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

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.

An Improved Method for Assessing Macroscale Diffusion through Osteonal Bone

The characterization of diffusion through biological tissues has played an important role in fundamental medical research and product development. Understanding the diffusion phenomena allows for the identification of new concepts in fundamental science, evolving medical knowledge and improving future standards and protocols. To illustrate, the structure of cortical bone changes upon the onset of osteoporosis, altering the limited porous compartment through which nutrients and essential signaling molecules travel to bone cells. Estrogen hormone replacement therapy (HRT) is one of the gold standard treatments to attempt to mitigate the effects that this structural change exerts in menopausal osteoporosis patients; however, HRT effectiveness is often variable in these patients, likely due to variability in bone structure and physiology, and thus transport rates. Scientists have studied diffusion in cortical bone tissue for decades. Current methodological standards include fluorescence recovery after photobleaching and computed tomography finite element analysis. Both techniques limit areas of tissue to microscale (1-100 µm2) analysis - only examining a few osteocytes within the structure at a time - and adopt assumptions that oversimplify in vivo tissue structure and transport phenomena. As well, the range of diffusion tracers is limited by the sensitivities of the analytical equipment, typically requiring tracer concentrations in the micromolar range. Herein is described a novel device for directly assessing the diffusion coefficient of 3H-estradiol at 37°C in macroscale osteonal bone specimens (1.4 cm2) - assessing a much larger portion of the total tissue than previously reported - while using radioisotope tracers for much higher sensitivity, thus achieving physiologically relevant estradiol concentrations. The current diffusion chamber device represents a cost-effective and validated method to mitigate these shortcomings. The device provides long-term diffusion data through macroscale (greater than 1 mm2) tissue areas, presenting a more physiologically accurate way to assess cortical bone diffusion. The device can assess solute diffusion through other tissues or materials and may easily be scaled up to run multiple diffusion experiments simultaneously.

Lactation alters fluid flow and solute transport in maternal skeleton: A multiscale modeling study on the effects of microstructural changes and loading frequency

The female skeleton undergoes significant material and ultrastructural changes to meet high calcium demands during reproduction and lactation. Through the peri-lacunar/canalicular remodeling (PLR), osteocytes actively resorb surrounding matrix and enlarge their lacunae and canaliculi during lactation, which are quickly reversed after weaning. How these changes alter the physicochemical environment of osteocytes, the most abundant and primary mechanosensing cells in bone, are not well understood. In this study, we developed a multiscale poroelastic modeling technique to investigate lactation-induced changes in stress, fluid pressurization, fluid flow, and solute transport across multiple length scales (whole bone, porous midshaft cortex, lacunar-canalicular pore system (LCS), and pericellular matrix (PCM) around osteocytes) in murine tibiae subjected to axial compression at 3 N peak load (~320 με) at 0.5, 2, or 4 Hz. Based on previously reported skeletal anatomical measurements from lactating and nulliparous mice, our models demonstrated that loading frequency, LCS porosity, and PCM density were major determinants of fluid and solute flows responsible for osteocyte mechanosensing, cell-cell signaling, and metabolism. When loaded at 0.5 Hz, lactation-induced LCS expansion and potential PCM reduction promoted solute transport and osteocyte mechanosensing via primary cilia, but suppressed mechanosensing via fluid shear and/or drag force on the cell membrane. Interestingly, loading at 2 or 4 Hz was found to overcome the mechanosensing deficits observed at 0.5 Hz and these counter effects became more pronounced at 4 Hz and with sparser PCM in the lactating bone. Synergistically, higher loading frequency (2, 4 Hz) and sparser PCM enhanced flow-mediated mechanosensing and diffusion/convection of nutrients and signaling molecules for osteocytes. In summary, lactation-induced structural changes alter the local environment of osteocytes in ways that favor metabolism, mechanosensing, and post-weaning recovery of maternal bone. Thus, osteocytes play a role in balancing the metabolic and mechanical functions of female skeleton during reproduction and lactation.

