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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...
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Citations
... Bone marrow is a viscous fluid, and its viscosity is generated by intercellular interactions [9]. When the bone is subjected to external loads, the deformation of the bone matrix can cause fluid flow in the cancellous bone system [10][11][12][13]. Studies have shown that when bone perceives mechanical stimulation, fluid shear stress will be generated, which will cause osteoblasts or osteoclasts on the surface of cancellous bone to respond, and ultimately regulate bone remodeling to adapt bone to its mechanical environment [14][15][16][17][18]. ...
Background
The purpose of this study was to investigate the effects of four different doses of verapamil on the mechanical behaviors of solid and the characteristics of fluid flow in cancellous bone of distal femur of type 2 diabetes rats under dynamic external load.
Methods
Based on the micro-CT images, the finite element models of cancellous bones and fluids at distal femurs of rats in control group, diabetes group, treatment groups VER 4, VER 12, VER 24, and VER 48 (verapamil doses of 4, 12, 24, and 48 mg/kg/day, respectively) were constructed. A sinusoidal time-varying displacement load with an amplitude of 0.8 μm and a period of 1s was applied to the upper surface of the solid region. Then, fluid-solid coupling numerical simulation method was used to analyze the magnitudes and distributions of von Mises stress, flow velocity, and fluid shear stress of cancellous bone models in each group.
Results
The results for mean values of von Mises stress, flow velocity and FSS (t = 0.25s) were as follows: their values in control group were lower than those in diabetes group; the three parameters varied with the dose of verapamil; in the four treatment groups, the values of VER 48 group were the lowest, they were the closest to control group, and they were smaller than diabetes group. Among the four treatment groups, VER 48 group had the highest proportion of the nodes with FSS = 1-3 Pa on the surface of cancellous bone, and more areas in VER 48 group were subjected to fluid shear stress of 1-3 Pa for more than half of the time.
Conclusion
It could be seen that among the four treatment groups, osteoblasts on the cancellous bone surface in the highest dose group (VER 48 group) were more easily activated by mechanical loading, and the treatment effect was the best. This study might help in understanding the mechanism of verapamil’s effect on the bone of type 2 diabetes mellitus, and provide theoretical guidance for the selection of verapamil dose in the clinical treatment of type 2 diabetes mellitus.
... For bone and cartilage, linear poroelasticity has been used to model the macroscopic mechanical response and/or the distribution of pore pressure during small periodic deformations (e.g. Zhang & Cowin 1994;Manfredini et al. 1999;Riches et al. 2002;Kameo, Adachi & Hojo 2008;Yaogeng et al. 2018). Zhang & Cowin (1994) showed that the magnitude and distribution of pore pressure depend strongly on the loading period, introducing the ratio of the loading period to the poroelastic relaxation time as a key dimensionless control parameter. ...
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically investigated. Here, we fill this gap by identifying and exploring the complete parameter space associated with periodic deformations in the context of a one-dimensional model problem. We use large-deformation poroelasticity to consider a wide range of loading periods and amplitudes. We identify two distinct mechanical regimes, distinguished by whether the loading period is slow or fast relative to the characteristic poroelastic timescale. We develop analytical solutions for slow loading at any amplitude and for infinitesimal amplitude at any period. We use these analytical solutions and a full numerical solution to explore the localisation of the deformation near the permeable boundary as the period decreases and the emergence of nonlinear effects as the amplitude increases. We show that large deformations lead to asymmetry between the loading and unloading phases of each cycle in terms of the distributions of porosity and fluid flux.
... In this regime, poroelasticity is physically diffusive with a characteristic poroelastic relaxation time. For bone and cartilage, linear poroelasticity has been used to model the macroscopic mechanical response and/or the distribution of pore pressure during small periodic deformations [e.g., 5,13,14,41,42]. Zhang and Cowin [13] showed that the magnitude and distribution of pore pressure depend strongly on the loading period, introducing the ratio of the loading period to the poroelastic relaxation time as a key dimensionless control parameter. For cartilage and hydrogel scaffolds, both linear and nonlinear poroelasticity have been used to model the impact of periodic deformations on the transport of solutes, typically by comparing the concentration profile at the end of loading across a small set of different loading conditions [e.g., 4,[6][7][8][43][44][45]. ...
