Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment

Non-Newtonian lacuno-canalicular fluid flow in bone altered by mechanical loading and magnetic field

As humans age, they experience deformity and a decrease in their bone strength, such brittleness in the bones ultimately lead to bone fracture. Magnetic field exposure combined with physical exercise may be useful in mitigating age-related bone loss by improving the canalicular fluid motion within the bone's lacuno-canalicular system (LCS). Nevertheless, an adequate amount of fluid induced shear stress is necessary for the bone mechano-transduction and solute transport in the case of brittle bone diseases. The underlying mechanisms of how magnetic fields, in combination to mechanical loading, affects the canalicular fluid motion still need to be explored. Accordingly, this study aims to develop a computer model to investigate the role of magnetic fields on loading-induced canalicular fluid flow in a curvy lacunar canalicular space with irregular osteocyte cell processes and walls. Moreover, this study considers canalicular fluid as non-Newtonian fluid, i.e., Jeffery fluid. In addition, a machine learning model was further employed for the estimation of parameters which significantly influence the canalicular fluid flow in response to loading and magnetic field. The results show that static magnetic field modulates the loading-induced canalicular fluid flow. Additionally, present study accelerates the fluid induced wall shear stress in case of osteoporosis.

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.

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.

Tension force causes cell cycle arrest at G2/M phase in osteocyte-like cell line MLO-Y4

Bone remodelling is the process of bone resorption and formation, necessary to maintain bone structure or for adaptation to new conditions. Mechanical loadings, such as exercise, weight bearing and orthodontic force, play important roles in bone remodelling. During the remodelling process, osteocytes play crucial roles as mechanosensors to regulate osteoblasts and osteoclasts. However, the precise molecular mechanisms by which the mechanical stimuli affect the function of osteocytes remain unclear. In the present study, we analysed viability, cell cycle distribution and gene expression pattern of murine osteocyte-like MLO-Y4 cells exposed to tension force (TF). Cells were subjected to TF with 18% elongation at 6 cycles/min for 24 h using Flexcer Strain Unit (FX-3000). We found that TF stimulation induced cell cycle arrest at G2/M phase but not cell death in MLO-Y4 cells. Differentially expressed genes (DEGs) between TF-stimulated and unstimulated cells were identified by microarray analysis, and a marked increase in glutathione-S-transferase α (GSTA) family gene expression was observed in TF-stimulated cells. Enrichment analysis for the DEGs revealed that Gene Ontology (GO) terms and Kyoto Encyclopedia Genes and Genomes (KEGG) pathways related to the stress response were significantly enriched among the upregulated genes following TF. Consistent with these results, the production of reactive oxygen species (ROS) was elevated in TF-stimulated cells. Activation of the tumour suppressor p53, and upregulation of its downstream target GADD45A, were also observed in the stimulated cells. As GADD45A has been implicated in the promotion of G2/M cell cycle arrest, these observations may suggest that TF stress leads to G2/M arrest at least in part in a p53-dependent manner.

Temporal changes in cortical microporosity during estrogen deficiency associated with perilacunar resorption and osteocyte apoptosis: A pilot study

Osteocytes can actively regulate bone microporosity, through either perilacunar resorption or micropetrosis following apoptosis. Osteocyte apoptosis is more prevalent in estrogen deficiency and changes in the lacunar-canalicular network of osteocytes have been reported. Temporal changes in bone mineralisation and osteocytes cellular strains occur, which might be associated with osteocyte-driven microporosity changes, although time dependant changes in bone microporosity are not yet fully understood. In this pilot study we conducted micro-CT analysis, backscatter electron imaging and histological analysis of femoral cortical bone form an ovariectomized rat model of osteoporosis to investigate whether estrogen deficiency causes temporal changes in lacunar and vascular porosity. We also assessed MMP14 expression, lacunar occupancy and mineral infilling, as indicators of perilacunar resorption and micropetrosis. We report temporal changes in cortical microporosity in estrogen deficiency. Specifically, canalicular and vascular porosity initially increased (4 weeks post-OVX), coinciding with the period of rapid bone loss, whereas in the longer term (14 weeks post-OVX) lacunar and canalicular diameter decreased. Interestingly, these changes coincided with an increased prevalence of empty lacunae and osteocyte lacunae were observed to be more circular with a mineralised border around the lacunar space. In addition we report an increase in MMP14+ osteocytes, which also suggests active matrix degradation by these cells. Together these results provide an insight into the temporal changes in cortical microporosity during estrogen deficiency and suggest the likelihood of occurrence of both perilacunar resorption and osteocyte apoptosis leading to micropetrosis. We propose that microporosity changes arise due to processes driven by distinct populations of osteocytes, which are either actively resorbing their matrix or have undergone apoptosis and are infilling lacunae by micropetrosis.

