and canaliculi on the osteocyte mechanosensing mechanism.

     

A biochemical and immuno-electron microscopical analysis of chondroitin sulphate-rich proteoglycans in human alveolar bone

This study used biochemical and immunohistochemical methods to characterize the chondroitin sulphate-rich proteoglycans from human alveolar bone obtained from an oral source. Proteoglycans were extracted from bone by a sequential 4 m guanidine HCl extraction process, and purified by DEAE-ion exchange chromatography. SDS-PAGE and Western blot analysis, using CS-56 monoclonal antibody, demonstrated one major proteoglycan species with a core protein of 58 kDa, glycosaminoglycan chains of 45--66 kDa and a mean molecular weight of 205 kDa. This work confirmed the biochemistry of chondroitin sulphate-rich proteoglycans from a novel source of adult human alveolar bone, and pointed towards a proteoglycan with a high glutamate, glycine, aspartate, alanine, serine and leucine content. Sections of alveolar bone were embedded in LR White resin, labelled with CS-56 antibody and examined with the light and electron microscopes. At the light microscope level, labelling was restricted to the osteocyte lacunae and canaliculi. Ultrastructural observations showed that the labelling was localized to fine filamentous material in the walls of the osteocytes and canaliculi. Sparse labelling was associated with the collagen fibres immediately subjacent to the lamina limitans, but no labelling of the mineralized matrix was observed. These findings also indicated subtle differences in the distribution of chondroitin sulphate compared with previously reported work, which may indicate species or age differences in the samples used in this study. Ultrastructural analysis confirmed and extended observations of glycosaminoglycan localization at the osteocyte cell membrane of mature human alveolar bone     

Three‐dimensional characterization of osteocyte volumes at multiple scales,and its relationship with bone biology and genome evolution in ray‐finned fishes

Osteocytes, cells embedded within the bone mineral matrix, inform on key aspects of vertebrate biology. In particular, a relationship between volumes of the osteocytes and bone growth and/or genome size has been proposed for several tetrapod lineages. However, the variation in osteocyte volume across different scales is poorly characterized and mostly relies on incomplete, two‐dimensional information. In this study, we characterize the variation of osteocyte volumes in ray‐finned fishes (Actinopterygii), a clade including more than half of modern vertebrate species in which osteocyte biology is poorly known. We use X‐ray synchrotron micro‐computed tomography (SRµCT) to achieve a three‐dimensional visualization of osteocyte lacunae and direct measurement of their size (volumes). Our specimen sample is designed to characterize variation in osteocyte lacuna morphology at three scales: within a bone, among the bones of one individual and among species. At the intra‐bone scale, we find that osteocyte lacunae vary noticeably in size between zones of organized and woven bone (being up to six times larger in woven bone), and across cyclical bone deposition. This is probably explained by differences in bone deposition rate, with larger osteocyte lacunae contained in bone that deposits faster. Osteocyte lacuna volumes vary 3.5‐fold among the bones of an individual, and this cannot readily be explained by variation in bone growth rate or other currently observable factors. Finally, we find that genome size provides the best explanation of variation in osteocyte lacuna volume among species: actinopterygian taxa with larger genomes (polyploid taxa in particular) have larger osteocyte lacunae (with a ninefold variation in median osteocyte volume being measured). Our findings corroborate previous two‐dimensional studies in tetrapods that also observed similar patterns of intra‐individual variation and found a correlation with genome size. This opens new perspectives for further studies on bone evolution, physiology and palaeogenomics in actinopterygians, and vertebrates as a whole.     

Osteocyte lacuna size and shape in women with and without osteoporotic fracture

Osteocytes have been hypothesized to control the amount and location of bone tissue which is resorbed or formed, based on the strain magnitude they perceive, and therefore may play a role in the bone loss of osteoporosis. The shape of osteocyte lacunae influences the mechanical strain applied to the osteocyte; thus, it is important to quantify their shape to further understand the mechanical environment of this cell. Previous studies of the size and shape of lacunae have been contradictory and limited to two-dimensional measurements on iliac crest biopsies. This investigation measured the size and shape of osteocyte lacunae in trabecular bone near a typical fracture site from three-dimensional image sets obtained by confocal microscopy. Bone tissue specimens were obtained from individuals undergoing hip replacement subsequent to fracture, and matched cadaveric specimens without fracture. After extensive image processing to differentiate the lacunae from the matrix, the volume and anisotropy of the lacuna were determined. No significant difference was found in the size (volume) or shape (anisotropy) of the lacunae between women with and without osteoporotic fracture, although there was a large range of sizes and shapes in both groups. These results suggest that the size or shape of the lacunae, which influences the strain in osteocytes, does not play a role in osteoporotic fracture. In addition, this study provides geometric measures of lacunae that are important in computational modeling of the mechanical environment of osteocytes.     