Soft porous materials are exposed to periodic deformations in a variety of natural and industrial contexts. For example, many biological tissues experience periodic compression due to natural pulsation or basic biomechanical function. This loading can have practical implications for the stimulation of cell growth, the evolution of material structure through degradation or consolidation, and the transport of waste, nutrients, and contaminants. However, the detailed flow and mechanics of these deformations have not yet been systematically investigated. Here, we fill this gap by identifying and exploring the complete parameter space associated with periodic deformations in the context of a 1D model problem. We use large-deformation poroelasticity to consider a wide range of loading periods and amplitudes. We identify two distinct mechanical regimes, distinguished by whether the loading period is slow or fast relative to the characteristic poroelastic timescale. We develop analytical solutions for slow loading at any amplitude and for infinitesimal amplitude at any period. We use these analytical solutions and a full numerical solution to explore the emergence of nonlinear effects as the amplitude increases and the localisation of the deformation near the permeable boundary as the period decreases. We show that the latter effect leads to asymmetry between the loading and unloading phases of each cycle in terms of the distributions of porosity and fluid flux.
... Oblique fracture propagation appears to occur in single osteon bending tests [98]. Models that assume osteons are composed of concentric cylinders [99][100][101][102][103][104][105] that may find interlamellar shearing behaviour under tension, compression and torsion as the surfaces are all parallel or orthogonal to the loading axis. On the other hand, a stack of cones could behave as a series of wedges under compression, converting an axial force into radial compression as a function of wedge angle. ...
Lamellae are sheets of mineralized collagen 1–20 µm thick, extending over hundreds of µm in bone tissue, occupying bone's structural hierarchy at a level above collagen fibres and osteocytes, and below osteons and trabeculae. Osteons are tubular arrangements of lamellae surrounding central neurovascular canals. Lamellae in osteons are usually described as concentric cylinders based on their annular appearance in transverse section. In this review, I provide a perspective on current understanding of the relationship between geometry of the bone formation front and the shape of lamellae produced at it, reaching the conclusion that the ‘closing cone’ bone formation front in secondary osteonal remodelling must necessarily result in cone-shaped lamellae in the mature secondary osteon. Secondary osteons replace primary osteons through a tunnelling process of bone turnover, meaning that conical lamellae may become more common in older and damaged bone which is at greatest risk of fracture. Visualization and measurement of three-dimensional lamellar shape over hundreds of microns is needed to provide data for accurate micromechanical simulations. Treating secondary osteonal lamellae as a ‘stack of cones’ rather than ‘nested cylinders’ may have important implications for our appreciation of bone's function as a load-bearing tissue and of its behaviour in fracture.
... However, osteocytes are embedded in a mineralized extracellular matrix, making it difficult to apply direct experimental approaches. Therefore, mathematical models of fluid flow in the bone matrix have been established [17][18][19][20]. Poroelasticity is a well-developed concept for investigating the interaction of fluid and solid phases in the bone [3,[21][22][23]. ...
... Due to the periodicity of the geometrical configuration, we defined the representative elementary volume (REV) by CUPC. The poroelasticity theory efficiently describes the fluid flow behavior of the osteon [3,4,7,19,35]. The osteon was illustrated as a solid-liquid coupling porous elastic material composed of CUPC units in this study. ...
... The following governing equations could describe the poroelastic behavior of the bone, and no body forces were considered. Constitutive laws for the solid matrix material and the saturating fluid were as follows [19,35]: ...
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.
... [22] This concept was confirmed in a dynamic model of bone remodelling [104] and is now implemented in many recent osteon models. [56,95,102,[105][106][107] Yet there are deviations from osteon alignment along the lines of principal stress: osteons do not align perfectly in parallel and there are Volkmann's canals that connect adjacent osteons. [19,21] What could be the origin of this? ...
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 depo-sition in newly formed osteons. K E Y W O R D S BMU, bone deposition, bone remodeling, fluid flow, osteoblast, osteocyte, shear strain rate
... PG refers to the change of pressure per unit length along the direction of fluid flow. This important parameter is often not discussed in previous studies [4,6,19,20]. ...
... Due to the periodicity of geometrical configuration, we defined the representative elementary volume (REV) by CUPC. Using poroelasticity theory to describe the fluid flow behavior in osteon was proved to be efficient [4,5,8,19,20]. ...
... The osteon was illustratesed as a solid-liquid coupling porous elastic material composed of CUPC units in this study, and As shown in Fig. 8, the osteon was regarded as a hollow annular cylinder under cyclic loading in longitudinal orientation.The following governing equations could be used to describe the poroelastic behavior of bone, and nobody forces were taken into account. Constitutive laws for the solid matrix material and the saturating fluid were written as [20]: ...
Background: Load-induced pressure gradients (PG) result in interstitial fluid flow in bone tissue, which is not only provides sufficient nutrient supply and metabolic pathway for the bone cells, but also enables bone cells to accept external mechanical signals.