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.

Remodelling of trabecular bone in human distal tibia: A model based on an in-vivo HR-pQCT study

An abnormal remodelling process of bones can lead to various bone disorders, such as osteoporosis, making them prone to fracture. Simulations of load-induced remodelling of trabecular bone were used to investigate its response to mechanical signal. However, the role of mechanostat in trabecular-bone remodelling has not yet been investigated in simulations underpinned by a longitudinal in-vivo study in humans. In this work, a finite-element model based on a 6-month longitudinal in-vivo HR-pQCT study was developed and validated to investigate the effect of mechanical stimuli on bone remodelling. The simulated changes in microstructural parameters and density of trabecular bone were compared with respective experimental results. A maximum principal strain (MPS) and a maximum principal strain gradient (∇MPS) were used as mechanical signals to drive a five-stage mechanostat remodelling model, including additional over-strain and damage stages. It was found that the density distribution varied with the studied mechanical signals, along with decreasing with time levels of bone volume fraction BV/TV, trabecular thickness Tb.Th and bone surface area Tb.BS as well as increased trabecular separation Tb.Sp. Among these parameters, BV/TV and Tb.Th together with the bone-remodelling parameters from the MPS model demonstrated a significant correlation with the experimental data. The developed model provides a good foundation for further development and investigation of the relationships between mechanical loading and human-bone microarchitecture.

THEORETICAL ANALYSIS OF THE LEAKAGE THROUGH THE CEMENT LINE OF A SINGLE OSTEON

This work focuses on the Lacunar–Canalicular Porosity (PLC) of cortical bone which includes the osteons. Osteons are semicylindrical porous structures saturated with fluid within the bone and are approximately 250[Formula: see text][Formula: see text]m in diameter. The outer boundary of the osteon is called the cement line. Some studies suggested that the cement line is less highly mineralized and produced evidence that it has less calcium and phosphorus and more sulfur than the neighboring bone lamellae. Most authors assume that the cement line is impermeable, while others assume that some canaliculi are crossing the cement line which will make it permeable to certain degree. The objective of this work is to develop a theoretical analysis to study the leakage through the cement line and its relationship with the pore pressure distribution. The theoretical analysis is developed using our previous analysis for osteon under harmonic loading with addition of leakage parameter. The leakage parameter varies from 0 to 1, where a value of 0 indicates free flow through the cement line and a value of 1 indicates no flow through the cement line. Experimental results could be compared to this developed theoretical solution to get in depth understanding of the effect of leakage on osteon poroelastic properties. Additionally, the developed theoretical solution will give insight into sensitivity of osteon pore pressure to leakage through the cement line.

The effects of estrogen deficiency on cortical bone microporosity and mineralization

Recent studies have demonstrated matrix-mineral alterations in bone tissue surrounding osteocytes in estrogen-deficient animals. While cortical bone porosity has been shown to be a contributor to the mechanical properties of bone tissue, little analysis has been done to investigate the effects of estrogen deficiency on bone's microporosities, including the vascular and osteocyte lacunar porosities. In this study we examined alterations in cortical bone microporosity, mineralization, and cancellous bone architecture due to estrogen deficiency in the ovariectomized rat model of postmenopausal osteoporosis. Twenty-week-old female Sprague-Dawley rats were subjected to either ovariectomy or sham surgery. Six weeks post-surgery tibiae were analyzed using high-resolution micro-CT, backscattered electron imaging, nanoindentation, and dynamic histomorphometry. Estrogen deficiency caused an increase in cortical bone vascular porosity, with enlarged vascular pores and little change in tissue mineral density in the proximal tibial metaphysis. Measurements of cancellous architecture corresponded to previous studies reporting a decrease in bone volume fraction, an increase in trabecular separation, and a decrease in trabecular number in the proximal tibia due to estrogen deficiency. Nanoindentation results showed no differences in matrix stiffness in osteocyte-rich areas of the proximal tibia of estrogen-deficient rats, and bone labeling and backscattered electron imaging showed no significant changes in mineralization around the vascular pores. The findings demonstrate local surface alterations of vascular pores due to estrogen deficiency. An increase in cortical vascular porosity may diminish bone strength as well as alter bone mechanotransduction via interstitial fluid flow, both of which could contribute to bone fragility during postmenopausal osteoporosis.