Metabolic pathways of the fossil dinosaur bones. Part III. Intermediary and other osteocytes in the system of metabolic pathways of dinosaur bone

The fossil dinosaur bone material, 80 million years old was studied. Samples for analysis were prepared with specially elaborated methods. Images obtained in the light, transmission electron, and scanning electron microscopes revealed the spatial distribution of the osteocytes lying near and far from the vascular canal. Osteocytes of particular kind were found to be present in the immediate vicinity of the canal. The characteristic morphological structure and the localization of this osteocytes between the vascular canal and the osteocytes lying farther from the canal, as well as the mediation of this cell in the system of connections between those elements, served as a basis for the separation of this cells as the intermediary osteocyte. Among the osteocytes situated farther from the vascular canal, three kinds were distinguished: mono-, bi-, and multipolar, according to the kinds of processes and their distribution in relation to the mother cell body. By analogy with modern bone, in dinosaur bone specific functions may be ascribed to the distinguished types of osteocytes and to their differentiated processes in the conduction of nutrient and building elements and metabolites from the vascular canal to the intermediary osteocytes and, with their participation, to other osteocytes lying farther from the canal. This should naturally be analysed as the two-way tract.     

Strain Concentrations Surrounding an Ellipsoid Model of Lacunae and Osteocytes

Direct cell sensing of tissue matrix strains is one possible signaling mechanism for mechanically mediated bone adaptation. We utilized homogenization theory lo estimate bone tissue matrix strains surrounding osteocytes using two sets of models. The first set of models estimated the strain levels surrounding the lacunae and canaliculi, taking into account variations in lamellar properties. The second set estimated strain levels in the osteocyte and the surrounding matrix for different cellular mechanical properties. The results showed that the strain levels found in and surrounding osteocytes, 1700 to 2700 microstrain (denoted as μe; 1 =.0001% strain), were significantly greater than the trabecular tissue level strains of [1325 μe, 287 μe, 87 μe] used for model input. Variation in lamellar properties did not affect strain levels, except at lamellar boundaries. Strain in and surrounding the osteocyte was not significantly affected by cellular stiffness ranging between 28 and 28,000 Pascals (Pa). Strain levels surrounding lacunae and canaliculi were approximately equivalent.     

Strain Concentrations Surrounding an Ellipsoid Model of Lacunae and Osteocytes

Direct cell sensing of tissue matrix strains is one possible signaling mechanism for mechanically mediated bone adaptation. We utilized homogenization theory to estimate bone tissue matrix strains surrounding osteocytes using two sets of models. The first set of models estimated the strain levels surrounding the lacunae and canaliculi, taking into account variations in lamellar properties. The second set estimated strain levels in the osteocyte and the surrounding matrix for different cellular mechanical properties. The results showed that the strain levels found in and surrounding osteocytes, 1700 to 2700 microstrain (denoted as μe; 1 μe =.0001% strain), were significantly greater than the trabecular tissue level strains of {1325 μe, 287 μe, 87 μe} used for model input. Variation in lamellar properties did not affect strain levels, except at lamellar boundaries. Strain in and surrounding the osteocyte was not significantly affected by cellular stiffness ranging between 28 and 28, 000 Pascals (Pa). Strain levels surrounding lacunae and canaliculi were approximately equivalent.     

Functions of the osteocyte network in the regulation of bone mass

Osteocytes establish an extensive intracellular and extracellular communication system via gap-junction-coupled cell processes and canaliculi throughout bone and the communication system is extended to osteoblasts on the bone surface. The osteocyte network is an ideal mechanosensory system and suitable for mechanotransduction. However, the overall function of the osteocyte network remains to be clarified, since bone resorption is enhanced by osteocyte apoptosis, which is followed by a process of secondary necrosis attributable to the lack of scavengers. The enhanced bone resorption is caused by the release of intracellular content, including immunostimulatory molecules that activate osteoclastogenesis through the canaliculi. Therefore, a mouse model is required in which the osteocyte network is disrupted but in which no bone resorption is induced, in order to evaluate the overall functions of the osteocyte network. One such model is the BCL2 transgenic mouse, in which the osteocyte network, including both intracellular and extracellular networks, is disrupted. Another model is the osteocyte-specific Gja1 knockout mouse, in which intercellular communication through gap junctions is impaired but the canalicular system is intact. Combining the findings from these mouse models with previous histological observations showing the inverse linkage between osteocyte density and bone formation, we conclude that the osteocyte network enhances bone resorption and inhibits bone formation under physiological conditions. Further, studies with BCL2 transgenic mice show that these osteocyte functions are augmented in the unloaded condition. In this condition, Rankl upregulation in osteoblasts and Sost upregulation in osteocytes are, at least in part, responsible for enhanced bone resorption and suppressed bone formation, respectively.     