Methods: We calculate the number and distribution of bone canaliculus around the osteocyte based on the varying shape of osteocyte, and then use these calculated parameters and other microstructure data of bone tissue to estimate the anisotropy permeability of the lacunar–canalicular. Finally, according to the calculated parameters, the poroelastic finite element models of the osteon are established, and the influence of the osteocyte shape on the fluid flow properties of osteon under the axial displacement load is analyzed. Two kinds of boundary conditions are considered on the cement line of osteon, elastic restrained (BC1) and displacement confined (BC2).
Results: In the range of parameters we studied, the changes of osteocyte shape (Case1-Case6) make the maximum value of PG, pore pressure (PP), fluid velocity (FV) and fluid shear stress (FSS) 33.36%, 67.67%, 8.6% and 26.6% larger than the Reference model in BC1, respectively. And the maximum value of PG, PP, FV and FSS are 65.39%, 67.67%, 8.4% and 29% larger than reference model in BC2. The maximum PG, PP, FV and FSS in BC2 are 96.72%, 95.51%, 97.87% and 97.13% larger than that in BC1, respectively. The permeability of elongated osteocyte model (Case 3, Case 4 and Case 6) have a difference of one magnitude order in X and Y direction.
Conclusion: The changes of osteocyte shape has a significant impact on the degrees of anisotropy for fluid flow and porous media of osteon. This model can facilitate better accurately quantifying the fluid flow in lacuna-canalicular system.
... The present study observes a similar response in OI osteon as well, however, the pressure does not change much along the loading cycle in comparison to ordinary osteon. Chen et al. [43] examined the effect of bone architecture and their properties on canalicular fluid flow through multi-layered hollow osteon model under cyclic loading. They also noticed similar trends of pore-pressure distribution along the radius of the osteon. ...
... The pore-pressure magnitude is maximum near the mid-osteon wall thickness. Chen et al.[43] also observed a similar trend of the pore-pressure distribution in a hollow osteon model under cyclic loading. A significant change in pore-pressure distribution and the magnitude is observed in healthy osteon along the gait loading cycle. ...
Osteogenesis Imperfecta (OI), also known as 'brittle bone disease', is a genetic bone disorder. OI bones experience frequent fractures. It is 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 stimulates bone remodeling activities. Several studies have characterized strain environment in OI bones, whereas, a very few studies attempted to characterize the interstitial fluid flow. OI significantly affect bone microarchitecture. Thus, the present study anticipates that canalicular fluid flow reduces in OI bone in comparison to healthy bone in response to physiological loading due to altered poromechanical properties. Hence, this work attempts to understand the canalicular fluid distribution in the single osteon model of OI and healthy bones. 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 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. The present work attempts to identify the plausible explanation behind low mechano-transduction capability of OI bone. This work may further be extended in designing better biomechanical strategies to enhance fluid flow in order to improve osteogenic activities in OI bone.
... As shown in Fig.1(a) (Natalie et al., 2014;Yaogeng C et al., 2018), the cortical bone layer is composed of osteon orientation and bone matrix, and the osteon orientation is a fundamental building unit of the cortical bone at the microscopic scale which are filled with a hard matrix,and has a length of 3-5 mm and a diameter of 50-250μm. There is a relatively thin layer of cement line between a single osteon orientation and the matrix, between 1-5μm thick, which separates the osteon orientation from the matrix. ...
... There is a relatively thin layer of cement line between a single osteon orientation and the matrix, between 1-5μm thick, which separates the osteon orientation from the matrix. The osteon orientation and the matrix are "glued", the strength of the cement line is smaller than the osteon orientation and the matrix, so when the bone breaks, the crack generally expands along the cement line.As shown in Fig.1(b) (Natalie et al., 2014;Yaogeng et al., 2018), the Harvard canal (also known as the second osteon orientation), which exists inside the osteon orientation, is mainly responsible for transporting blood.Therefore, the structure of the cortical bone makes the bone anisotropic, that is, exhibits different thermodynamic properties in different directions. Studies have shown that the stiffness and strength of the osteon orientation in the longitudinal direction is higher than the matrix and the cement line, and the matrix portion is isotropic.It can be found from the cross-section perpendicular to the axis of the osteon orientation that the osteon orientations are randomly distributed, but when the numerical simulation model is established, it is generally assumed that it is distributed according to a certain regularity, such as a regular hexagonal distribution or a regular quadrilateral distribution.The ABAQUS was used to simulate the two types of arrangement, and compared with the cutting experiment, it was found that the regular quadrilateral arrangement is closer to the experimental results (Yin J , 2016). ...
