Poroelastic finite element analysis of a bone specimen under cyclic loading

Computational modeling based on confocal imaging predicts changes in osteocyte and dendrite shear stress due to canalicular loss with aging

Exercise and physical activity exert mechanical loading on the bones which induces bone formation. However, the relationship between the osteocyte lacunar-canalicular morphology and mechanical stress experienced locally by osteocytes transducing signals for bone formation is not fully understood. In this study, we used computational modeling to predict the effect of canalicular density, the number of fluid inlets, and load direction on fluid flow shear stress (FFSS) and bone strains and how these might change following the microstructural deterioration of the lacunar-canalicular network that occurs with aging. Four distinct computational models were initially generated of osteocytes with either ten or eighteen dendrites using a fluid-structure interaction method with idealized geometries. Next, a young and a simulated aged osteocyte were developed from confocal images after FITC staining of the femur of a 4-month-old C57BL/6 mouse to estimate FFSS using a computational fluid dynamics approach. The models predicted higher fluid velocities in the canaliculi versus the lacunae. Comparison of idealized models with five versus one fluid inlet indicated that with four more inlets, one-half of the dendrites experienced FFSS greater than 0.8 Pa, which has been associated with osteogenic responses. Confocal image-based models of real osteocytes indicated a six times higher ratio of canalicular to lacunar surface area in the young osteocyte model than the simulated aged model and the average FFSS in the young model (FFSS = 0.46 Pa) was three times greater than the aged model (FFSS = 0.15 Pa). Interestingly, the surface area with FFSS values above 0.8 Pa was 23 times greater in the young versus the simulated aged model. These findings may explain the impaired mechano-responsiveness of osteocytes with aging.

Multiscale morphological analysis of bone microarchitecture around Mg-10Gd implants

The utilization of biodegradable magnesium (Mg)-based implants for restoration of bone function following trauma represents a transformative approach in orthopaedic application. One such alloy, magnesium-10 weight percent gadolinium (Mg-10Gd), has been specifically developed to address the rapid degradation of Mg while enhancing its mechanical properties to promote bone healing. Previous studies have demonstrated that Mg-10Gd exhibits favorable osseointegration; however, it exhibits distinct ultrastructural adaptation in comparison to conventional implants like titanium (Ti). A crucial aspect that remains unexplored is the impact of Mg-10Gd degradation on the bone microarchitecture. To address this, we employed hierarchical three-dimensional imaging using synchrotron radiation in conjunction with image-based finite element modelling. By using the methods outlined, the vascular porosity, lacunar porosity and the lacunar-canaliculi network (LCN) morphology of bone around Mg-10Gd in comparison to Ti in a rat model from 4 weeks to 20 weeks post-implantation was investigated. Our investigation revealed that within our observation period, the degradation of Mg-10Gd implants was associated with significantly lower (p < 0.05) lacunar density in the surrounding bone, compared to Ti. Remarkably, the LCN morphology and the fluid flow analysis did not significantly differ for both implant types. In summary, a more pronounced lower lacunae distribution rather than their morphological changes was detected in the surrounding bone upon the degradation of Mg-10Gd implants. This implies potential disparities in bone remodelling rates when compared to Ti implants. Our findings shed light on the intricate relationship between Mg-10Gd degradation and bone microarchitecture, contributing to a deeper understanding of the implications for successful osseointegration.

Computation of physiological loading induced interstitial fluid motion in muscle standardized femur: Healthy vs. osteoporotic bone

BACKGROUND AND OBJECTIVES

Physiological loading-induced mechanical environments regulate bone modeling and remodeling. Thus, loading-induced normal strain is typically considered a stimulus to osteogenesis. However, several studies noticed new bone formation near the sites of minimal normal strain, e.g., the neutral axis of bending in long bones, which raises a question on how bone mass is maintained near these sites. Secondary mechanical components such as shear strain and interstitial fluid flow also stimulate bone cells and regulate bone mass. However, the osteogenic potential of these components is not well established. Accordingly, the present study estimates the distribution of physiological muscle loading-induced mechanical environments such as normal strain, shear strain, pore pressure, and interstitial fluid flow in long bones.

METHODS

A poroelastic finite element muscle standardized femur (MuscleSF) model is developed to compute the distribution of the mechanical environment as a function of bone porosities associated with osteoporotic and disuse bone loss.

