Poroelastic Evaluation of Fluid Movement Through the Lacunocanalicular System

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

BACKGROUND AND OBJECTIVES

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Effects of Osteocyte Shape on Fluid Flow and Fluid Shear Stress of the Loaded Bone

This study was conducted to better understand the specific behavior of the intraosseous fluid flow. We calculated the number and distribution of bone canaliculi around the osteocytes based on the varying shapes of osteocytes. We then used these calculated parameters and other bone microstructure data to estimate the anisotropy permeability of the lacunar-canalicular network. Poroelastic finite element models of the osteon were established, and the influence of the osteocyte shape on the fluid flow properties of osteons under an axial displacement load was analyzed. Two types of boundary conditions (BC) that might occur in physiological environments were considered on the cement line of the osteon. BC1 allows free fluid passage from the outer elastic restraint boundary, and BC2 is impermeable and allows no free fluid passage from outer displacement constrained boundary. They both have the same inner boundary conditions that allow fluid to pass through. Changes in the osteocyte shape altered the maximum value of pressure gradient (PG), pore pressure (PP), fluid velocity (FV), and fluid shear stress (FSS) relative to the reference model (spherical osteocytes). The maximum PG, PP, FV, and FSS in BC2 were nearly 100% larger than those in BC1, respectively. It is found that the BC1 was closer to the real physiological environment. The fluid flow along different directions in the elongated osteocyte model was more evident than that in other models, which may have been due to the large difference in permeability along different directions. Changes in osteocyte shape significantly affect the degrees of anisotropy of fluid flow and porous media of the osteon. The model presented in this study can accurately quantify fluid flow in the lacunar-canalicular network.

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

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

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.

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.

Local stimulation of osteocytes using a magnetically actuated oscillating beam

Mechanical loading on bone tissue is an important physiological stimulus that plays a key role in bone growth, fracture repair, and treatment of bone diseases. Osteocytes (bone cells embedded in bone matrix) are well accepted as the sensor cells to mechanical loading and play a critical role in regulating the bone structure in response to mechanical loading. To understand the response of osteocytes to differential mechanical stimulation in physiologically relevant arrangements, there is a need for a platform which can locally stimulate bone cells with different levels of fluid shear stress. In this study, we developed a device aiming to achieve non-contact local mechanical stimulation of osteocytes with a magnetically actuated beam that generates the fluid shear stresses encountered in vivo. The stimulating beam was made from a composite of magnetic powder and polymer, where a magnetic field was used to precisely oscillate the beam in the horizontal plane. The beam is placed above a cell-seeded surface with an estimated gap height of 5 μm. Finite element simulations were performed to quantify the shear stress values and to generate a shear stress map in the region of interest. Osteocytes were seeded on the device and were stimulated while their intracellular calcium responses were quantified and correlated with their position and local shear stress value. We observed that cells closer to the oscillating beam respond earlier compared to cells further away from the local shear stress gradient generated by the oscillating beam. We have demonstrated the capability of our device to mimic the propagation of calcium signalling to osteocytes outside of the stimulatory region. This device will allow for future studies of osteocyte network signalling with a physiologically accurate localized shear stress gradient.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980’s and early 1990’s. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

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.

Histologic analysis of medication-related osteonecrosis of the jaw compared with antiresorptive-exposed bone and other infectious, inflammatory, and necrotic jaw diseases

OBJECTIVE

This study characterized histologic features of medication-related osteonecrosis of the jaw (MRONJ) through analysis of tissues from patients and healthy individuals.

STUDY DESIGN

Bone biopsies were collected from various infectious, inflammatory, and necrotic jaw diseases. Samples were divided into bone exposed to bisphosphonates or denosumab, as well as bisphosphonate-related osteonecrosis of the jaw (BRONJ), denosumab-related osteonecrosis of the jaw (DRONJ), and mixed necrosis, enabling us to identify features of single agent necrosis without influence from previous therapies. Hematoxylin and eosin (H&E), receptor activator of nuclear factor κ-Β ligand (RANKL), tartrate-resistant acid phosphatase (TRAP), osteoprotegerin, toluidine blue, CD14, and CD68 staining and micro-computed tomography (micro-CT) analysis were performed. Groups were compared by using analysis of variance (ANOVA).