Physiological Loading-Induced Interstitial Fluid Dynamics in Osteon of Osteogenesis Imperfecta Bone

Osteogenesis imperfecta (OI), also known as "brittle bone disease," is a genetic bone disorder. OI bones experience frequent fractures. Surgical procedures are usually followed by clinicians in the management of OI. It has been observed physical activity is equally beneficial in reducing OI bone fractures in both children and adults as mechanical stimulation improves bone mass and strength. Loading-induced mechanical strain and interstitial fluid flow stimulate bone remodeling activities. Several studies have characterized strain environment in OI bones, whereas very few studies attempted to characterize the interstitial fluid flow. OI significantly affects bone micro-architecture. Thus, this study anticipates that canalicular fluid flow reduces in OI bone in comparison to the healthy bone in response to physiological loading due to altered poromechanical properties. This work attempts to understand the canalicular fluid distribution in single osteon models of OI and healthy bone. A poromechanical model of osteon is developed to compute pore-pressure and interstitial fluid flow as a function of gait loading pattern reported for OI and healthy subjects. Fluid distribution patterns are compared at different time-points of the stance phase of the gait cycle. It is observed that fluid flow significantly reduces in OI bone. Additionally, flow is more static than dynamic in OI osteon in comparison to healthy subjects. This work attempts to identify the plausible explanation behind the diminished mechanotransduction capability of OI bone. This work may further be extended for designing better biomechanical therapies to enhance the fluid flow in order to improve osteogenic activities in OI bone.

Perspective on optical imaging for functional assessment in musculoskeletal extremity trauma surgery

SIGNIFICANCE

Extremity injury represents the leading cause of trauma hospitalizations among adults under the age of 65 years, and long-term impairments are often substantial. Restoring function depends, in large part, on bone and soft tissue healing. Thus, decisions around treatment strategy are based on assessment of the healing potential of injured bone and/or soft tissue. However, at the present, this assessment is based on subjective clinical clues and/or cadaveric studies without any objective measure. Optical imaging is an ideal method to solve several of these issues.

AIM

The aim is to highlight the current challenges in assessing bone and tissue perfusion/viability and the potentially high impact applications for optical imaging in orthopaedic surgery.

APPROACH

The prospective will review the current challenges faced by the orthopaedic surgeon and briefly discuss optical imaging tools that have been published. With this in mind, it will suggest key research areas that could be evolved to help make surgical assessments more objective and quantitative.

RESULTS

Orthopaedic surgical procedures should benefit from incorporation of methods to measure functional blood perfusion or tissue metabolism. The types of measurements though can vary in the depth of tissue sampled, with some being quite superficial and others sensing several millimeters into the tissue. Most of these intrasurgical imaging tools represent an ideal way to improve surgical treatment of orthopaedic injuries due to their inherent point-of-care use and their compatibility with real-time management.

CONCLUSION

While there are several optical measurements to directly measure bone function, the choice of tools can determine also the signal strength and depth of sampling. For orthopaedic surgery, real-time data regarding bone and tissue perfusion should lead to more effective patient-specific management of common orthopaedic conditions, requiring deeper penetrance commonly seen with indocyanine green imaging. This will lower morbidity and result in decreased variability associated with how these conditions are managed.

A Chemo-poroelastic Analysis of Mechanically Induced Fluid and Solute Transport in an Osteonal Cortical Bone

It is well known that transport of nutrients and wastes as solute in bone fluid plays an important role in bone remodeling and damage healing. This work presents a chemo-poroelastic model for fluid and solute transport in the lacunar-canalicular network of an osteonal cortical bone under cyclic axial mechanical loading or vascular pressure. Analytical solutions are obtained for the pore fluid pressure, and fluid and solute velocities. Numerical results for fluid and calcium transport indicate that under a cyclic stress of 20 MPa, the magnitudes of the fluid and calcium velocities increase with an increase in the loading frequency for the frequency range considered (≤ 3 Hz) and peak at the inner boundary. The peak magnitude of calcium velocity reaches 18.9 μm/s for an osteon with a permeability of 1.5 × 10^-19 m² under a 3 Hz loading frequency. The magnitude of calcium velocity under a vascular pressure of 50 mmHg is found to be two orders of magnitude smaller than that under the mechanical load. These results have the potential to be important in understanding fundamental aspects of cortical bone remodeling as transport characteristics of calcium and other nutrients at the osteon scale influence bone metabolism.