Computational Investigation on the Biomechanical Responses of the Osteocytes to the Compressive Stimulus: A Poroelastic Model

Osteocytes, the major type of bone cells embedded in the bone matrix and surrounded by the lacunar and canalicular system, can serve as biomechanosensors and biomechanotranducers of the bone. Theoretical analytical methods have been employed to investigate the biomechanical responses of osteocytes in vivo; the poroelastic properties have not been taken into consideration in the three-dimensional (3D) finite element model. In this study, a 3D poroelastic idealized finite element model was developed and was used to predict biomechanical behaviours (maximal principal strain, pore pressure, and fluid velocity) of the osteocyte-lacunar-canalicular system under 150-, 1000-, 3000-, and 5000-microstrain compressive loads, respectively, representing disuse, physiological, overuse, and pathological overload loading stimuli. The highest local strain, pore pressure, and fluid velocity were found to be highest at the proximal region of cell processes. These data suggest that the strain, pore pressure, and fluid velocity of the osteocyte-lacunar-canalicular system increase with the global loading and that the poroelastic material property affects the biomechanical responses to the compressive stimulus. This new model can be used to predict the mechanobiological behaviours of osteocytes under the four different compressive loadings and may provide an insight into the mechanisms of mechanosensation and mechanotransduction of the bone.

Microstructural changes associated with osteoporosis negatively affect loading-induced fluid flow around osteocytes in cortical bone

Loading-induced interstitial fluid flow in the microporosities of bone is critical for osteocyte mechanotransduction and for the maintenance of tissue health, enhancing convective transport in the lacunar-canalicular system. In recent studies, our group has reported alterations of bone's vascular porosity and lacunar-canalicular system microarchitecture in a rat model of postmenopausal osteoporosis. In this work, poroelastic finite element analysis was used to investigate whether these microstructural changes can affect interstitial fluid flow around osteocytes. Animal-specific finite element models were developed combining micro-CT reconstructions of bone microstructure and measures of the poroelastic material properties. These models were used to quantify and compare loading-induced fluid flow in the lacunar-canalicular system of ovariectomized and sham-operated rats. A parametric analysis was also used to quantify the influence of the lacunar-canalicular permeability and vascular porosity on the fluid velocity magnitude. Results show that mechanically-induced interstitial fluid velocity can be significantly reduced in the lacunar-canalicular system of ovariectomized rats. Interestingly, the vascular porosity is shown to have a major influence on interstitial fluid flow, while the lacunar-canalicular permeability influence is limited when larger than 10^-20m². Altogether our results suggest that microstructural changes associated with the osteoporotic condition can negatively affect interstitial fluid flow around osteocytes in the lacunar-canalicular system of cortical bone. This fluid flow reduction could impair mechanosensation of the osteocytic network, possibly playing a role in the initiation and progression of age-related bone loss and postmenopausal osteoporosis.

Blood and interstitial flow in the hierarchical pore space architecture of bone tissue

There are two main types of fluid in bone tissue, blood and interstitial fluid. The chemical composition of these fluids varies with time and location in bone. Blood arrives through the arterial system containing oxygen and other nutrients and the blood components depart via the venous system containing less oxygen and reduced nutrition. Within the bone, as within other tissues, substances pass from the blood through the arterial walls into the interstitial fluid. The movement of the interstitial fluid carries these substances to the cells within the bone and, at the same time, carries off the waste materials from the cells. Bone tissue would not live without these fluid movements. The development of a model for poroelastic materials with hierarchical pore space architecture for the description of blood flow and interstitial fluid flow in living bone tissue is reviewed. The model is applied to the problem of determining the exchange of pore fluid between the vascular porosity and the lacunar-canalicular porosity in bone tissue due to cyclic mechanical loading and blood pressure. These results are basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells.