... Tian, Zheng, Wang, Li and Yao, Journal of Biomechanical Science and Engineering, Vol.15, No.4 (2020) [DOI: 10.1299/jbse.20-00012] (a) (b) Fig.1 (a) Microstructure of bone and (b) Longitudinal cross section of a single cylindrical osteon (Yaogeng C et al., 2018) ...
Grinding methods have been widely used in orthopedic surgery, which has high requirements for surface quality, grinding force and temperature control. It is necessary to explore the influence of micro-grinding parameters on the grinding force temperature from a microscopic perspective. This paper describes the micro structure, composition and thermodynamic properties of bone. From the perspective of the single abrasive grain, the single abrasive grain cutting model is established, and the single abrasive grain cutting force equation is derived. ABAQUS is used to establish a 2D cutting simulation model of abrasive grains, and the internal structure of the bone material is considered, and the bone micro structure model (including osteon orientation , matrix, cement line ) is established. The simulation study is carried out on the cutting direction of the abrasive grains in parallel, vertical and cross with the axial unit axis. The study of the relationship between force and temperature and cutting parameters shows that the abrasive cutting force increases with the increase of grinding speed and grinding depth. The cutting force is the largest in the vertical cutting mode, the cutting force is the second in the cross cutting mode, and the cutting force is the smallest in the parallel cutting mode. Finally, the comparison between theory and simulation shows that the theoretical analysis results are consistent with the finite element simulation results, which verifies the correctness of the theoretical model of single abrasive grain cutting force.
... Multiscale model of bone can alternative material parameter of any hierarchical level to determine its effect on bone properties, such as porosity, elastic modulus [3], and permeability [10]. A scaffold composed of materials with multiscale porosity can be used to direct bone regeneration and morphology by controlling the hierarchical structure of the scaffold [11]. ...
... Our study found that the heterogeneous distribution of permeability in osteon lamella had a significant effect on FP and FV (Fig. 8). The FV was found to fluctuate at bone lamellae and cement line that was different from the findings of [10,26]. In reality, the micropore of bone tissue may pass through the cement line [30], so the cement line may be permeable. ...
... The surface of periosteum and bone marrow were set to the same value as the macroscopic model. The FP of Haversian canal was always ignored in previous study [10,14,27]; however, the span of both k vp and k lcp was very large [28], and when the gap of permeability value between k vp and k lcp was not that big, the FP of Haversian canal couldn't be ignored. In macro-mesoscopic model, the FP of Haversian canal was derived from the calculation results of the corresponding locations of macroscale model. ...
Background:
Bone is a hierarchically structured composite material, and different hierarchical levels exhibit diverse material properties and functions. The stress and strain distribution and fluid flow in bone play an important role in the realization of mechanotransduction and bone remodeling.
Methods:
To investigate the mechanotransduction and fluid behaviors in loaded bone, a multiscale method was developed. Based on poroelastic theory, we established the theoretical and FE model of a segment bone to provide basis for researching more complex bone model. The COMSOL Multiphysics software was used to establish different scales of bone models, and the properties of mechanical and fluid behaviors in each scale were investigated.
Results:
FE results correlated very well with analytical in macroscopic scale, and the results for the mesoscopic models were about less than 2% different compared to that in the macro-mesoscale models, verifying the correctness of the modeling. In macro-mesoscale, results demonstrated that variations in fluid pressure (FP), fluid velocity (FV), von Mises stress (VMS), and maximum principal strain (MPS) in the position of endosteum, periosteum, osteon, and interstitial bone and these variations can be considerable (up to 10, 8, 4 and 3.5 times difference in maximum FP, FV, VMS, and MPS between the highest and the lowest regions, respectively). With the changing of Young's modulus (E) in each osteon lamella, the strain and stress concentration occurred in different positions and given rise to microscale spatial variations in the fluid pressure field. The heterogeneous distribution of lacunar-canalicular permeability (klcp) in each osteon lamella had various influence on the FP and FV, but had little effect on VMS and MPS.
Conclusion:
Based on the idealized model presented in this article, the presence of endosteum and periosteum has an important influence on the fluid flow in bone. With the hypothetical parameter values in osteon lamellae, the bone material parameters have effect on the propagation of stress and fluid flow in bone. The model can also incorporate alternative material parameters obtained from different individuals. The suggested method is expected to provide dependable biological information for better understanding the bone mechanotransduction and signal transduction.