RESULTS

The results indicate the presence of higher shear strain and interstitial fluid motion near the minimal strain sites, i.e., the neutral axis of bending of femoral cross-sections. This suggests that secondary stimuli may maintain the bone mass at these locations. Pore pressure and interstitial fluid motion reduce with the increased porosity associated with bone disorders, possibly resulting in diminished skeletal mechano-sensitivity to exogenous loading.

CONCLUSIONS

These outcomes present a better understanding of mechanical environment-mediated regulation of site-specific bone mass, which can be beneficial in developing prophylactic exercise to prevent bone loss in osteoporosis and muscle disuse.

Using Finite Element Modeling in Bone Mechanoadaptation

PURPOSE OF THE REVIEW

Bone adapts structure and material properties in response to its mechanical environment, a process called mechanoadpatation. For the past 50 years, finite element modeling has been used to investigate the relationships between bone geometry, material properties, and mechanical loading conditions. This review examines how we use finite element modeling in the context of bone mechanoadpatation.

RECENT FINDINGS

Finite element models estimate complex mechanical stimuli at the tissue and cellular levels, help explain experimental results, and inform the design of loading protocols and prosthetics. FE modeling is a powerful tool to study bone adaptation as it complements experimental approaches. Before using FE models, researchers should determine whether simulation results will provide complementary information to experimental or clinical observations and should establish the level of complexity required. As imaging technics and computational capacity continue increasing, we expect FE models to help in designing treatments of bone pathologies that take advantage of mechanoadaptation of bone.

On computational predictions of fluid flow and its effects on bone healing in dental implant treatments: an investigation of spatiotemporal fluid flow in cyclic loading

Fluid flow in (porous) bone plays an important role in its maintenance, adaptation, and healing after an injury. Experimental and computational studies apply mechanical loading on bone to predict fluid flow development and/or to find its material properties. In most cases, mechanical loading is applied as a linear function in time. Multiple loading functions-with identical peak load and loading frequency-were used to investigate load-induced fluid flow and predict bone healing surrounding a dental implant. Implementing an instantaneous healing stimulus led to major differences in healing predictions for slightly different loading functions. Load-induced fluid flow was found to be displacement-rate dependent with complex spatial-temporal variations and not necessarily symmetrical during loading and unloading phases. Haversine loading resulted in more numerical stability compared to ramped/triangular loading, providing the opportunity for further investigation of the effects of various physiological masticatory loadings. It was concluded that using the average healing stimulus during cyclic loading gives the most robust bone healing predictions.

Interactive effects of various loading parameters on the fluid dynamics within the lacunar-canalicular system for a single osteocyte

The osteocyte lacunar-canalicular system (LCS) serves as a mechanotransductive core where external loading applied to the skeleton is transduced into mechanical signals (e.g., fluid shear) that can be sensed by mechanosensors (osteocytes). The fluid velocity and shear stress within the LCS are affected by various loading parameters. However, the interactive effect of distinct loading parameters on the velocity and shear stress in the LCS remains unclear. To address this issue, we developed a multiscale modeling approach, combining a poroelastic finite element (FE) model with a single osteocytic LCS unit model to calculate the flow velocity and shear stress within the LCS. Next, a sensitivity analysis was performed to investigate individual and interactive effects of strain magnitude, strain rate, number of cycles, and intervening short rests between loading cycles on the velocity and shear stress around the osteocyte. Lastly, we developed a relatively simple regression model to predict those outcomes. Our results demonstrated that the strain magnitude or rate alone were the main factors affecting the velocity and shear stress; however, the combination of these two was not directly additive, and addition of a short rest between cycles could enhance the combination of these two related factors. These results show highly interactive effects of distinct loading parameters on fluid velocity and shear stress in the LCS. Specifically, our results suggest that an enhanced fluid dynamics environment in the LCS can be achieved with a brief number of load cycles combined with short rest insertion and high strain magnitude and rate.

