Influence of interstitial bone microcracks on strain-induced fluid flow

Human cortical bone intrinsic permeability distribution based on 3D canalicular morphology

Bone permeability is a key parameter that drives osteocyte-based mechanobiological modelling and remodelling. While previous experimental and numerical studies have estimated bone permeability based on the morphology of the lacuno-canalicular network, these studies often relied on simplified geometries. In the current study, bone permeability was characterized using more realistic canalicular geometry for the morphological data. Bone samples harvested from 27 human femoral bones were investigated using synchrotron radiation-based nano-computed tomography with a voxel size of 100 nm. After segmenting the canaliculi and lacunae, each canaliculus was investigated individually by applying a distance map and watershed algorithms. Bone permeability based on canalicular morphology was then assessed using the Kozeny relation, which defines the permeability of a porous medium with capillary-like pores. An averaged intrinsic permeability value of 8.8 10-18 m2 was obtained. It should be noted that this study considered an empty canalicular network, however in vivo, both cellular and peri-cellular matrices decrease space for interstitial fluid flow and thus permeability. Furthermore, a voxel size of 100 nm does not allow for the detection of smaller canaliculi, which may also modify average permeability. With the current data set and the analytic process applied, the results showed a heterogeneous permeability distribution within bone tissue, both when comparing osteonal and interstitial tissues and within an individual osteon. A difference was observed between male and female samples, and permeability appeared to significantly decrease with age. Finally, a significant correlation was found between permeability and canalicular length density, defined as canalicular length per unit bone volume. This study proposes a new form of the Kozeny law to express bone canalicular permeability as a proportional relationship with the canalicular length density. Importantly, this parameter can be directly quantified through confocal fluorescence microcopy, which is more convenient than synchrotron radiation-based nano-computed tomography. In conclusion, the current study confirms that confocal microscopy can be serve as a reliable tool to estimate bone permeability. However, the permeability values calculated here are solely based on canalicular morphology and do not consider cellular and peri-cellular intra-canalicular features.

Influence of interstitial fluid pressure, porosity, loading magnitude, and anisotropy in cortical bone adaptation

Adaptive elasticity in cortical bone has traditionally been modeled using Strain Energy Density (SED). Recent studies have highlighted the importance of interstitial fluid in bone adaptation, yet no research has quantified the role of interstitial fluid pressure and its effects, specifically incorporating both SED and interstitial fluid pressure in the adaptation process. This study introduces a novel formulation combining theory of porous media and theory of adaptive elasticity that considers both SED and interstitial fluid's pressure in cortical bone adaptation. The formulation is solved using ANSYS Fluent and a MATLAB script, and sensitivity analyses were conducted, analyzing various porosities, loading magnitudes, anisotropic properties of cortical bone, and involvement coefficients of interstitial fluid's pressure. This study reveals that bones with different vascular porosities (PV) tend to achieve similar density distributions under uniform loading over time. This highlights the significant role of interstitial fluid pressure in accelerating the convergence to optimal bone properties, especially in specimens with larger PV porosities. The findings emphasize the importance of fluid pressure in bone remodeling, aligning with previous studies. Furthermore, this study demonstrates that considering transversely isotropic material properties can significantly alter the remodeling configuration compared to isotropic material properties. This highlights the importance of accurately representing the anisotropic nature of cortical bone in models to better predict its adaptive responses. However, aspects such as fluid density variations and bone geometry changes remain unexplored, suggesting directions for future research. Overall, this research enhances the understanding of cortical bone adaptation and its mechanical interactions.

Influence of intramedullary pressure on Lacuno-Canalicular fluid flow: A systematic review

While most of current models investigating bone remodelling are based on matrix deformation, intramedullary pressure also plays a role. Bone remodelling is orchestrated by the Lacuno-Canalicular Network (LCN) fluid-flow. The aim of this review was hence to assess the influence of intramedullary pressure on the fluid circulation within the LCN. Three databases (Science Direct, Web of Science, and PubMed) were used. The first phase of the search returned 731 articles, of which 9 respected the inclusion/exclusion criteria and were included. These studies confirm the association between intramedullary pressure and fluid dynamics in the LCN. Among the included studies, 7 experimental studies using animal models and 2 numerical models were found. The studies were then ranked according to the nature of the applied loading, either axial compression or direct cyclic intramedullary pressure. The current review revealed that there is an influence of intramedullary pressure on LCN fluid dynamics and that this influence depends on the magnitude and the frequency of the applied pressure. Two studies confirmed that the influence was effective even without bone matrix deformation. While intramedullary pressure is closely associated with LCN fluid, there is a severe lack of studies on this topic. STATEMENT OF SIGNIFICANCE: Since the 1990's, numerical models developed to investigate fluid flow in bone submicrometric porous network are based on the flow induced by matrix deformation. Bone fluid flow is known to be involved in cells stimulation and hence directly influences bone remodeling. Different studies have shown that intramedullary pressure is also associated with bone mechanosensitive adaptation. This pressure is developed in bone due to blood circulation and is increased during loading or muscle stimulation. The current article reviews the studies investigating the influence of this pressure on bone porous fluid flow. They show that fluid flow is involved by this pressure even without bone matrix deformation. The current review article highlights the severe lack of studies about this mechanism.