Network architecture strongly influences the fluid flow pattern through the lacunocanalicular network in human osteons

A popular hypothesis explains the mechanosensitivity of bone due to osteocytes sensing the load-induced flow of interstitial fluid squeezed through the lacunocanalicular network (LCN). However, the way in which the intricate structure of the LCN influences fluid flow through the network is largely unexplored. We therefore aimed to quantify fluid flow through real LCNs from human osteons using a combination of experimental and computational techniques. Bone samples were stained with rhodamine to image the LCN with 3D confocal microscopy. Image analysis was then performed to convert image stacks into mathematical network structures, in order to estimate the intrinsic permeability of the osteons as well as the load-induced fluid flow using hydraulic circuit theory. Fluid flow was studied in both ordinary osteons with a rather homogeneous LCN as well as a frequent subtype of osteons-so-called osteon-in-osteons-which are characterized by a ring-like zone of low network connectivity between the inner and the outer parts of these osteons. We analyzed 8 ordinary osteons and 9 osteon-in-osteons from the femur midshaft of a 57-year-old woman without any known disease. While the intrinsic permeability was 2.7 times smaller in osteon-in-osteons compared to ordinary osteons, the load-induced fluid velocity was 2.3 times higher. This increased fluid velocity in osteon-in-osteons can be explained by the longer path length, needed to cross the osteon from the cement line to the Haversian canal, including more fluid-filled lacunae and canaliculi. This explanation was corroborated by the observation that a purely structural parameter-the mean path length to the Haversian canal-is an excellent predictor for the average fluid flow velocity. We conclude that osteon-in-osteons may be particularly significant contributors to the mechanosensitivity of cortical bone, due to the higher fluid flow in this type of osteons.

A Perfusion Culture System for Assessing Bone Marrow Stromal Cell Differentiation on PLGA Scaffolds for Bone Repair

Biomaterials development for bone repair is currently hindered by the lack of physiologically relevant in vitro testing systems. Here we describe the novel use of a bi-directional perfusion bioreactor to support the long term culture of human bone marrow stromal cells (BMSCs) differentiated on polylactic co-glycolic acid (PLGA). Primary human BMSCs were seeded onto porous PLGA scaffolds and cultured in static vs. perfusion culture conditions for 21 days in osteogenic vs. control media. PLGA scaffolds were osteoconductive, supporting a mature osteogenic phenotype as shown by the upregulation of Runx2 and the early osteocyte marker E11. Perfusion culture enhanced the expression of osteogenic genes Osteocalcin and Osteopontin. Extracellular matrix deposition and mineralisation were spatially regulated within PLGA scaffolds in a donor dependant manner. This, together with the observed upregulation of Collagen type X suggested an environment permissive for the study of differentiation pathways associated with both intramembranous and endochondral ossification routes of bone healing. This culture system offers a platform to assess BMSC behavior on candidate biomaterials under physiologically relevant conditions. Use of this system may improve our understanding of the environmental cues orchestrating BMSC differentiation and enable fine tuning of biomaterial design as we develop tissue-engineered strategies for bone regeneration.

Solute Transport in the Bone Lacunar-Canalicular System (LCS)

PURPOSE OF REVIEW

Solute transport in the lacunar-canalicular system (LCS) plays important roles in osteocyte metabolism and cell-cell signaling. This review will summarize recent studies that establish pericellular matrix (PCM), discovered inside the LCS, as a crucial regulator of solute transport in bone.

RECENT FINDINGS

Utilizing confocal imaging and mathematical modeling, recent studies successfully quantified molecular diffusion and convection in the LCS as well as the size-dependent sieving effects of the PCM, leading to the quantification of the effective PCM fiber spacing (10 to 17 nm) in murine adult bones. Perlecan/HSPG2, a large linear proteoglycan, was identified to be an essential PCM component. The PCM-filled LCS is bone's chromatographic column, where fluid/solute transport to and from the osteocytes is regulated. The chemical composition, deposition rate, and turnover rate of the osteocyte PCM should be further defined to better understand osteocyte physiology and bone metabolism.

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.