Modeling of transient wave propagation in a heterogeneous solid layer coupled with fluid: application to long bones

The aim of this work is to evaluate the effects of the heterogeneity and anisotropy of material properties of cortical bone on its ultrasonic response obtained by using axial transmission method. The heterogeneity and anisotropy of material properties are introduced by using a parametric probabilistic model. The geometrical configuration of the tested sample is described by a tri-layer medium composed of a heterogeneous and anisotropic solid layer sandwiched between two acoustic fluid layers of which one of these layers is excited by an acoustic linear source. The numerical results focus on studying of an interest quantity, called velocity of the first arriving signal, showing that it strongly depends on the dispersion induced by statistical fluctuations of stochastic elasticity field.

3D assessment of cortical bone porosity and tissue mineral density using high-resolution µCT: effects of resolution and threshold method

Current micro-computed tomography (µCT) systems allow scanning bone at resolutions capable of three-dimensional (3D) characterization of intracortical vascular porosity and osteocyte lacunae. However, the scanning and reconstruction parameters along with the image segmentation method affect the accuracy of the measurements. In this study, the effects of scanning resolution and image threshold method in quantifying small features of cortical bone (vascular porosity, vascular canal diameter and separation, lacunar porosity and density, and tissue mineral density) were analyzed. Cortical bone from the tibia of Sprague-Dawley rats was scanned at 1-µm and 4-µm resolution, reconstructions were density-calibrated, and volumes of interest were segmented using approaches based on edge-detection or histogram analysis. In 1-µm resolution scans, the osteocyte lacunar spaces could be visualized, and it was possible to separate the lacunar porosity from the vascular porosity. At 4-µm resolution, the vascular porosity and vascular canal diameter were underestimated, and osteocyte lacunae were not effectively detected, whereas the vascular canal separation and tissue mineral density were overestimated compared to 1-µm resolution. Resolution had a much greater effect on the measurements than did threshold method, showing partial volume effects at resolutions coarser than 2 µm in two separate analyses, one of which assessed the effect of resolution on an object of known size with similar architecture to a vascular pore. Although there was little difference when using the edge-detection versus histogram-based threshold approaches, edge-detection was somewhat more effective in delineating canal architecture at finer resolutions (1-2 µm). In addition, use of a high-resolution (1 µm) density-based threshold on lower resolution (4 µm) density-calibrated images was not effective in improving the lower-resolution measurements. In conclusion, if measuring cortical vascular microarchitecture, especially in small animals, a µCT resolution of 1 to 2 µm is appropriate, whereas a resolution of at least 1 µm is necessary when assessing osteocyte lacunar porosity.

Dynamic permeability of the lacunar-canalicular system in human cortical bone

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar-canalicular permeability [Formula: see text] in bone. The interest in the permeability of the lacunar-canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from [Formula: see text] to [Formula: see text]. However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the [Formula: see text] to be on the order of [Formula: see text] for human osteonal bone. It was found that the [Formula: see text] has a linear dependence on loading frequency, decreasing at a rate of [Formula: see text]/Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the [Formula: see text] variability.

Advances in assessment of bone porosity, permeability and interstitial fluid flow

This contribution reviews recent research performed to assess the porosity and permeability of bone tissue with the objective of understanding interstitial fluid movement. Bone tissue mechanotransduction is considered to occur due to the passage of interstitial pore fluid adjacent to dendritic cell structures in the lacunar-canalicular porosity. The movement of interstitial fluid is also necessary for the nutrition of osteocytes. This review will focus on four topics related to improved assessment of bone interstitial fluid flow. First, the advantages and limitations of imaging technologies to visualize bone porosities and architecture at several length scales are summarized. Second, recent efforts to measure the vascular porosity and lacunar-canalicular microarchitecture are discussed. Third, studies associated with the measurement and estimation of the fluid pressure and permeability in the vascular and lacunar-canalicular domains are summarized. Fourth, the development of recent models to represent the interchange of fluids between the bone porosities is described.

