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.     

Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.     

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.     

Mechanosensation and fluid transport in living bone

The mechanosensory mechanisms in bone include (i) the cell system that is stimulated by external mechanical loading applied to the bone; (ii) the system that transduces that mechanical loading to a communicable signal; and (iii) the systems that transmit that signal to the effector cells for the maintenance of bone homeostasis and for strain adaptation of the bone structure. The effector cells are the osteoblasts and the osteoclasts. These systems and the mechanisms that they employ have not yet been unambiguously identified. The candidate systems will be reviewed. It will be argued that the current theoretical and experimental evidence suggests that osteocytes are the principal mechanosensory cells of bone, that they are activated by shear stress from fluid flowing through the osteocyte canaliculi, and that the electrically coupled three-dimensional network of osteocytes and lining cells is a communications system for the control of bone homeostasis and structural strain adaptation. The movement of bone fluid from the region of the bone vasculature through the canaliculi and the lacunae of the surrounding mineralized tissue accomplishes three important tasks. First, it transports nutrients to the osteocytes in the lacunae buried in the mineralized matrix. Second, it carries away the cell waste. Third, the bone fluid exerts a force on the cell process, a force that is large enough for the cell to sense. This is probably the basic mechanotransduction mechanism in bone, the way in which bone senses the mechanical load to which it is subjected. The mechanisms of bone fluid flow are described with particular emphasis on mechanotransduction. Also described is the cell to cell communication by which higher frequency signals might be transferred, a potential mechanism in bone by which the small whole tissue strain is amplified so the bone cells can respond to it. One of the conclusions is that higher frequency low amplitude strains can maintain bone as effectively as low frequency high amplitude strains. This conclusion leads to a paradigm shift in how to treat osteoporosis and how to cope with microgravity.     

Function of osteocytes in bone

Although the structural design of cellular bone (i.e., bone containing osteocytes that are regularly spaced throughout the bone matrix) dates back to the first occurrence of bone as a tissue in evolution, and although osteocytes represent the most abundant cell type of bone, we know as yet little about the role of the osteocyte in bone metabolism. Osteocytes descend from osteoblasts. They are formed by the incorporation of osteoblasts into the bone matrix. Osteocytes remain in contact with each other and with cells on the bone surface via gap junction–coupled cell processes passing through the matrix via small channels, the canaliculi, that connect the cell body–containing lacunae with each other and with the outside world. During differentiation from osteoblast to mature osteocyte the cells lose a large part of their cell organelles. Their cell processes are packed with microfilaments. In this review we discuss the various theories on osteocyte function that have taken in consideration these special features of osteocytes. These are (1) osteocytes are actively involved in bone turnover; (2) the osteocyte network is through its large cell-matrix contact surface involved in ion exchange; and (3) osteocytes are the mechanosensory cells of bone and play a pivotal role in functional adaptation of bone. In our opinion, especially the last theory offers an exciting concept for which some biomechanical, biochemical, and cell biological evidence is already available and which fully warrants further investigations. © 1994 Wiley-Liss, Inc.     

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.     

Measurement of microstructural strain in cortical bone

It is well known that mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Current theories suggest that bone modeling and remodeling is controlled at the cellular level through signals mediated by osteocytes. The objective of this study was to investigate how macroscopically applied bone strains similar in magnitude to those that occur in vivo are manifest at the microscopic level in the bone matrix. Using a digital image correlation strain measurement technique, experimentally determined bone matrix strains around osteocyte lacuna resulting from macroscopic strains of approximately 2,000 microstrain (0.2%) reach levels of over 30,000 microstrain (3%) over fifteen times greater than the applied macroscopic strain. Strain patterns were highly heterogeneous and in some locations similar to observed microdamage around osteocyte lacuna indicating the resulting strains may represent the precursors to microdamage. This information may lead to a better understanding of how bone cells are affected by whole bone functional loading.     

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.     

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.     

Osteocyte-osteoclast morphological relationships and the putative role of osteocytes in bone remodeling

An osteocyte lacunae differential count under the light microscope (LM) (1-lacunae with live osteocytes, 2-empty lacunae and lacunae with degenerating osteocytes) was carried out outside the reversal lines of osteonic lamellar bone from various mammals and man to evaluate the possibility of osteocyte survival where osteoclast resorption had occurred. The polarized light microscope (PLM) was used to establish the curvature of bony lamellae outside the convexity of reversal lines: concave lamellae indicate osteocytes reabsorbed on their vascular side where they radiate long vascular dendrites; convex lamellae indicate bone resorption on the osteocyte mineral side, radiating short dendrites. In all samples it was found that: a) about 60% of osteocytes outside the reversal lines were live; b) the percentage of alive osteocytes close to reversal lines is higher when they are attacked on their mineral side. The present data support our view that surviving osteocytes, particularly those attacked from their mineral side, might intervene in the final phase of bone resorption (osteoclast inhibition?). The fact that under the transmission electron microscope (TEM) intercellular contacts were never observed between osteocytes and osteoclasts indicates that if a modulation should occur between these two cellular types it could take place by a paracrine route only. The putative role of the cells of the osteogenic system, particularly osteocytes, in the bone remodeling cycle is also discussed.     