A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone

The transport of fluid, nutrients, and signaling molecules in the bone lacunar–canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30–50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

Seeing through Musculoskeletal Tissues: Improving In Situ Imaging of Bone and the Lacunar Canalicular System through Optical Clearing

In situ, cells of the musculoskeletal system reside within complex and often interconnected 3-D environments. Key to better understanding how 3-D tissue and cellular environments regulate musculoskeletal physiology, homeostasis, and health is the use of robust methodologies for directly visualizing cell-cell and cell-matrix architecture in situ. However, the use of standard optical imaging techniques is often of limited utility in deep imaging of intact musculoskeletal tissues due to the highly scattering nature of biological tissues. Drawing inspiration from recent developments in the deep-tissue imaging field, we describe the application of immersion based optical clearing techniques, which utilize the principle of refractive index (RI) matching between the clearing/mounting media and tissue under observation, to improve the deep, in situ imaging of musculoskeletal tissues. To date, few optical clearing techniques have been applied specifically to musculoskeletal tissues, and a systematic comparison of the clearing ability of optical clearing agents in musculoskeletal tissues has yet to be fully demonstrated. In this study we tested the ability of eight different aqueous and non-aqueous clearing agents, with RIs ranging from 1.45 to 1.56, to optically clear murine knee joints and cortical bone. We demonstrated and quantified the ability of these optical clearing agents to clear musculoskeletal tissues and improve both macro- and micro-scale imaging of musculoskeletal tissue across several imaging modalities (stereomicroscopy, spectroscopy, and one-, and two-photon confocal microscopy) and investigational techniques (dynamic bone labeling and en bloc tissue staining). Based upon these findings we believe that optical clearing, in combination with advanced imaging techniques, has the potential to complement classical musculoskeletal analysis techniques; opening the door for improved in situ investigation and quantification of musculoskeletal tissues.

Altered mechanical environment of bone cells in an animal model of short- and long-term osteoporosis

Alterations in bone tissue composition during osteoporosis likely disrupt the mechanical environment of bone cells and may thereby initiate a mechanobiological response. It has proved challenging to characterize the mechanical environment of bone cells in vivo, and the mechanical environment of osteoporotic bone cells is not known. The objective of this research is to characterize the local mechanical environment of osteocytes and osteoblasts from healthy and osteoporotic bone in a rat model of osteoporosis. Using a custom-designed micromechanical loading device, we apply strains representative of a range of physical activity (up to 3000 με) to fluorescently stained femur samples from normal and ovariectomized rats. Confocal imaging was simultaneously performed, and digital image correlation techniques were applied to characterize cellular strains. In healthy bone tissue, osteocytes experience higher maximum strains (31,028 ± 4213 με) than osteoblasts (24,921 ± 3,832 με), whereas a larger proportion of the osteoblast experiences strains >10,000 με. Most interestingly, we show that osteoporotic bone cells experience similar or higher maximum strains than healthy bone cells after short durations of estrogen deficiency (5 weeks), and exceeded the osteogenic strain threshold (10,000 με) in a similar or significantly larger proportion of the cell (osteoblast, 12.68% vs. 13.68%; osteocyte, 15.74% vs. 5.37%). However, in long-term estrogen deficiency (34 weeks), there was no significant difference between bone cells in healthy and osteoporotic bone. These results suggest that the mechanical environment of bone cells is altered during early-stage osteoporosis, and that mechanobiological responses act to restore the mechanical environment of the bone tissue after it has been perturbed by ovariectomy.

Poromicromechanics reveals that physiological bone strains induce osteocyte-stimulating lacunar pressure