RESULTS

In total, 156 bone samples were collected from 105 patients. MRONJ variants exhibited more infectious infiltration. Bisphosphonate (P < .001) and mixed necrosis (P = .002) demonstrated more RANKL- and TRAP-positive osteoclasts. Denosumab necrosis (P = .007), and bone exposed to bisphosphonates (P = .028) in combination with denosumab (P = .022) demonstrated significantly lower numbers of osteocytes per area. CD14 and CD68 positivity was increased for BRONJ (P = .008; P < .001, respectively). MRONJ variants exhibited the widest trabecular width and decreased medullary space to bone. No diminished vascular network in MRONJ samples was observed.

CONCLUSIONS

Histologic features differ among MRONJ variants, with oversuppressed bone turnover, dysfunctional bone resorption, and a disturbed osteocyte network as potential mechanisms of pathogenesis.

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.

Lacunar-canalicular network in femoral cortical bone is reduced in aged women and is predominantly due to a loss of canalicular porosity

The lacunar-canalicular network (LCN) of bone contains osteocytes and their dendritic extensions, which allow for intercellular communication, and are believed to serve as the mechanosensors that coordinate the processes of bone modeling and remodeling. Imbalances in remodeling, for example, are linked to bone disease, including fragility associated with aging. We have reported that there is a reduction in scale for one component of the LCN, osteocyte lacunar volume, across the human lifespan in females. In the present study, we explore the hypothesis that canalicular porosity also declines with age. To visualize the LCN and to determine how its components are altered with aging, we examined samples from young (age: 20–23 y; n = 5) and aged (age: 70–86 y; n = 6) healthy women donors utilizing a fluorescent labelling technique in combination with confocal laser scanning microscopy. A large cross-sectional area of cortical bone spanning the endosteal to periosteal surfaces from the anterior proximal femoral shaft was examined in order to account for potential trans-cortical variation in the LCN. Overall, we found that LCN areal fraction was reduced by 40.6% in the samples from aged women. This reduction was due, in part, to a reduction in lacunar density (21.4% decline in lacunae number per given area of bone), but much more so due to a 44.6% decline in canalicular areal fraction. While the areal fraction of larger vascular canals was higher in endosteal vs. periosteal regions for both age groups, no regional differences were observed in the areal fractions of the LCN and its components for either age group. Our data indicate that the LCN is diminished in aged women, and is largely due to a decline in the canalicular areal fraction, and that, unlike vascular canal porosity, this diminished LCN is uniform across the cortex.

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The lacunar-canalicular network (LCN) is reduced by 40.6% in aged women

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The lacunar density (lacunae number per given area of bone) is reduced by 21.4% in aged women

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The reduction in LCN in aged women is primarily due to a 44.6% loss of canaliculi

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No endosteal vs. periosteal regional differences were observed in the LCN and its components in either young or aged women

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A reduction in canaliculi with age may contribute to bone fragility in aged women

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.

Building a 3D Virtual Liver: Methods for Simulating Blood Flow and Hepatic Clearance on 3D Structures

In this paper, we develop a spatio-temporal modeling approach to describe blood and drug flow, as well as drug uptake and elimination, on an approximation of the liver. Extending on previously developed computational approaches, we generate an approximation of a liver, which consists of a portal and hepatic vein vasculature structure, embedded in the surrounding liver tissue. The vasculature is generated via constrained constructive optimization, and then converted to a spatial grid of a selected grid size. Estimates for surrounding upscaled lobule tissue properties are then presented appropriate to the same grid size. Simulation of fluid flow and drug metabolism (hepatic clearance) are completed using discretized forms of the relevant convective-diffusive-reactive partial differential equations for these processes. This results in a single stage, uniformly consistent method to simulate equations for blood and drug flow, as well as drug metabolism, on a 3D structure representative of a liver.

Changes in cortical bone channels network and osteocyte organization after the use of zoledronic acid

OBJECTIVE

The aim of this study was to evaluate the effects of zoledronic acid (ZA) on the cortical bone channels network (CBCN) and osteocyte organization in relation to the bone channels.