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.

Closing the osteon: Do osteocytes sense strain rate rather than fluid flow?

Osteons are cylindrical structures of bone created by matrix resorbing osteoclasts, followed by osteoblasts that deposit new bone. Osteons align with the principal loading direction and it is thought that the osteoclasts are directed by osteocytes, the mechanosensitive cells that reside inside the bone matrix. These osteocytes are presumably controlled by interstitial fluid flow, induced by the physiological loading of bones. Here I consider the stimulation of osteocytes while the osteon is closed by osteoblasts. In a conceptual finite element model, bone is considered a poro-elastic material and subjected to locomotion-induced loading conditions. It appears that the magnitude of flow is constant along the closing cone, while shear strain rate in the bone matrix diminishes linearly with the deposition of bone. This suggests that shear strain rate, rather than fluid flow, is the physical cue that controls osteocytes and bone deposition in newly formed osteons.

A review on computer modeling of bone piezoelectricity and its application to bone adaptation and regeneration

Bone is a hierarchical, multiphasic and anisotropic structure which in addition possess piezoelectric properties. The generation of piezoelectricity in bone is a complex process which has been shown to play a key role both in bone adaptation and regeneration. In order to understand the complex biological, mechanical and electrical interactions that take place during these processes, several computer models have been developed and used to test hypothesis on potential mechanisms behind experimental observations. This paper aims to review the available literature on computer modeling of bone piezoelectricity and its application to bone adaptation and healing. We first provide a brief overview of the fundamentals of piezoelectricity and bone piezoelectric effects. We then review how these properties have been used in computational models of bone adaptation and electromechanical behaviour of bone. In addition, in the last section, we summarize current limitations and potential directions for future work.

Migration and differentiation of osteoclast precursors under gradient fluid shear stress

The skeleton can adapt to mechanical loading through bone remodeling, and osteoclasts close to microdamages are believed to initiate bone resorption. However, whether local mechanical loading, such as fluid flow, regulates recruitment and differentiation of osteoclast precursors at the site of bone resorption has yet to be investigated. In the present study, finite element analysis first revealed the existence of a low-fluid shear stress (FSS) field inside microdamage. Based on a custom-made device of cone-and-plate fluid chamber, finite element analysis and particle image velocimetry measurement were performed to verify the formation of gradient FSS flow field. Furthermore, the effects of gradient FSS on the migration, aggregation, and fusion of osteoclast precursors were observed. Osteoclast precursor RAW264.7 cells migrated along a radial direction toward the region with decreased FSS during exposure to gradient FSS stimulation for 40 min, thereby deviating from the direction of actual fluid flow indicated by fluorescent particles. When calcium signaling pathway was inhibited by gadolinium and thapsigargin, cell migration toward a low-FSS region was significantly reduced. For the other cell lines MC3T3-E1, PDLF, rat mesenchymal stem cells, and Madin-Darby canine kidney epithelial cells, gradient FSS stimulation did not lead to low-FSS inclined migration. After being cultured under gradient FSS stimulation for 6 days, RAW264.7 cells showed significantly higher density and ratio of TRAP-positive multinucleated osteoclasts in the low-FSS region to those in the high-FSS region. Therefore, osteoclast precursor cells may exhibit the special ability to sense FSS gradient and tend to actively migrate toward low-FSS regions, which are regulated by calcium signaling pathway.

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.

Mathematically modeling fluid flow and fluid shear stress in the canaliculi of a loaded osteon

Background

Mechanical load-induced intraosseous pressure gradients may result in some fluid stimuli effects, such as fluid flow and fluid shear stress (FSS), which may enable bone cells to detect external mechanical signals. Interstitial bone fluid flow is known to occur in lacunar–canalicular porosity (PLC).

Methods

In order to characterize lacunar–canalicular fluid flow behavior, a hierarchical osteon system is developed. The osteon is modeled as a poroelastic annular cylinder with two types of impermeable boundary cases considered on its outer wall: one is elastic restrained (Case I), whereas the other is displacement confined (Case II). Analytical solutions such as canalicular fluid velocity, pressure, fluid flow rate (FFR), and shear stress are obtained.