Disrupted osteocyte connectivity and pericellular fluid flow in bone with aging and defective TGF-β signaling

Skeletal fragility in the elderly does not simply result from a loss of bone mass. However, the mechanisms underlying the concurrent decline in bone mass, quality, and mechanosensitivity with age remain unclear. The important role of osteocytes in these processes and the age-related degeneration of the intricate lacunocanalicular network (LCN) in which osteocytes reside point to a primary role for osteocytes in bone aging. Since LCN complexity severely limits experimental dissection of these mechanisms in vivo, we used two in silico approaches to test the hypothesis that LCN degeneration, due to aging or an osteocyte-intrinsic defect in transforming growth factor beta (TGF-β) signaling (TβRIIocy-/-), is sufficient to compromise essential osteocyte responsibilities of mass transport and exposure to mechanical stimuli. Using reconstructed confocal images of bone with fluorescently labeled osteocytes, we found that osteocytes from aged and TβRIIocy-/- mice had 33 to 45% fewer, and more tortuous, canaliculi. Connectomic network analysis revealed that diminished canalicular density is sufficient to impair diffusion even with intact osteocyte numbers and overall LCN architecture. Computational fluid dynamics predicts that the corresponding drop in shear stress experienced by aged or TβRIIocy-/- osteocytes is highly sensitive to canalicular surface area but not tortuosity. Simulated expansion of the osteocyte pericellular space to mimic osteocyte perilacunar/canalicular remodeling restored predicted shear stress for aged osteocytes to young levels. Overall, these models show how loss of LCN volume through LCN pruning may lead to impaired fluid dynamics and osteocyte exposure to mechanostimulation. Furthermore, osteocytes emerge as targets of age-related therapeutic efforts to restore bone health and function.

Interstitial fluid velocity is decreased around cortical bone vascular pores and depends on osteocyte position in a rat model of disuse osteoporosis

Muscle paralysis induced with botulinum toxin (Botox) injection increases vascular porosity and reduces osteocyte lacunar density in the tibial cortical bone of skeletally mature rats. These morphological changes potentially affect interstitial fluid flow in the lacunar-canalicular porosity, which is thought to play a role in osteocyte mechanotransduction. The aim of this study was to investigate the effects of disuse-induced morphological changes on interstitial fluid velocity around osteocytes in the bone cortex. Micro-CT images from a previous study that quantified the effects of Botox-induced muscle paralysis on bone microarchitecture in skeletally mature rats were used to create high-resolution, animal-specific finite element models that included the vascular pores and osteocyte lacunae within the tibial metaphysis of Botox-injected (BTX, n = 8) and saline-injected control (CTRL, n = 8) groups. To quantify fluid flow, lacunar and canalicular porosities were modeled as fluid-saturated poroelastic materials, and boundary conditions were applied to simulate physiological loading. This modeling approach allowed a detailed quantification of the fluid flow velocities around osteocytes in a relatively large volume of bone tissue. The analysis demonstrated that interstitial fluid velocity at the vascular pore surfaces was significantly lower in BTX compared to CTRL because of the decreased vascular canal separation. No significant differences in average fluid velocity were observed at the osteocyte lacunae and no correlation was found between the fluid velocity and the lacunar density, which was significantly lower in BTX. Instead, the lacunar fluid velocity was dependent on the osteocyte's specific position in the bone cortex and its proximity to a vascular pore.

INTERSTITIAL FLUID FLOW BEHAVIOR IN OSTEON WALL UNDER NON-AXISYMMETRIC LOADING: A FINITE ELEMENT STUDY

Physiological loads are non-axisymmetric and can lead to interstitial bone fluid flow, particularly in osteon. According to research, interstitial bone fluid flow plays a key role in bone mechanotransduction. To evaluate the poroelastic responses of a non-axisymmetric loaded osteon, this paper presents a finite element osteon model that is bulit by using the Comsol Multiphysics software. Obtained results show that under the same loading amplitude, the generated pressure and velocity amplitudes in the axial compression loading case are the largest, followed by that in the compressive bending loading, and smallest in the bending case. Moreover, the induced pressure and velocity amplitudes in axial compression loading exhibit an axial symmetrical distribution and axial centrosymmetric distribution in the compressive bending. In the bend loading case, the pressure amplitude presents an antisymmetric distribution, but the velocity amplitude is axially symmetrically distributed. Therefore, the distributions of pressure and velocity are definitely affected by load types, which lead to different bone fluid stimuli in mechanotransduction.