Mechanical loads which are macroscopically acting onto bony organs, are known to influence the activities of biological cells located in the pore spaces of bone, in particular so the signaling and production processes mediated by osteocytes. The exact mechanisms by which osteocytes are actually able to “feel” the mechanical loading and changes thereof, has been the subject of numerous studies, and, while several hypotheses have been brought forth over time, this topic has remained a matter of debate. Relaxation times reported in a recent experimental study of Gardinier et al. (Bone 46(4):1075–1081, 2010) strongly suggest that the lacunar pores are likely to experience, during typical physiological load cycles, not only fluid transport, but also undrained conditions. The latter entail the buildup of lacunar pore pressures, which we here quantify by means of a thorough multiscale modeling approach. In particular, the proposed model is based on classical poroelasticity theory, and able to account for multiple pore spaces. First, the model reveals distinct nonlinear dependencies of the resulting lacunar (and vascular) pore pressures on the underlying bone composition, highlighting the importance of a rigorous multiscale approach for appropriate computation of the aforementioned pore pressures. Then, the derived equations are evaluated for macroscopic (uniaxial as well as hydrostatic) mechanical loading of physiological magnitude. The resulting model-predicted pore pressures agree very well with the pressures that have been revealed, by means of in vitro studies, to be of adequate magnitude for modulating the responses of biological cells, including osteocytes. This underlines that osteocytes may respond to many types of loading stimuli at the same time, in particular so to fluid flow and hydrostatic pressure.

The dependences of osteocyte network on bone compartment, age, and disease

Osteocytes, the most abundant bone cells, form an interconnected network in the lacunar-canalicular pore system (LCS) buried within the mineralized matrix, which allows osteocytes to obtain nutrients from the blood supply, sense external mechanical signals, and communicate among themselves and with other cells on bone surfaces. In this study, we examined key features of the LCS network including the topological parameter and the detailed structure of individual connections and their variations in cortical and cancellous compartments, at different ages, and in two disease conditions with altered mechanosensing (perlecan deficiency and diabetes). LCS network showed both topological stability, in terms of conservation of connectivity among osteocyte lacunae (similar to the "nodes" in a computer network), and considerable variability the pericellular annular fluid gap surrounding lacunae and canaliculi (similar to the "bandwidth" of individual links in a computer network). Age, in the range of our study (15-32 weeks), affected only the pericellular fluid annulus in cortical bone but not in cancellous bone. Diabetes impacted the spacing of the lacunae, while the perlecan deficiency had a profound influence on the pericellular fluid annulus. The LCS network features play important roles in osteocyte signaling and regulation of bone growth and adaptation.

Perlecan-containing pericellular matrix regulates solute transport and mechanosensing within the osteocyte lacunar-canalicular system

The pericellular matrix (PCM), a thin coating surrounding nearly all mammalian cells, plays a critical role in many cell-surface phenomena. In osteocytes, the PCM is believed to control both "outside-in" (mechanosensing) and "inside-out" (signaling molecule transport) processes. However, the osteocytic PCM is challenging to study in situ because it is thin (∼100 nm) and enclosed in mineralized matrix. To this end, we recently developed a novel tracer velocimetry approach that combined fluorescence recovery after photobleaching (FRAP) imaging with hydrodynamic modeling to quantify the osteocytic PCM in young murine bone. In this study, we applied the technique to older mice expressing or deficient for perlecan/HSPG2, a large heparan-sulfate proteoglycan normally secreted in osteocytic PCM. The objectives were (1) to characterize transport within an altered PCM; (2) to test the sensitivity of our approach in detecting the PCM alterations; and (3) to dissect the roles of the PCM in osteocyte mechanosensing. We found that: (1) solute transport increases in the perlecan-deficient (hypomorphic [Hypo]) mice compared with control mice; (2) PCM fiber density decreases with aging and perlecan deficiency; (3) osteocytes in the Hypo bones are predicted to experience higher shear stress (+34%), but decreased fluid drag force (-35%) under 3-N peak tibial loading; and (4) when subjected to tibial loading in a preliminary in vivo experiment, the Hypo mice did not respond to the anabolic stimuli as the CTL mice did. These findings support the hypothesis that the PCM fibers act as osteocyte's sensing antennae, regulating load-induced cellular stimulations and thus bone's sensitivity and in vivo bone adaptation. If this hypothesis is further confirmed, osteocytic PCM could be new targets to develop osteoporosis treatments by modulating bone's intrinsic sensitivity to mechanical loading and be used to design patient-specific exercise regimens to promote bone formation.

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.