Evidence of interlinks between bioelectromagnetics and biomechanics: from biophysics to medical physics

A vast literature on electromagnetic and mechanical bioeffects at the bone and soft tissue level, as well as at the cellular level (osteoblasts, osteoclasts, keratinocytes, fibroblasts, chondrocytes, nerve cells, endothelial and muscle cells) has been reviewed and analysed in order to show the evident connections between both types of physical energies. Moreover, an intimate link between the two is suggested by transduction phenomena (electromagnetic-acoustic transduction and its reverse) occurring in living matter, as a sound biophysical literature has demonstrated. However, electromagnetic and mechanical signals are not always interchangeable, depending on their respective intensity. Calculations are reported in order to show in which cases (read: for which values of electric field in V/m and of mechanical pressure in Pa) a given electromagnetic or mechanical bioeffect is only due to the directly impinging energy or even to the indirect transductional energy. The relevance of the treated item for the applications of medical physics to regenerative medicine is stressed.

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu: a multi-parametric sensitivity analysis

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.

Modeling of cortical bone adaptation in a rat ulna: effect of frequency

We employ a recently developed model for the adaptation of cortical bone in response to mechanical loading to study the effect of loading frequency on the computed response, and we compare our results to previous experimental measurements on rat ulnae. We represent the cortical bone as a poroelastic material with orthotropic permeability. Bone adaptation in the model is related to a mechanical stimulus derived from the dissipation energy of the poroelastic flow induced by deformation. We account for a non-locality in the mechanotransduction of osteocytes present in the lacunae by using a "zone of influence." Calculations are done using the finite element method applied to a rat ulna whose geometry is obtained from micro-computed tomography images. We show that the change in the second moment of inertia of the cross-section increases non-linearly and saturates at higher frequency range. The numerical results are then compared quantitatively to experimental data from the literature. Finally, we examine the role of local narrowing of intramedullary canal in our specific ulna in the development of local irregularities in growth.

Analytical basis for the determination of the lacunar-canalicular permeability of bone using cyclic loading

An analytical model for the determination of the permeability in the lacunar-canalicular porosity of bone using cyclic loading is described in this contribution. The objective of the analysis presented is to relate the lacunar-canalicular permeability to a particular phase angle that is measurable when the bone is subjected to infinitesimal cyclic strain. The phase angle of interest is the lag angle between the applied strain and the resultant stress. Cyclic strain causes the interstitial fluid to move. This movement is essential for the viability of osteocytes and is believed to play a major role in the bone mechanotransduction mechanism. However, certain bone fluid flow properties, notably the permeability of the lacunar-canalicular porosity, are still not accurately determined. In this paper, formulas for the phase angle as a function of permeability for infinitesimal cyclic strain are presented and mathematical expressions for the storage modulus, loss modulus, and loss tangent are obtained. An accurate determination of the PLC permeability will improve our ability to understand mechanotransduction and mechanosensory mechanisms, which are fundamental to the understanding of how to treat osteoporosis, how to cope with microgravity in long-term manned space flights, and how to increase the longevity of prostheses that are implanted in bone tissue.

Strain driven transport for bone modeling at the periosteal surface

Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E2 (PGE2), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling.

In situ permeability measurement of the mammalian lacunar-canalicular system

Bone is capable of adapting its mass and structure under mechanical cues. Bone cells respond to various mechanical stimuli including substrate strain, fluid pressure, and fluid flow (shear stress) in vitro. Although tissue-level strains are well documented experimentally, microfluidic parameters around bone cells are quantified mainly through theoretical modeling. A key model parameter, the Darcy permeability of the bone lacunar-canalicular system (LCS), is difficult to measure using traditional methods due to the co-existence of the larger vascular and smaller LCS porosities. In this paper, we developed a novel method to measure the LCS permeability by rapid compaction of intact mammalian bones and recording the intramedullary pressure (IMP). Six canine metacarpals were subjected to three step compression tests with peak loads of 50, 100, or 200lbs, while the IMP was simultaneously recorded using a catheter pressure transducer. The loading ramp time was chosen to be ~2ms, which was long enough to allow pressure equilibrium to be established between the marrow cavity and the vascular pores, but short enough to observe the LCS fluid flowing into and out of the vascular pores. This loading scheme permitted us to differentiate the contribution of the two intermingled porosities to the IMP responses. The time constant of the IMP pressurization and relaxation due to the LCS was found to be 8.1+/-3.6s (n=18). The mid-shaft cortex of the metacarpals mainly consisted of osteons with an average radial thickness of 65+/-27microm, which served as the characteristic distance for the LCS fluid to relax. The LCS permeability was obtained via poroelastic analysis to be 2.8+/-1.8x10(-)(23)m(2), which was smaller than previous theoretical predictions (order of 10(-)(19) to 10(-)(22)m(2)), but within the range of previous experimentally based estimations (order of 10(-)(22) to 10(-)(25)m(2)). Our results also show that osteoblasts and osteocytes experience hydraulic pressures that differ by three orders of magnitude under physiological compressive strains. These estimates of the in vivo mechanical environments may be used to design in vitro models for elucidating the cellular and molecular mechanisms of bone adaptation and pathological bone loss.