Canaliculi in the tessellated skeleton of cartilaginous fishes

The endoskeletal elements of sharks and rays are comprised of an uncalcified, hyaline cartilage‐like core overlain by a thin fibro‐ceramic layer of mineralized hexagonal tiles (tesserae) adjoined by intertesseral fibers. The basic spatial relationships of the constituent tissues (unmineralized cartilage, mineralized cartilage, fibrous tissue) are well‐known – endoskeletal tessellation is a long‐recognized synapomorphy of elasmobranch fishes – but a high‐resolution and three‐dimensional (3D) understanding of their interactions has been hampered by difficulties in sample preparation and lack of technologies adequate for visualizing microstructure and microassociations. We used cryo‐electron microscopy and synchrotron radiation tomography to investigate tessellated skeleton ultrastructure but without damage to the delicate relationships between constituent tissues or to the tesserae themselves. The combination of these techniques allowed visualization of never before appreciated internal structures, namely passages connecting the lacunar spaces within tesserae. These intratesseral ‘canaliculi’ link consecutive lacunar spaces into long lacunar strings, radiating outward from the center of tesserae. The continuity of extracellular matrix throughout the canalicular network may explain how chondrocytes in tesserae remain vital despite encasement in mineral. Extracellular fluid exchange may also permit transmission of nutrients, and mechanical and mineralization signals among chondrocytes, in a manner similar to the canalicular network in bone. These co‐adapted mechanisms for the facilitated exchange of extracellular material suggest a level of parallelism in early chondrocyte and osteocyte evolution.     

Morphological differentiation of the fossil dinosaur bone cells. Light, transmission electron-, and scanning electron-microscopic studies.

The investigation was carried out on the fossil dinosaur bone from before 80 million years. Samples for examination were prepared with specially elaborated methods. Thus the isolated osteocytes of the dinosaur bone, which had previously undergone natural fossilizing processes, were obtained. This permitted their morphological assessment. On the basis of the images obtained in the light, transmission electron, and scanning electron microscopes, two types of osteocytes were distinguished. Type I was characterized by an elongated shape, its length exceeding the width several times; the mean dimensions of this osteocyte amounted to 28.8/7.03 micron. Type II was shorter, its mean dimensions being equal to 20.28/6.88 micron. Moreover, two types of osteocytes processes were differentiated: the first was represented by thick processes, so-called 'axial processes', whose diameter ranged from 0.5 to 1.5 micron, and which, as a rule, departed from the pole of the cell. They ran farther from the mother cell body to more distant osteocytes. The other type consisted of thin processes departing from various points of the cell body in no particular arrangement but always extrapolarly. They branched off in a close vicinity of the mother osteocyte. Their diameter ranged between 0.076 and 0.35 micron.     

The osteocyte lineage

The osteocyte resides in the lacuna/canalicular system in bone and has been hypothesized to orchestrate local bone remodeling. Certainly the identification of the osteocyte as the source of Sclerostin, a molecule that regulates osteoblast function, has supported this possibility. As our understanding of this cell increases it has become clear that it has more far reaching influence than simply local bone turnover activity. The osteocyte is also the source of DMP-1 and FGF-23, the later being a hormone that regulates kidney function in terms of phosphate uptake. We now see the osteocyte as having important roles both locally in the skeleton and also in other distant tissues. The study of osteocyte biology has reached a particularly exiting level of maturity and illustrates the value of this cell type as a drug discovery target.     

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells’ metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte’s dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.     

Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue

Bone tissue is a complex multilevel composite which has the ability to sense ad respond to its mechanical environment. It is believed that bone cells called osteocytes within the bone matrix sense the mechanical environment and determine whether structural alterations are needed. At present it is not known, however, how loads are transferred from the whole bone level to cells. A computational procedure combining representative volume element (RVE) based homogenization theory with digital imaging is proposed to estimate strains at various levels of bone structure. Bone tissue structural organization and RVE based analysis are briefly reviewed. The digital image based computational procedure was applied to estimate strains in individual trabeculae (first-level microstructure). Homogenization analysis of an idealized model was used to estimate strains at one level of bone structure around osteocyte lacunae (second-level trabecular microstructure). The results showed that strain at one level of bone structure is amplified to a broad range at the next microstructural level. In one case, a zeor-level tensile principal strain of 495 muE engendered strains ranging between -1000 and 7000 muE in individual trabeculae (first-level microstructure). Subsequently, a first-level tensile principal strains of 1325 muE within an inidividual trabecula engendered strains ranging between 782 and 2530 muE around osteocyte lacunae. Lacunar orientation was found to influence strains around osteocyte lacunae much more than lacunar ellipticity. In conclusion, the computational procedure combining homogenization theory with digital imaging can proveide estimates of cell level strains within whole bones. Such results may be used to bridge experimental studies of bone adaptation at the whole bone and cell culture level. (c) 1994 John Wiley & Sons, Inc.