Quantifying load-induced solute transport and solute-matrix interaction within the osteocyte lacunar-canalicular system

Osteocytes, the most abundant cells in bone, are essential in maintaining tissue homeostasis and orchestrating bone's mechanical adaptation. Osteocytes depend upon load-induced convection within the lacunar-canalicular system (LCS) to maintain viability and to sense their mechanical environment. Using the fluorescence recovery after photobleaching (FRAP) imaging approach, we previously quantified the convection of a small tracer (sodium fluorescein, 376 Da) in the murine tibial LCS under intermittent cyclic loading. In the present study, we first expanded the investigation of solute transport using a larger tracer (parvalbumin, 12.3 kDa), which is comparable in size to some signaling proteins secreted by osteocytes. Murine tibiae were subjected to sequential FRAP tests under rest-inserted cyclic loading while the loading magnitude (0, 2.8, or 4.8 N) and frequency (0.5, 1, or 2 Hz) were varied. The characteristic transport rate k and the transport enhancement relative to diffusion (k/k0) were measured under each loading condition, from which the peak solute velocity in the LCS was derived using our LCS transport model. Both the transport enhancement and solute velocity increased with loading magnitude and decreased with loading frequency. Furthermore, the solute-matrix interaction, quantified in terms of the reflection coefficient through the osteocytic pericellular matrix (PCM), was measured and theoretically modeled. The reflection coefficient of parvalbumin (σ = 0.084) was derived from the differential fluid and solute velocities within loaded bone. Using a newly developed PCM sieving model, the PCM's fiber configurations accounting for the measured interactions were obtained for the first time. The present study provided not only new data on the micro-fluidic environment experienced by osteocytes in situ but also a powerful quantitative tool for future study of the PCM, the critical interface that controls both outside-in and inside-out signaling in osteocytes during normal bone adaptation and in pathological conditions.

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.

Skeletal adaptation to intramedullary pressure-induced interstitial fluid flow is enhanced in mice subjected to targeted osteocyte ablation

Interstitial fluid flow (IFF) is a potent regulatory signal in bone. During mechanical loading, IFF is generated through two distinct mechanisms that result in spatially distinct flow profiles: poroelastic interactions within the lacunar-canalicular system, and intramedullary pressurization. While the former generates IFF primarily within the lacunar-canalicular network, the latter generates significant flow at the endosteal surface as well as within the tissue. This gives rise to the intriguing possibility that loading-induced IFF may differentially activate osteocytes or surface-residing cells depending on the generating mechanism, and that sensation of IFF generated via intramedullary pressurization may be mediated by a non-osteocytic bone cell population. To begin to explore this possibility, we used the Dmp1-HBEGF inducible osteocyte ablation mouse model and a microfluidic system for modulating intramedullary pressure (ImP) to assess whether structural adaptation to ImP-driven IFF is altered by partial osteocyte depletion. Canalicular convective velocities during pressurization were estimated through the use of fluorescence recovery after photobleaching and computational modeling. Following osteocyte ablation, transgenic mice exhibited severe losses in bone structure and altered responses to hindlimb suspension in a compartment-specific manner. In pressure-loaded limbs, transgenic mice displayed similar or significantly enhanced structural adaptation to Imp-driven IFF, particularly in the trabecular compartment, despite up to ∼50% of trabecular lacunae being uninhabited following ablation. Interestingly, regression analysis revealed relative gains in bone structure in pressure-loaded limbs were correlated with reductions in bone structure in unpressurized control limbs, suggesting that adaptation to ImP-driven IFF was potentiated by increases in osteoclastic activity and/or reductions in osteoblastic activity incurred independently of pressure loading. Collectively, these studies indicate that structural adaptation to ImP-driven IFF can proceed unimpeded following a significant depletion in osteocytes, consistent with the potential existence of a non-osteocytic bone cell population that senses ImP-driven IFF independently and potentially parallel to osteocytic sensation of poroelasticity-derived IFF.

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.