Mechanical signals as anabolic agents in bone

Aging and a sedentary lifestyle conspire to reduce bone quantity and quality, decrease muscle mass and strength, and undermine postural stability, culminating in an elevated risk of skeletal fracture. Concurrently, a marked reduction in the available bone-marrow-derived population of mesenchymal stem cells (MSCs) jeopardizes the regenerative potential that is critical to recovery from musculoskeletal injury and disease. A potential way to combat the deterioration involves harnessing the sensitivity of bone to mechanical signals, which is crucial in defining, maintaining and recovering bone mass. To effectively utilize mechanical signals in the clinic as a non-drug-based intervention for osteoporosis, it is essential to identify the components of the mechanical challenge that are critical to the anabolic process. Large, intense challenges to the skeleton are generally presumed to be the most osteogenic, but brief exposure to mechanical signals of high frequency and extremely low intensity, several orders of magnitude below those that arise during strenuous activity, have been shown to provide a significant anabolic stimulus to bone. Along with positively influencing osteoblast and osteocyte activity, these low-magnitude mechanical signals bias MSC differentiation towards osteoblastogenesis and away from adipogenesis. Mechanical targeting of the bone marrow stem-cell pool might, therefore, represent a novel, drug-free means of slowing the age-related decline of the musculoskeletal system.

Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar-canalicular porosity (PLC) in bone tissue due to cyclic mechanical loading and blood pressure oscillations. The result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells. A formula for the volume of fluid that moves between the PLC and PV in a cyclic loading is obtained as a function of the cyclic mechanical loading and blood pressure oscillations. Formulas for the oscillating fluid pore pressure in both the PLC and the PV are obtained as functions of the two driving forces, the cyclic mechanical straining and the blood pressure, both with specified amplitude and frequency. The results of this study also suggest a PV permeability greater than 10(-9) m(2) and perhaps a little lower than 10(-8) m(2). Previous estimates of this permeability have been as small as 10(-14) m(2).

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.

Modeling fluorescence recovery after photobleaching in loaded bone: potential applications in measuring fluid and solute transport in the osteocytic lacunar-canalicular system

Solute transport through the bone lacunar-canalicular system is essential for osteocyte viability and function, and it can be measured using fluorescence recovery after photobleaching (FRAP). The mathematical model developed here aims to analyze solute transport during FRAP in mechanically loaded bone. Combining both whole bone-level poroelasticity and cellular-level solute transport, we found that load-induced solute transport during FRAP is characterized by an exponential recovery rate, which is determined by the dimensionless Strouhal (St) number that characterizes the oscillation effects over the mean flows, and that significant transport occurs only for St values below a threshold, when the solute stroke displacement exceeds the distance between the source and sink (the canalicular length). This threshold mechanism explains the general flow behaviors such as increasing transport with increasing magnitude and decreasing frequency. Mechanical loading is predicted to enhance transport of all tracers relative to diffusion, with the greatest enhancement for medium-sized tracers and less enhancement for small and large tracers. This study provides guidelines for future FRAP experiments, based on which the model can be used to quantify bone permeability, solute-matrix interaction, and flow velocities. These studies should provide insights into bone adaptation and metabolism, and help to treat various bone diseases and conditions.