Observations of microdamage around osteocyte lacunae in bone

Tensile microdamage was examined using laser scanning confocal microscopy in beam specimens of bovine, equine and human long bones loaded in vitro and whole specimens of rat ulnae loaded in vivo. Microcracks were observed to initiate frequently at osteocyte lacunae. The implication is that osteocyte lacunae act as stress concentrating features in bone. This association provides a potential mechanism for the detection of strain and/ or damage by osteocytes in bone.     

Uptake of horseradish peroxidase by bone cells during endochondral bone development

Summary To investigate the mechanisms whereby bone cells absorb organic bone-matrix components during endochondral bone development, rat humeri were examined, employing horseradish peroxidase as a soluble protein tracer.Intravenously-injected peroxidase filled the osteoid layer and penetrated into the osteocyte lacunae and canaliculi, but did not enter the mineralized bone matrix. Whereas osteocytes rarely took up exogenous peroxidase, osteoblasts and osteoclasts actively endocytosed peroxidase in pinocytotic coated vesicles, tubular structures, and vacuoles. They also formed endocytotic vacuoles containing peroxidase in the Golgi area. The Golgi apparatus and dense bodies of these bone cells were, however, free of reaction products. Osteoclast ruffled borders were responsible for peroxidase absorption. In the osteoblast, osteocyte and osteoclast, endogenous peroxidatic reaction was detected only in mitochondria and not in other membrane-bounded vesicles and bodies. These results strongly suggest that both osteoblasts and osteoclasts participate in the resorption of bone-matrix organic components during bone remodelling.     

Matrix mineralization as a trigger for osteocyte maturation.

The morphology of the osteocyte changes during the cell's lifetime. Shortly after becoming buried in the matrix, an osteocyte is plump with a rich rough endoplasmic reticulum and a well-developed Golgi complex. This "immature" osteocyte reduces its number of organelles to become a "mature" osteocyte when it comes to reside deeper in the bone matrix. We hypothesized that mineralization of the surrounding matrix is the trigger for osteocyte maturation. To verify this, we prevented mineralization of newly formed matrix by administration of 1-hydroxyethylidene-1,1-bisphosphonate (HEBP) and then examined the morphological changes in the osteocytes in rats. In the HEBP group, matrix mineralization was disturbed, but matrix formation was not affected. The osteocytes found in the unmineralized matrix were immature. Mature osteocytes were seen in the corresponding mineralized matrix in the control group. The immature osteocytes in the unmineralized matrix failed to show immunoreactivity with anti-sclerostin antibody, whereas mature osteocytes in the mineralized matrix showed immunoreactivity in both control and HEBP groups. These findings suggest that mineralization of the matrix surrounding the osteocyte is the trigger for cytodifferentiation from a plump immature form to a mature osteocyte. The osteocyte appears to start secreting sclerostin only after it matures in the mineralized bone matrix.     

Biochemical and immunocytochemical characterization of mineral binding proteoglycans in rat bone

We examined biochemically and immunocytochemically the type and distribution of mineral binding proteoglycans (PGs) in rat mid-shaft subperiosteal bone using three monoclonal antibodies (MAb 1-B-5, 9-A-2, and 3-B-3) which specifically recognize unsulfated chondroitin, chondroitin 4-sulfate (C4-S) and dermatan sulfate (DS), and chondroitin 6-sulfate. Bone proteins were extracted from fresh specimens with a three-step technique: 4 M guanidine HCl (GdnCl), aqueous EDTA without GdnCl (E-extract), followed by GdnCl. Western blot analysis of SDS-polyacrylamide gel electrophoresis revealed that E-extract after chondroitinase ABC digestion reacted strongly with MAb 9-A-2 but not with MAb 1-B-5 or 3-B-3. After adehyde fixation, ethanolic trimethylammonium EDTA was used as a demineralizing agent for light and electron immunocytochemistry. This provided good retention of water-soluble PGs in the specimens. After chondroitinase ABC pre-treatment of tissue sections, MAb 9-A-2 specifically stained C4-S and/or DS in the walls of osteocyte lacunae and bone canaliculi in the mineralized matrix as well as in the unmineralized matrix such as pre-bone, vascular canals, and pericellular matrix surrounding osteocytes; the remainder of the mineralized matrix lacked staining. These results indicate that mineral binding PGs contain C4-S and/or DS and are exclusively localized in the walls of the bone lacuna and canaliculus.     

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.