Real-time measurement of solute transport within the lacunar-canalicular system of mechanically loaded bone: direct evidence for load-induced fluid flow

Since proposed by Piekarski and Munro in 1977, load-induced fluid flow through the bone lacunar-canalicular system (LCS) has been accepted as critical for bone metabolism, mechanotransduction, and adaptation. However, direct unequivocal observation and quantification of load-induced fluid and solute convection through the LCS have been lacking due to technical difficulties. Using a novel experimental approach based on fluorescence recovery after photobleaching (FRAP) and synchronized mechanical loading and imaging, we successfully quantified the diffusive and convective transport of a small fluorescent tracer (sodium fluorescein, 376 Da) in the bone LCS of adult male C57BL/6J mice. We demonstrated that cyclic end-compression of the mouse tibia with a moderate loading magnitude (-3 N peak load or 400 µε surface strain at 0.5 Hz) and a 4-second rest/imaging window inserted between adjacent load cycles significantly enhanced (+31%) the transport of sodium fluorescein through the LCS compared with diffusion alone. Using an anatomically based three-compartment transport model, the peak canalicular fluid velocity in the loaded bone was predicted (60 µm/s), and the resulting peak shear stress at the osteocyte process membrane was estimated (∼5 Pa). This study convincingly demonstrated the presence of load-induced convection in mechanically loaded bone. The combined experimental and mathematical approach presented herein represents an important advance in quantifying the microfluidic environment experienced by osteocytes in situ and provides a foundation for further studying the mechanisms by which mechanical stimulation modulates osteocytic cellular responses, which will inform basic bone biology, clinical understanding of osteoporosis and bone loss, and the rational engineering of their treatments.

Quantification of Lacunar-Canalicular Interstitial Fluid Flow Through Computational Modeling of Fluorescence Recovery After Photobleaching

Skeletal adaptation to mechanical loading has been widely hypothesized to involve the stimulation of osteocytes by interstitial fluid flow (IFF). However, direct investigation of this hypothesis has been difficult due in large part to the inability to directly measure IFF velocities within the lacunar-canalicular system. Measurements of fluorescence recovery after photobleaching (FRAP) within individual lacunae could be used to quantify lacunar-canalicular IFF when combined with mathematical modeling. In this study, we used a computational transport model to characterize the relationship between flow frequency (0.5-10 Hz), peak flow velocity (0-300 μm/s), tracer diffusion coefficient (100-300 μm(2)/s), and transport enhancement (i.e., (k/k(0)) - 1, where k and k(0) are the transport rates in the presence/absence of flow) during lacunar FRAP investigations. We show that this relationship is well described by a simple power law with frequency-dependent coefficients, and is relatively insensitive to variations in lacunar geometry. Using this power law relationship, we estimated peak IFF velocities in hindlimb mice subjected to intramedullary pressurization using values of k and k(0) previously obtained from ex vivo lacunar FRAP investigations. Together, our findings suggest that skeletal adaptation in hindlimb suspended mice subjected to dynamic intramedullary pressure occurred in the presence of IFF at levels associated with physiological loading.

Does blood pressure enhance solute transport in the bone lacunar-canalicular system?

Solute transport through bone plays an important role in tissue metabolism and cellular mechanotransduction. Due to limited diffusion within the mineralized bone matrix, both mechanical loading and vascular pressure have been proposed to drive interstitial fluid flow within the lacunar-canalicular system (LCS); thereby augmenting solute diffusion in bone. Although blood supply is critical for bone nutrition, growth, and fracture healing, whether physiological blood pressures can drive significant fluid and solute convection remains controversial within the literature. The goal of this study was to directly test the hypothesis that in vivo blood pressures enhance solute transport in the bone LCS. Using a newly developed imaging approach based on fluorescence recovery after photobleaching (FRAP), we first measured the transport rate of sodium fluorescein (M.W. 376 Da) through the tibial LCS in four anesthetized mice (in the presence of vascular pressure). These data were then compared with the tracer transport rates at the same locations/lacunae after sacrifice (in the absence of vascular pressure). Using paired FRAP experiments we did not detect differences in tracer transport rates between bones from live anesthetized animals versus those in postmortem bodies (p>0.05, N=18). In a separate cohort of four anesthetized mice a mean jugular pulse pressure of approximately 10 mmHg at approximately 10 Hz was measured. Further theoretical analysis showed that for bones from both small and large animal species the blood pressure-driven convection of either small (376 Da) or large (43,000 Da) molecules was at least one order of magnitude smaller than diffusion under either normal or elevated pressure conditions. We conclude that despite the extreme importance of vasculature in bone physiology, vascular pressure itself does not enhance acute solute transport within the bone LCS. Therefore, mechanisms other than the vascular pressure-induced fluid flow such as altered biochemical factors may account for the bone adaptation associated with altered circulation. The present study helped clarify a long-standing controversy regarding vascular pressure-induced bone fluid flow and provided a better understanding of bone adaptation in both physiological and pathological conditions.