Osteocytes, mechanosensing and Wnt signaling

The majority of bone cell biology focuses on activity on the surface of the bone with little attention paid to the activity that occurs below the surface. However, with recent new discoveries, osteocytes, cells embedded within the mineralized matrix of bone, are becoming the target of intensive investigation. In this article, the distinctions between osteoblasts and their descendants, osteocytes, are reviewed. Osteoblasts are defined as cells that make bone matrix and osteocytes are thought to translate mechanical loading into biochemical signals that affect bone (re)modeling. Osteoblasts and osteocytes should have similarities as would be expected of cells of the same lineage, yet these cells also have distinct differences, particularly in their responses to mechanical loading and utilization of the various biochemical pathways to accomplish their respective functions. For example, the Wnt/beta-catenin signaling pathway is now recognized as an important regulator of bone mass and bone cell functions. This pathway is important in osteoblasts for differentiation, proliferation and the synthesis bone matrix, whereas osteocytes appear to use the Wnt/beta-catenin pathway to transmit signals of mechanical loading to cells on the bone surface. New emerging evidence suggests that the Wnt/beta-catenin pathway in osteocytes may be triggered by crosstalk with the prostaglandin pathway in response to loading which then leads to a decrease in expression of negative regulators of the pathway such as Sost and Dkk1. The study of osteocyte biology is becoming an intense area of research interest and this review will examine some of the recent findings that are reshaping our understanding of bone/bone cell biology.

A Finite Element Dual Porosity Approach to Model Deformation-Induced Fluid Flow in Cortical Bone

Fluid flow through the osteocyte canaliculi network is widely believed to be a main factor that controls bone adaptation. The difficulty of in vivo measurement of this flow within cortical bone makes computational models an appealing alternative to estimate it. We present in this paper a finite element dual porosity macroscopic model that can contribute to evaluate the interstitial fluid flow induced by mechanical loads in large pieces of bone. This computational model allows us to predict the macroscopic fluid flow at both vascular and canalicular porosities in a whole loaded bone. Our results confirm that the general trend in the fluid flow field predicted is similar to the one obtained with previous microscopic models, and that in a whole bone model it is able to estimate the zones with higher bone remodeling.

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.

Age-dependent change in the 3D structure of cortical porosity at the human femoral midshaft

Microstructural change associated with cortical bone remodeling has been extensively explored with 2D techniques. However, relatively little is known regarding the 3D dynamic microstructure of cortical bone. Therefore, we employed micro-CT imaging to investigate 3D remodeling-related change in the structure of cortical bone porosity across the human lifespan. Anterior femoral midshaft specimens (n=51 male, 28 female) spanning 18 to 92 years of age were scanned with 7 mum nominal isotropic resolution. Canal volume fraction (Ca.V/TV), mean diameter (Ca.Dm), mean separation (Ca.Sp), degree of anisotropy (DA), connectivity density (Ca.ConnD), and number (Ca.N) were calculated for subperiosteal cylindrical regions of interest. Ca.N was calculated in 2D (Ca.N(2D)) and 3D (Ca.N(3D)). Regression was used to examine the relation between the structural parameters and age. Additionally, the impact of sex, height, and weight were investigated collectively (MANCOVA) and individually (ANCOVA). For all analyses, Ca.V/TV and Ca.Dm were inverted (Ca.V/TV(-1), Ca.Dm(-1)) to establish normality and linear relations with age. Ca.N values (2D and 3D) were non-linearly (quadratic) related to age, increasing until the 6th decade then decreasing. This relation was only significant for the pooled sexes Ca.N(3D) values (p=0.012). Ca.ConnD was positively related to age (p<0.05), while all remaining 3D parameters, except DA for males (p=0.070), were negatively related (p<0.05). In all cases, the relation with age was strongest for females. MANCOVA revealed that age was the only significant (p<0.001) covariate overall. Univariate ANCOVA indicated significant differences between the sexes for Ca.V/TV(-1) and Ca.Dm(-1) (p=0.018 and 0.010, respectively). Relative to males, females had lower values for these parameters, translating into larger mean canal diameter and overall porosity. Body weight had a significant (p=0.043) positive relation with Ca.Dm(-1), indicating lower weight was also associated with increased mean canal diameter. Therefore, while age was the most important factor, sex and body size were found to play a role in parameters related to canal size and the overall level of porosity. This study is unique in that changes in cortical bone microstructure were examined across the adult human lifespan in three rather than two dimensions.

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.