     

The role of osteocytes in bone regulation: mineral homeostasis versus mechanoreception

Early work on the role of osteocytes in bone regulation suggested that the primary function of these cells was osteolysis. This lytic function was not precisely defined but included mineral homeostasis and at least the initiation of matrix remodeling, if not a primary role in remodeling. This paper is an attempt to promote the concept of osteocytic osteolysis as a method of systemic mineral homeostasis and to separate it from bone remodeling. Although recent investigations have pointed to mechanotransduction as a primary function of osteocytes, resulting in a general abandonment of the osteocytic osteolysis concept, the corpus of evidence suggests that osteocytes likely have a multipurpose role in the biology of bone. The osteocyte network represents an enormous surface area over which the cells interface with the surrounding matrix, useful for both strain detection and matrix mineral access. Osteocytes have been found to possess receptors for PTH, a known regulator of mineral ion homeostasis. Cultured osteocytes placed on dentin slices demonstrated no capacity to pit the dentin, but they were not treated with a regulating factor such as PTH, nor does mineral homeostasis require substantial bone volume removal. Scaling relationships suggest that osteocyte density is inversely proportional to body mass, R(2) = 0.86, and thus directly proportional to metabolic rate. Thus, species with higher metabolic rates (and therefore a greater demand for immediate access to minerals) have more osteocytes per bone volume. Finally, osteocytes express molecules typically associated with nerve cells and which are involved with glutamate neurotransmission. By this system, almost instantaneous messages may be transmitted throughout the network, an important feature in cells whose homeostatic function would be utilized on a scale of seconds, rather than hours or days. Experimental procedures for determining the role of the osteocyte in mineral homeostasis would require calcium mobilization from the bone matrix on a relatively immediate time scale. The experimental procedure would then be coupled with a high resolution histomorphometric analysis of lacunar radiographic area and mineral density. Added to this would be an in vitro study of mineral activation capacity via cultured osteocytes treated with PTH. Osteocytic osteolysis would be confirmed by an increase in the demineralized volume of osteocytic lacunae and the identification of a chemical mechanism by which osteocytes can readily access the mineral portion of their immediate bone matrix. It should also be true that a reverse capacity exists by which osteocytes can remineralize their immediate matrix utilizing alkaline phosphatase for example, a chemical which they, like osteoblasts, are known to generate. It is thus proposed that osteocytes are both mechanoreceptors and systemic mineral homeostasis regulators.     

Fluid flow in the osteocyte mechanical environment: a fluid–structure interaction approach

Osteocytes are believed to be the primary sensor of mechanical stimuli in bone, which orchestrate osteoblasts and osteoclasts to adapt bone structure and composition to meet physiological loading demands. Experimental studies to quantify the mechanical environment surrounding bone cells are challenging, and as such, computational and theoretical approaches have modelled either the solid or fluid environment of osteocytes to predict how these cells are stimulated in vivo. Osteocytes are an elastic cellular structure that deforms in response to the external fluid flow imposed by mechanical loading. This represents a most challenging multi-physics problem in which fluid and solid domains interact, and as such, no previous study has accounted for this complex behaviour. The objective of this study is to employ fluid–structure interaction (FSI) modelling to investigate the complex mechanical environment of osteocytes in vivo. Fluorescent staining of osteocytes was performed in order to visualise their native environment and develop geometrically accurate models of the osteocyte in vivo. By simulating loading levels representative of vigorous physiological activity ( $3,000\,\upmu \upvarepsilon $ compression and 300 Pa pressure gradient), we predict average interstitial fluid velocities $(\sim 60.5\,\upmu \text{ m/s })$ and average maximum shear stresses $(\sim 11\, \text{ Pa })$ surrounding osteocytes in vivo. Interestingly, these values occur in the canaliculi around the osteocyte cell processes and are within the range of stimuli known to stimulate osteogenic responses by osteoblastic cells in vitro. Significantly our results suggest that the greatest mechanical stimulation of the osteocyte occurs in the cell processes, which, cell culture studies have indicated, is the most mechanosensitive area of the cell. These are the first computational FSI models to simulate the complex multi-physics mechanical environment of osteocyte in vivo and provide a deeper understanding of bone mechanobiology.     

Comparison of strain measurement in the mouse forearm using subject-specific finite element models,strain gaging,and digital image correlation

Mechanical loading in bone leads to the activation of bone-forming pathways that are most likely associated with a minimum strain threshold being experienced by the osteocyte. To investigate the correlation between cellular response and mechanical stimuli, researchers must develop accurate ways to measure/compute strain both externally on the bone surface and internally at the osteocyte level. This study investigates the use of finite element (FE) models to compute bone surface strains on the mouse forearm. Strains from three FE models were compared to data collected experimentally through strain gaging and digital image correlation (DIC). Each FE model was assigned subject-specific bone properties and consisted of one-dimensional springs representing the interosseous membrane. After three-point bending was performed on the ulnae and radii, moment of inertia was determined from microCT analysis of the bone region between the supports and then used along with standard beam analyses to calculate the Young’s modulus. Non-contact strain measurements from DIC were determined to be more suitable for validating numerical results than experimental data obtained through conventional strain gaging. When comparing strain responses in the three ulnae, we observed a 3–14% difference between numerical and DIC strains while the strain gage values were 37–56% lower than numerical values. This study demonstrates a computational approach for capturing bone surface strains in the mouse forearm. Ultimately, strains from these macroscale models can be used as inputs for microscale and nanoscale FE models designed to analyze strains directly in the osteocyte lacunae.