Microfluidic enhancement of intramedullary pressure increases interstitial fluid flow and inhibits bone loss in hindlimb suspended mice

Interstitial fluid flow (IFF) has been widely hypothesized to mediate skeletal adaptation to mechanical loading. Although a large body of in vitro evidence has demonstrated that fluid flow stimulates osteogenic and antiresorptive responses in bone cells, there is much less in vivo evidence that IFF mediates loading-induced skeletal adaptation. This is due in large part to the challenges associated with decoupling IFF from matrix strain. In this study we describe a novel microfluidic system for generating dynamic intramedullary pressure (ImP) and IFF within the femurs of alert mice. By quantifying fluorescence recovery after photobleaching (FRAP) within individual lacunae, we show that microfluidic generation of dynamic ImP significantly increases IFF within the lacunocanalicular system. In addition, we demonstrate that dynamic pressure loading of the intramedullary compartment for 3 minutes per day significantly eliminates losses in trabecular and cortical bone mineral density in hindlimb suspended mice, enhances trabecular and cortical structural integrity, and increases endosteal bone formation rate. Unlike previously developed modalities for enhancing IFF in vivo, this is the first model that allows direct and dynamic modulation of ImP and skeletal IFF within mice. Given the large number of genetic tools for manipulating the mouse genome, this model is expected to serve as a powerful investigative tool in elucidating the role of IFF in skeletal adaptation to mechanical loading and molecular mechanisms mediating this process.

An in-situ fluorescence-based optical extensometry system for imaging mechanically loaded bone

The application and quantification of well-controlled tissue strains is required for investigations into mechanisms of tissue adaptation within the musculoskeletal system. Although many commercial and custom extensometry systems exist for large biological samples, integrated loading/strain measurement for small samples is not as readily available. Advanced imaging modules such as laser scanning microscopy provide in situ, minimally invasive tools to probe cellular and molecular processes with high spatiotemporal resolution. Currently, a need exists to devise loading/strain measurement systems that can be integrated with such advanced imaging modules. We describe the development and validation of a fluorescence-based, optical extensometry system directly integrated within a confocal microscopy platform. This system allows in situ measurement of surface strain and is compatible with the direct imaging of cellular processes within small bone samples. This optical extensometry system can accurately and reproducibly measure physiologically relevant surface strains (200 to 3000 microstrain) in beams machined from various well-characterized materials, including bovine femoral cortex, and in intact murine tibia. This simple system provides a powerful tool to further our investigation of the relationships between mechanical loading, fluid and solute transport, and mechanosensation within the musculoskeletal system.

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.

Anatomic variations of the lacunar-canalicular system influence solute transport in bone

Solute transport in the lacunar-canalicular system (LCS) is essential for bone metabolism and mechanotransduction. Using the technique of fluorescence recovery after photobleaching (FRAP) we have been quantifying solute transport in the LCS of murine long bone as a function of loading parameters and molecular size. However, the influence of LCS anatomy, which varies among animal species, bone type and location, age and health condition, is not well understood. In this study, we developed a mathematical model to simulate solute convection in the LCS during a FRAP experiment under a physiological cyclic flow. We found that the transport rate (the reciprocal time constant for refilling the photobleached lacuna) increased linearly with canalicular number and decreased with canalicular length for both diffusion and convection. As a result, the transport enhancement of convection over diffusion was much less sensitive to the variations associated with chick, mouse, rabbit, bovine, dog, horse, and human LCS anatomy, when compared with the rates of diffusion or convection alone. Canalicular density did not affect transport enhancement, while solute size and the lacunar density had more complicated, non-linear effects. This parametric study suggests that solute transport could be altered by varying LCS parameters, and that the anatomical details of the LCS need systemic examination to further understand the etiology of aged and osteoporotic bones.