Exercise for people with osteoporosis: translating the science into clinical practice

The "holy grail" of inquiry regarding exercise and osteoporosis has been identifying a type of exercise that builds bone. Investigation using animal models has provided many insights into how bone responds to mechanical loading, but translating these findings into an exercise prescription for patients with osteoporosis is difficult. Patients expect bone to respond to exercise in a linear fashion, such as they are accustomed to experiencing with muscles in response to progressive strength training or with the cardiopulmonary system in response to endurance training. If the skeleton accrued greater mass in response to increasing intensity and duration of mechanical strain, our bones would weigh so much that we could not move. A unique requirement of bone is that adaptations to loading produce the strongest and the lightest structure. More exercise is not always better, but we are not yet sure exactly what and how much is enough and what and how much is too much. This complexity stymies clear communication, both in the clinic and in public health initiatives.

Low-level, high-frequency mechanical signals enhance musculoskeletal development of young women with low BMD

The potential for brief periods of low-magnitude, high-frequency mechanical signals to enhance the musculoskeletal system was evaluated in young women with low BMD. Twelve months of this noninvasive signal, induced as whole body vibration for at least 2 minutes each day, increased bone and muscle mass in the axial skeleton and lower extremities compared with controls.

INTRODUCTION

The incidence of osteoporosis, a disease that manifests in the elderly, may be reduced by increasing peak bone mass in the young. Preliminary data indicate that extremely low-level mechanical signals are anabolic to bone tissue, and their ability to enhance bone and muscle mass in young women was investigated in this study.

MATERIALS AND METHODS

A 12-month trial was conducted in 48 young women (15-20 years) with low BMD and a history of at least one skeletal fracture. One half of the subjects underwent brief (10 minutes requested), daily, low-level whole body vibration (30 Hz, 0.3g); the remaining women served as controls. Quantitative CT performed at baseline and at the end of study was used to establish changes in muscle and bone mass in the weight-bearing skeleton.

RESULTS

Using an intention-to-treat (ITT) analysis, cancellous bone in the lumbar vertebrae and cortical bone in the femoral midshaft of the experimental group increased by 2.1% (p = 0.025) and 3.4% (p < 0.001), respectively, compared with 0.1% (p = 0.74) and 1.1% (p = 0.14), in controls. Increases in cancellous and cortical bone were 2.0% (p = 0.06) and 2.3% (p = 0.04) greater, respectively, in the experimental group compared with controls. Cross-sectional area of paraspinous musculature was 4.9% greater (p = 0.002) in the experimental group versus controls. When a per protocol analysis was considered, gains in both muscle and bone were strongly correlated to a threshold in compliance, where the benefit of the mechanical intervention compared with controls was realized once subjects used the device for at least 2 minute/day (n = 18), as reflected by a 3.9% increase in cancellous bone of the spine (p = 0.007), 2.9% increase in cortical bone of the femur (p = 0.009), and 7.2% increase in musculature of the spine (p = 0.001) compared with controls and low compliers (n = 30).

CONCLUSIONS

Short bouts of extremely low-level mechanical signals, several orders of magnitude below that associated with vigorous exercise, increased bone and muscle mass in the weight-bearing skeleton of young adult females with low BMD. Should these musculoskeletal enhancements be preserved through adulthood, this intervention may prove to be a deterrent to osteoporosis in the elderly.

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.

Hydraulic strengthening affects the stiffness and strength of cortical bone

A nonlinear, interstitial fluid flow constitutive model for cortical bone was developed to study the strain-rate dependency of cortical bone apparent modulus (Ea). Nine representative volume element (RVE) structural models of cortical bone spanning an effective pore volume fraction P range of 1-40% were examined. Dynamic loading conditions were used to study the fluid flow contribution or hydraulic strengthening (HS) effect on Ea for each RVE model. The model indicated that there is an upper and lower asymptotic bound of strain-rate (10(+/-3) sec(-1)) above or below which there are no further HS effects on Ea. At certain strain-rates (10(-1) to 10(0) sec(-1)) variations in cortical bone porosity had little or no influence on Ea. At lower and higher frequencies, the loss tangent, hence the magnitude of viscoelastic effects is greater. For strain-rates less than 10(-1) sec(-1), lower porosity RVE models were always stiffer than higher porosity RVE models. A generalized power law model is proposed to account for the fact that HS in cortical bone exhibits an upper and lower asymptotic bound and is bi-modal in terms of strain-rate.