On the paradoxical determinations of the lacuno-canalicular permeability of bone

3D quantification of the lacunocanalicular network on human femoral diaphysis through synchrotron radiation-based nanoCT

Osteocytes are the major actors in bone mechanobiology. Within bone matrix, they are trapped close together in a submicrometric interconnected network: the lacunocanalicular network (LCN). The interstitial fluid circulating within the LCN transmits the mechanical information to the osteocytes that convert it into a biochemical signal. Understanding the interstitial fluid dynamics is necessary to better understand the bone mechanobiology. Due to the submicrometric dimensions of the LCN, making it difficult to experimentally investigate fluid dynamics, numerical models appear as a relevant tool for such investigation. To develop such models, there is a need for geometrical and morphological data on the human LCN. This study aims at providing morphological data on the human LCN from measurement of 27 human femoral diaphysis bone samples using synchrotron radiation nano-computed tomography with an isotropic voxel size of 100 nm. Except from the canalicular diameter, the canalicular morphological parameters presented a high variability within one sample. Some differences in terms of both lacunar and canalicular morphology were observed between the male and female populations. But it has to be highlighted that all the canaliculi cannot be detected with a voxel size of 100 nm. Hence, in the current study, only a specific population of large canaliculi that could be characterize. Still, to the authors knowledge, this is the first time such a data set was introduced to the community. Further processing will be achieved in order to provide new insight on the LCN permeability.

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.

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 multi-layered poroelastic slab model under cyclic loading for a single osteon

Background

An osteon consists of a multi-layered bone matrix and interstitial fluid flow in the lacunar–canalicular system. Loading-induced interstitial fluid flow in the lacunar–canalicular system is critical for osteocyte mechanotransduction and bone remodelling.

Methods

To investigate the effects of the lamellar structure and heterogeneous material properties of the osteon on the distributions of interstitial fluid flow and seepage velocity, an osteon is idealized as a hollow two-dimensional poroelastic multi-layered slab model subjected to cyclic loading. Based on poroelastic theory, the analytical solutions of interstitial fluid pressure and seepage velocity in lacunar–canalicular pores were obtained.

Results

The results show that strain magnitude has a greater influence on interstitial fluid pressure than loading frequency. Interestingly, the heterogeneous distribution of permeability produces remarkable variations in interstitial fluid pressure and seepage velocity in the cross-section of cortical bone. In addition, interstitial fluid flow stimuli to osteocytes are mostly controlled by the value of permeability at the surface of the osteon rather than at the inner wall of the osteon.

Conclusion

Interstitial fluid flow induced by cycling loading stimuli to an osteocyte housed in a lacunar–canalicular pore is not only correlated with strain amplitude and loading frequency, but also closely correlated with the spatial gradient distribution of permeability. This model can help us better understand the fluid flow stimuli to osteocytes during bone remodelling.

In silico bone mechanobiology: modeling a multifaceted biological system

Mechanobiology, the study of the influence of mechanical loads on biological processes through signaling to cells, is fundamental to the inherent ability of bone tissue to adapt its structure in response to mechanical stimulation. The immense contribution of computational modeling to the nascent field of bone mechanobiology is indisputable, having aided in the interpretation of experimental findings and identified new avenues of inquiry. Indeed, advances in computational modeling have spurred the development of this field, shedding new light on problems ranging from the mechanical response to loading by individual cells to tissue differentiation during events such as fracture healing. To date, in silico bone mechanobiology has generally taken a reductive approach in attempting to answer discrete biological research questions, with research in the field broadly separated into two streams: (1) mechanoregulation algorithms for predicting mechanobiological changes to bone tissue and (2) models investigating cell mechanobiology. Future models will likely take advantage of advances in computational power and techniques, allowing multiscale and multiphysics modeling to tie the many separate but related biological responses to loading together as part of a larger systems biology approach to shed further light on bone mechanobiology. Finally, although the ever‐increasing complexity of computational mechanobiology models will inevitably move the field toward patient‐specific models in the clinic, the determination of the context in which they can be used safely for clinical purpose will still require an extensive combination of computational and experimental techniques applied to in vitro and in vivo applications. WIREs Syst Biol Med 2016, 8:485–505. doi: 10.1002/wsbm.1356