MATERIALS AND METHODS

Eighteen male Wistar rats were divided into control (CG) and test groups (TG). Twelve animals from TG received 3 ZA doses (7.5 µg/kg), and 6 animals from CG did not receive any medication. TG animals were euthanized at 14 (n = 6) and 75 (n = 6) dadys after drug injection. CBCN was analyzed in mandibles and tibias using computational routines. The osteocyte organization was qualitatively evaluated in tibias using a three-dimensional reconstruction of images from serial histological sections.

RESULTS

Significant differences in CBCN of tibia were found between the treated and untreated rats, with a wider range of sizes and shapes of the channels after the use of ZA (channels area p = 0.0063, channels area SD p = 0.0276) and less bone matrix (bone volume p = 0.0388). The alterations in the channels' morphology were more evident at 75 days after the drug injection (channels perimeter p = 0.0286). No differences were found in mandibles CBCN. The osteocyte distribution revealed more variable patterns of cell distribution in ZA groups, with non-homogeneous distribution of cells in relation to the bone channels.

CONCLUSION

Zoledronic acid induces structural changes in CBCN and modifies the osteocyte arrangement in cortical bone in the tibia; also, the variability in the morphology of bone channels became more evident after a certain time of the use of the drug.

Strain amplification analysis of an osteocyte under static and cyclic loading: a finite element study

Osteocytes, the major type of bone cells which reside in their lacunar and canalicular system within the bone matrix, function as biomechanosensors and biomechanotransducers of the bone. Although biomechanical behaviour of the osteocyte-lacunar-canalicular system has been investigated in previous studies mostly using computational 2-dimensional (2D) geometric models, only a few studies have used the 3-dimensional (3D) finite element (FE) model. In the current study, a 3D FE model was used to predict the responses of strain distributions of osteocyte-lacunar-canalicular system analyzed under static and cyclic loads. The strain amplification factor was calculated for all simulations. Effects on the strain of the osteocyte system were investigated under 500, 1500, 2000, and 3000 microstrain loading magnitudes and 1, 5, 10, 40, and 100 Hz loading frequencies. The maximum strain was found to change with loading magnitude and frequency. It was observed that maximum strain under 3000-microstrain loading was higher than those under 500, 1500, and 2000 microstrains. When the loading strain reached the maximum magnitude, the strain amplification factor of 100 Hz was higher than those of the other frequencies. Data from this 3D FE model study suggests that the strain amplification factor of the osteocyte-lacunar-canalicular system increases with loading frequency and loading strain increasing.

A poroelastic model describing nutrient transport and cell stresses within a cyclically strained collagen hydrogel

In the creation of engineered tissue constructs, the successful transport of nutrients and oxygen to the contained cells is a significant challenge. In highly porous scaffolds subject to cyclic strain, the mechanical deformations can induce substantial fluid pressure gradients, which affect the transport of solutes. In this article, we describe a poroelastic model to predict the solid and fluid mechanics of a highly porous hydrogel subject to cyclic strain. The model was validated by matching the predicted penetration of a bead into the hydrogel from the model with experimental observations and provides insight into nutrient transport. Additionally, the model provides estimates of the wall-shear stresses experienced by the cells embedded within the scaffold. These results provide insight into the mechanics of and convective nutrient transport within a cyclically strained hydrogel, which could lead to the improved design of engineered tissues.

Textural versus electrostatic exclusion-enrichment effects in the effective chemical transport within the cortical bone: a numerical investigation

Interstitial fluid within bone tissue is known to govern the remodelling signals' expression. Bone fluid flow is generated by skeleton deformation during the daily activities. Due to the presence of charged surfaces in the bone porous matrix, the electrochemical phenomena occurring in the vicinity of mechanosensitive bone cells, the osteocytes, are key elements in the cellular communication. In this study, a multiscale model of interstitial fluid transport within bone tissues is proposed. Based on an asymptotic homogenization method, our modelling takes into account the physicochemical properties of bone tissue. Thanks to this multiphysical approach, the transport of nutrients and waste between the blood vessels and the bone cells can be quantified to better understand the mechanotransduction of bone remodelling. In particular, it is shown that the electrochemical tortuosity may have stronger implications in the mass transport within the bone than the purely morphological one.

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.