Mechanisms of osteocyte stimulation in osteoporosis

Experimental studies have shown that primary osteoporosis caused by oestrogen-deficiency results in localised alterations in bone tissue properties and mineral composition. Additionally, changes to the lacunar-canalicular architecture surrounding the mechanosensitive osteocyte have been observed in animal models of the disease. Recently, it has also been demonstrated that the mechanical stimulation sensed by osteocytes changes significantly during osteoporosis. Specifically, it was shown that osteoporotic bone cells experience higher maximum strains than healthy bone cells after short durations of oestrogen deficiency. However, in long-term oestrogen deficiency there was no significant difference between bone cells in healthy and normal bone. The mechanisms by which these changes arise are unknown. In this study, we test the hypothesis that complex changes in tissue composition and lacunar-canalicular architecture during osteoporosis alter the mechanical stimulation of the osteocyte. The objective of this research is to employ computational methods to investigate the relationship between changes in bone tissue composition and microstructure and the mechanical stimulation of osteocytes during osteoporosis. By simulating physiological loading, it was observed that an initial decrease in tissue stiffness (of 0.425GPa) and mineral content (of 0.66wt% Ca) relative to controls could explain the mechanical stimulation observed at the early stages of oestrogen deficiency (5 weeks post-OVX) during in situ bone cell loading in an oestrogen-deficient rat model of post-menopausal osteoporosis (Verbruggen et al., 2015). Moreover, it was found that a later increase in stiffness (of 1.175GPa) and mineral content (of 1.64wt% Ca) during long-term osteoporosis (34 weeks post-OVX), could explain the mechanical stimuli previously observed at a later time point due to the progression of osteoporosis. Furthermore, changes in canalicular tortuosity arising during osteoporosis were shown to result in increased osteogenic strain stimulation, though to a lesser extent than has been observed experimentally. The findings of this study indicate that changes in the extracellular environment during osteoporosis, arising from altered mineralisation and lacunar-canalicular architecture, lead to altered mechanical stimulation of osteocytes, and provide an enhanced understanding of changes in bone mechanobiology during osteoporosis.

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix--i.e., variations in material properties--on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.

Computational modeling of vibration-induced systemic hydration of vocal folds over a range of phonation conditions

Predicting phonation conditions that are benign to voice health remains a biomechanically relevant problem. Our objective is to provide insight into vocal fold (VF) hydration based on continuum-based VF models that are able to compute VF stresses during phonation and a scheme for the extraction and generalization of such computational data based on the principle of linear superposition. Because VF tissue is poroelastic, spatial gradients of VF hydrostatic stresses computed for a given phonation condition determine VF interstitial fluid flow. The present approach transforms, based on linear superposition principles, the computed interstitial fluid velocities at the particular phonation to those at an arbitrary phonation condition. Intersititial fluid flow characteristics for a range of phonation conditions are compared. For phonation conditions with no or moderate collision, no dehydration per vibration cycle is predicted throughout the VF. For more severe collision conditions, tissue dehydration is restricted to a region close to the glottal surface. Interstitial fluid displacement in the VF is found to be heterogeneous and strongly dependent on the phonation condition. A phonation condition is found to exist for which dehydration peaks. The proposed method significantly expands the scope and relevance of conducting isolated numerical simulations of VF vibration.

Effects of loading frequency on the functional adaptation of trabeculae predicted by bone remodeling simulation

The process of bone remodeling is regulated by metabolic activities of many bone cells. While osteoclasts and osteoblasts are responsible for bone resorption and formation, respectively, activities of these cells are believed to be controlled by a mechanosensory system of osteocytes embedded in the extracellular bone matrix. Several experimental and theoretical studies have suggested that the strain-derived interstitial fluid flow in lacuno-canalicular porosity serves as the prime mover for bone remodeling. Previously, we constructed a mathematical model for trabecular bone remodeling that interconnects the microscopic cellular activities with the macroscopic morphological changes in trabeculae through the mechanical hierarchy. This model assumes that fluid-induced shear stress acting on osteocyte processes is a driving force for bone remodeling. The validity of this model has been demonstrated with a remodeling simulation using a two-dimensional trabecular model. In this study, to investigate the effects of loading frequency, which is thought to be a significant mechanical factor in bone remodeling, we simulated morphological changes of a three-dimensional single trabecula under cyclic uniaxial loading with various frequencies. The results of the simulation show the trabecula reoriented to the loading direction with the progress of bone remodeling. Furthermore, as the imposed loading frequency increased, the diameter of the trabecula in the equilibrium state was enlarged by remodeling. These results indicate that our simulation model can successfully evaluate the relationship between loading frequency and trabecular bone remodeling.