Results

Results show that the amplitudes of FFR and FSS are proportional to strain amplitude and frequency. However, the key loading factor governing canalicular fluid flow behavior is the strain rate. The larger canalicular radius is, the larger amplitudes of FFR and FSS generalized, especially, the FSS amplitude is proportional to canalicular radius. In addition, both FFR and FSS amplitudes produced in case II are larger than those of case I.

Conclusion

Strain rate can be acted as a representative loading parameter governing the canalicular fluid flow behavior under a physiological state. This model can facilitate better understanding the load induced the fluid permeation in the PLC. The approach can also be used to analyze the structure of the proteoglycan matrix in the fluid space surrounding the osteocytic process in the canaliculus.

The effect of osteocyte apoptosis on signalling in the osteocyte and bone lining cell network: a computer simulation

Osteocytes play a critical role in the regulation of bone remodelling by translating strain due to mechanical loading into biochemical signals transmitted through the interconnecting lacuno-canalicular network to bone lining cells (BLCs) on the bone surface. This work aims to examine the effects of disruption of that intercellular communication by simulation of osteocyte apoptosis in the bone matrix. A model of a uniformly distributed osteocyte network has been developed that simulates the signalling through the network to the BLCs based on strain level. Bi-directional and asymmetric communication between neighbouring osteocytes and BLCs is included. The effect of osteocyte apoptosis is examined by preventing signalling at and through the affected cells. The simulation shows that apoptosis of only 3% of the osteocyte cells leads to a significant reduction in the peak signal at the BLCs. Furthermore, experiments with the model confirm how important the location and density of the apoptotic osteocytes are to the signalling received at the bone surface. With 5% and 9% osteocyte apoptosis, the mean peak BLC levels were reduced by 25% and 37% respectively. Such a significant reduction in the signal at the BLCs may explain a possible mechanism that leads to the increased remodelling and eventual bone loss observed with osteoporosis. More generally, it provides a unique framework for a broader exploration of the role of osteocyte and bi-directional and asymmetric cell-cell communication in mechanotransduction, and the effects of disruption to that communication.

The effect of rotative stress on CAII, FAS, FASL, OSCAR, and TRAP gene expression in osteoclasts

This study was designed to explore the effects of rotative stress on carbonic anhydrase II (CAII), TNF receptor superfamily member 6 (FAS), FAS ligand (FASL), osteoclast-associated receptor (OSCAR), and tartrate-resistant acid phosphatase (TRAP) gene expression in osteoclasts. Osteoclasts were induced from RAW264.7 cells cultured in medium containing recombinant murine soluble receptor activator of NF-Kβ ligand (sRANKL). The mRNA and protein expression of CAII, FAS, FASL, OSCAR, and TRAP genes in osteoclasts was detected by RT-PCR and Western blot, respectively, after osteoclasts were loaded at various rotative stress strengths and times. No significant differences in mRNA and protein expression were observed between any of the control groups (P > 0.05). Importantly, rotative stress had a significant effect on the mRNA and protein expression of these genes (P < 0.05). We found a negative relationship between rotative stress strength and prolonged loading time and the expression of FAS/FASL genes in osteoclasts. In addition, there was a positive relationship between rotative stress strength and prolonged loading time and the expression of CAII, OSCAR, or TRAP genes in osteoclasts. Based on these results, rotative stress has a significant effect on CAII, FAS, FASL, OSCAR, and TRAP gene expression in osteoclasts.

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.

Decreases in fluid shear stress due to microcracks: a possible primary pathogenesis of Kümmell's disease

The German doctor Hermann Kümmell described Kümmell's disease as the clinical scenario in which patients suffer a trivial spinal trauma, but develop a symptomatic, progressive, angular kyphosis after a symptom-free period of months to years. Since an intravertebral vacuum phenomenon, which is considered indicative of ischemic osteonecrosis, is often seen in the radiographs of patients with Kümmell's disease, most authors regard ischemic necrosis of the vertebral body as the primary pathogenesis of Kümmell's disease. However, we argue that Kümmell's disease is not commonly associated with typical avascular osteonecrosis of the femoral head and the intravertebral vacuum phenomenon is also present in other diseases. We postulated that even if ischemia plays a role in the pathogenesis of Kümmell's disease, it would not be the proximal cause of Kümmell's disease. In this article, we review the role of fluid shear stress in bone remolding and propose a microcosmic hypothesis in which microcracks lead to decreased fluid shear stress, which acts as the primary cause of Kümmell's disease. This was supported by conclusions drawn from a literature review: (1) fluid shear stress plays a crucial role in bone remodeling, and the osteocyte network is the main sensor of this mechanical stimulus; (2) decreased fluid shear stress will cause disequilibration of bone homeostasis, increasing bone resorption and reducing bone formation; and (3) the fluid flow of lacunar-canalicular porosity (PLC) and fluid shear stress near the microcracks decreases.