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Water in hydroxyapatite nanopores: Possible implications for interstitial bone fluid flow

The role of bone water in the activity of this organ is essential in structuring apatite crystals, providing pathways for nutrients and waste involved in the metabolism of bone cells and participating in bone remodelling mechanotransduction. It is commonly accepted that bone presents three levels of porosity, namely the vasculature, the lacuno-canalicular system and the voids of the collagen-apatite matrix. Due to the observation of bound state of water at the latter level, the interstitial nanoscopic flow that may exist within these pores is classically neglected. The aim of this paper is to investigate the possibility to obtain a fluid flow at the nanoscale. That is why a molecular dynamics based analysis of a water-hydroxyapatite system is proposed to analyze the effect of water confinement on transport properties. The main result here is that free water can be observed inside hydroxyapatite pores of a few nanometers. This result would have strong implications in the multiscale treatment of the poromechanical behaviour of bone tissue. In particular, the mechanical properties of the bone matrix may be highly controlled by nanoscopic water diffusion and the classical idea that osteocytic activity is only regulated by bone fluid flow within the lacuno-canalicular system may be discussed again.

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.

Periosteum, bone's "smart" bounding membrane, exhibits direction-dependent permeability

The periosteum serves as bone's bounding membrane, exhibits hallmarks of semipermeable epithelial barrier membranes, and contains mechanically sensitive progenitor cells capable of generating bone. The current paucity of data regarding the periosteum's permeability and bidirectional transport properties provided the impetus for the current study. In ovine femur and tibia samples, the periosteum's hydraulic permeability coefficient, k, was calculated using Darcy's Law and a custom-designed permeability tester to apply controlled, volumetric flow of phosphate-buffered saline through periosteum samples. Based on these data, ovine periosteum demonstrates mechanically responsive and directionally dependent (anisotropic) permeability properties. At baseline flow rates comparable to interstitial fluid flow (0.5 µL/s), permeability is low and does not exhibit anisotropy. In contrast, at high flow rates comparable to those prevailing during traumatic injury, femoral periosteum exhibits an order of magnitude higher permeability compared to baseline flow rates. In addition, at high flow rates permeability exhibits significant directional dependence, with permeability higher in the bone to muscle direction than vice versa. Furthermore, compared to periosteum in which the intrinsic tension (pre-stress) is maintained, free relaxation of the tibial periosteum after resection significantly increases its permeability in both flow directions. Hence, the structure and mechanical stress state of periosteum influences its role as bone's bounding membrane. During periods of homeostasis, periosteum may serve as a barrier membrane on the outer surface of bone, allowing for equal albeit low quiescent molecular communication between tissue compartments including bone and muscle. In contrast, increases in pressure and baseline flow rates within the periosteum resulting from injury, trauma, and/or disease may result in a significant increase in periosteum permeability and consequently in increased molecular communication between tissue compartments. Elucidation of the periosteum's permeability properties is key to understanding periosteal mechanobiology in bone health and healing, as well as to elucidate periosteum structure and function as a smart biomaterial that allows bidirectional and mechanically responsive fluid transport.

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.

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

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells' metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte's dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.

Possible role of calcium permselectivity in bone adaptation

According to the core activity of calcium in the bone cellular expression, a new hypothesis linking calcium transport with the mechanical loading is proposed to explain the mechano-adaptation of bone tissue. Due to the piezoelectric coupling, the tensile and compressive areas of bone produce different electrical environments for the osteocytic cells that are embedded in the lacuno-canalicular porosity. This electrical asymmetry engenders a calcium enrichment-exclusion effect that strongly changes the calcium concentration in the lacuno-canalicular fluid and thus modifies the remodelling process. A bibliographic body of evidence supporting this idea is given and its experimental validation is suggested.