Fluid and Solute Transport in Bone: Flow-Induced Mechanotransduction

Much recent evidence suggests that bone cells sense their mechanical environment via interstitial fluid flow. In this review, we summarize theoretical and experimental approaches to quantify fluid and solute transport in bone, starting with the early investigations of fluid shear stress applied to bone cells. The pathways of bone interstitial fluid and solute movement are high-lighted based on recent theoretical models, as well as a new generation of tracer experiments that have clarified and refined the structure and function of the osteocyte pericellular matrix. Then we trace how the fluid-flow models for mechanotransduction have evolved as new ultrastructural features of the osteocyte lacunar-canalicular porosity have been identified and how more recent in vitro fluid-flow and cell-stretch experiments have helped elucidate at the molecular level the possible pathways for cellular excitation in bone.

An estimate of anisotropic poroelastic constants of an osteon

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

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.

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.

Nano?Microscale Models of Periosteocytic Flow Show Differences in Stresses Imparted to Cell Body and Processes

In order to understand how local changes in mechanical environment are translated into cellular activity underlying tissue level bone adaptation, there is a need to explore fluid flow regimes at small scales such as the osteocyte. Recent developments in computational fluid dynamics (CFD) provide impetus to elucidate periosteocytic flow through development of a nanomicroscale model to study local effects of fluid flow on the osteocyte cell body, which contains the cellular organelles, and on the osteocyte processes, which connect the cell to the entire cellular network distributed throughout bone tissue. For each model, fluid flow was induced via a pressure gradient and the velocity profile and wall shear stress at the cell-fluid interface were calculated using a CFD software package designed for nano/micro-electromechanical-systems device development. Periosteocytic flow was modeled, taking into consideration the nanoscale dimensions of the annular channels and the flow pathways of the periosteocytic flow volume, to analyze the local effects of fluid flow on the osteocyte cell body (within the lacuna) and its processes (within the canaliculi). Based on the idealized model presented in this article, the osteocyte cell body is exposed primarily to effects of hydrodynamic pressure and the cell processes (CP) are exposed primarily to fluid shear stress, with highest stress gradients at sites where the process meets the cell body and where two CP link at the gap junction. Hence, this model simulates subcellular effects of fluid flow and suggests, for the first time to our knowledge, major differences in modes of loading between the domain of the cell body and that of the cell process.

A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone

Interstitial fluid flow through the lacunocanalicular cavities of mechanically loaded bone provides the biophysical basis for a number of postulates regarding mechanotransduction in bone. Recently, the existence of load-induced fluid flow and its influence on molecular transport through bone has been confirmed using tracer methods to visualize fluid flow induced by in vivo four-point-bending of rat tibiae. In this paper, we present a theoretical two-stage approach for the calculation of load-induced flow fields and for the evaluation of their influence on molecular transport in bone loaded in four-point bending, analogous to the aforementioned experimental model. In the first stage, the fluid velocities are calculated using a three-dimensional, poroelastic finite element model. In the second stage, mass transport analysis, this calculated fluid flow serves as a forced convection flow and its contribution to the total transport potential is determined. Based on this combined approach, the overall tracer concentration in the loaded bone is significantly higher than that in the unloaded bone. Furthermore, augmentation of mass transport through convective flow is more pronounced in the tension band of the tissue, as compared to the compression band. In general, augmentation of tracer concentration via convective mechanisms is most pronounced in areas corresponding to lowest fluid velocities, which is indicative of fluid flow direction and areas of increased "dwell time" or accumulation during the loading cycle. This theoretical model, in combination with the corresponding experimental model, provides unique insight into the role of mechanical loads in modulating local flow distributions and concentration gradients within bone tissue.

Bone poroelasticity

Poroelasticity is a well-developed theory for the interaction of fluid and solid phases of a fluid-saturated porous medium. It is widely used in geomechanics and has been applied to bone by many authors in the last 30 years. The purpose of this work is, first, to review the literature related to the application of poroelasticity to the interstitial bone fluid and, second, to describe the specific physical and modeling considerations that establish poroelasticity as an effective and useful model for deformation-driven bone fluid movement in bone tissue. The application of poroelasticity to bone differs from its application to soft tissues in two important ways. First, the deformations of bone are small while those of soft tissues are generally large. Second, the bulk modulus of the mineralized bone matrix is about six times stiffer than that of the fluid in the pores while the bulk moduli of the soft tissue matrix and the pore water are almost the same. Poroelasticity and electrokinetics can be used to explain strain-generated potentials in wet bone. It is noted that strain-generated potentials can be used as an effective tool in the experimental study of local bone fluid flow, and that the knowledge of this technique will contribute to the answers of a number of questions concerning bone mineralization, osteocyte nutrition and the bone mechanosensory system.