A physiologically-based flow network model for hepatic drug elimination I: regular lattice lobule model

We develop a physiologically-based lattice model for the transport and metabolism of drugs in the functional unit of the liver, called the lobule. In contrast to earlier studies, we have emphasized the dominant role of convection in well-vascularized tissue with a given structure. Estimates of convective, diffusive and reaction contributions are given. We have compared drug concentration levels observed exiting the lobule with their predicted detailed distribution inside the lobule, assuming that most often the former is accessible information while the latter is not.

A physiologically-based flow network model for hepatic drug elimination II: variable lattice lobule models

We extend a physiologically-based lattice model for the transport and metabolism of drugs in the liver lobule (liver functional unit) to consider structural and spatial variability. We compare predicted drug concentration levels observed exiting the lobule with their detailed distribution inside the lobule, and indicate the role that structural variation has on these results. Liver zonation and its role on drug metabolism represent another aspect of structural inhomogeneity that we consider here. Since various liver diseases can be thought to produce such structural variations, our analysis gives insight into the role of disease on liver function and performance. These conclusions are based on the dominant role of convection in well-vascularized tissue with a given structure.

Microscale fluid flow analysis in a human osteocyte canaliculus using a realistic high-resolution image-based three-dimensional model

Osteocytes play a pivotal role in the regulation of skeletal mass. Osteocyte processes are thought to sense the flow of interstitial fluid that is driven through the osteocyte canaliculi by mechanical stimuli placed upon bone, but how this flow elicits a cellular response is virtually unknown. Modern theoretical models assume that osteocyte canaliculi contain ultrastructural features that amplify the fluid flow-derived mechanical signal. Unfortunately the calcified bone matrix has considerably hampered studies on the osteocyte process within its canaliculus. Using one of the few ultra high voltage electron microscopes (UHVEM) available worldwide, we applied UHVEM tomography at 2 MeV to reconstruct unique three-dimensional images of osteocyte canaliculi in 1 μm sections of human bone. A realistic three-dimensional image-based model of a single canaliculus was constructed, and the fluid dynamics of a Newtonian fluid flow within the canaliculus was analyzed. We created virtual 2.2 nm thick sections through a canaliculus and found that traditional TEM techniques create a false impression that osteocyte processes are directly attached to the canalicular wall. The canalicular wall had a highly irregular surface and contained protruding axisymmetric structures similar in size and shape to collagen fibrils. We also found that the microscopic surface roughness of the canalicular wall strongly influenced the fluid flow profiles, whereby highly inhomogeneous flow patterns emerged. These inhomogeneous flow patterns may induce deformation of cytoskeletal elements in the osteocyte process, thereby amplifying mechanical signals. Based on these observations, new and realistic models can be developed that will significantly enhance our understanding of the process of mechanotransduction in bone.

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.

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.

An Integrative Review of Mechanotransduction in Endothelial, Epithelial (Renal) and Dendritic Cells (Osteocytes)

In this review we will examine from a biomechanical and ultrastructural viewpoint how the cytoskeletal specialization of three basic cell types, endothelial cells (ECs), epithelial cells (renal tubule) and dendritic cells (osteocytes), enables the mechano-sensing of fluid flow in both their native in vivo environment and in culture, and the downstream signaling that is initiated at the molecular level in response to fluid flow. These cellular responses will be discussed in terms of basic mysteries and paradoxes encountered by each cell type. In ECs fluid shear stress (FSS) is nearly entirely attenuated by the endothelial glycocalyx that covers their apical membrane and yet FSS is communicated to both intracellular and junctional molecular components in activating a wide variety of signaling pathways. The same is true in proximal tubule (PT) cells where a dense brush border of microvilli covers the apical surface and the flow at the apical membrane is negligible. A four decade old unexplained mystery is the ability of PT epithelia to reliably reabsorb 60% of the flow entering the tubule regardless of the glomerular filtration rate. In the cortical collecting duct (CCD) the flow rates are so low that a special sensing apparatus, a primary cilia is needed to detect very small variations in tubular flow. In bone it has been a century old mystery as to how osteocytes embedded in a stiff mineralized tissue are able to sense miniscule whole tissue strains that are far smaller than the cellular level strains required to activate osteocytes in vitro.

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.

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.