On bone adaptation due to venous stasis

This paper addresses the question of whether or not interstitial fluid flow due to the blood circulation accounts for the observed periosteal bone formation associated with comprised venous return (venous stasis). Increased interstitial fluid flow induced by increased intramedullary pressure has been proposed to account for the periosteal response in venous stasis. To investigate the shear stresses acting on bone cell processes due to the blood circulation-driven interstitial fluid flow, a poroelastic model is extended to the situation in which the interstitial fluid flow in an osteon is driven by the pulsatile extravascular pressure in the osteonal canal as well as by the applied cyclic mechanical loading. Our results show that under normal conditions, the pulsatile extravascular pressure in the osteonal canal due to cardiac contraction (10mm Hg at 2Hz) and skeletal muscle contraction (30mm Hg at 1Hz) induce peak shear stresses on the osteocyte cell processes that are two orders of magnitude lower than those induced by physiological mechanical loading (100 microstrain at 1Hz). In venous stasis the induced peak shear stress is reduced further compared to the normal conditions because, although the mean intramedullary pressure is increased, the amplitude of its pulsatile component is decreased. These results suggest that the interstitial fluid flow is unlikely to cause the periosteal bone formation in venous stasis. However, the mean interstitial fluid pressure is found to increase in venous stasis, which may pressurize the periosteum and thus play a role in periosteal bone formation.     

Micromechanically based poroelastic modeling of fluid flow in Haversian bone

To explore the hypothesis that load-induced fluid flow in bone is a mechano-transduction mechanism in bone adaptation, unit cell micro-mechanical techniques are used to relate the microstructure of Haversian cortical bone to its effective poroelastic properties. Computational poroelastic models are then applied to compute in vitro Haversian fluid flows in a prismatic specimen of cortical bone during harmonic bending excitations over the frequency range of 10(0) to 10(6) Hz. At each frequency considered, the steady state harmonic response of the poroelastic bone specimen is computed using complex frequency-domain finite element analysis. At the higher frequencies considered, the breakdown of Poisueille flow in Haversian canals is modeled by introduction of a complex fluid viscosity. Peak bone fluid pressures are found to increase linearly with loading frequency in proportion to peak bone stress up to frequencies of approximately 10 kHz. Haversian fluid shear stresses are found to increase linearly with excitation frequency and loading magnitude up until the breakdown of Poisueille flow. Tan delta values associated with the energy dissipated by load-induced fluid flow are also compared with values measured experimentally in a concurrent broadband spectral analysis of bone. The computational models indicate that fluid shear stresses and fluid pressures in the Haversian system could, under physiologically realistic loading, easily reach the level of a few Pascals, which have been shown in other works to elicit cell responses in vitro.     

Geometric determinants to cement line debonding and osteonal lamellae failure in osteon pushout tests

Cement lines are the boundaries between secondary osteons and the surrounding interstitial bone matrix in cortical bone. The interfacial properties of cement lines have been determined by osteon pushout tests. However, distinctively different material properties were obtained when osteon pushout tests were performed under different test geometries. In the present study, an axisymmetric two-dimensional finite element model was used to simulate an osteon pushout test using the test geometry of actual experiments. The results indicated that shear failure within the osteonal lamellae would occur when the osteon pushout test was performed under the condition of a thick specimen and large supporting hole. On the other hand, cement line debonding occurred when the osteon pushout test was performed using a thin specimen and small supporting hole. The finite element results were consistent with previous experiments of osteon pushout tests under different test geometries. Furthermore, the finite-element results suggest that a smoothly curved punch would most likely cause debonding at the cement line instead of osteonal lamellae.     

Fluid–structure interactions in micro-interlocked regions of the cement–bone interface

Experimental tests and computational modelling were used to explore the fluid dynamics at the trabeculae–cement interlock regions found in the tibial component of total knee replacements. A cement–bone construct of the proximal tibia was created to simulate the immediate post-operative condition. Gap distributions along nine trabeculae–cement regions ranged from 0 to 50.4 μm (mean = 12 μm). Micro-motions ranged from 0.56 to 4.7 μm with a 1 MPa compressive load to the cement. Fluid–structure analysis between the trabeculae and the cement used idealised models with parametric evaluation of loading direction, gap closing fraction (GCF), gap thickness, loading frequency and fluid viscosity. The highest fluid shear stresses (926 Pa) along the trabecular surface were found for conditions with very thin and large GCFs, much larger than reported physiological levels (～1–5 Pa). A second fluid–structure model was created with a provision for bone resorption using a constitutive model with resorption velocity proportional to fluid shear rate. A lower cut-off was used, below which bone resorption would not occur (50 s^? 1). Results showed that there was initially high shear rates (>1000 s^? 1) that diminished after initial trabecular resorption. Resorption continued in high shear rate regions, resulting in a final shape with bone left deep in the cement layer, and is consistent with morphology found in post-mortem retrievals. Small gaps between the trabecular surface and the cement in the immediate post-operative state produce fluid flow conditions that appear to be supra-physiologic; these may cause fluid-induced lysis of trabeculae in the micro-interlock regions.     

The relative effects of collagen fiber orientation, porosity, density, and mineralization on bone strength

This investigation determined the relative importance of collagen fiber orientation, porosity, density, and mineralization in determining the tensile strength of bovine cortical bone. Thirty-nine specimens were tested for failure stress and the values of eight histologic and compositional parameters: collagen fiber orientation, wet and dry apparent density, percent mineralization of the bone matrix, and several components of porosity (Haversian canals, Volkmann's canals, and plexiform vascular spaces). Linear regression analysis showed that collagen fiber orientation was consistently the single best predictor of strength. Mineralization of the bone matrix was generally a poor predictor of strength. Density and porosity ranked between these variables in importance. Multiple regression equations containing all significantly correlated variables achieved correlation coefficients of 0.607 for plexiform bone and 0.881 for osteonal bone. Also, separate analysis of plexiform and osteonal specimens showed that the latter group was weaker even though it was less porous, apparently because it had collagen fibers which were less longitudinally oriented. This study suggests it is feasible to develop better empirical formulae for the prediction of cortical bone strength than are currently available if a variety of variables is introduced. Additional data are needed to confirm these results.     

Estimates of the peak pressures in bone pore water.

The maximum pore fluid pressures due to uniaxial compression are determined for both the vascular porosity (Haversian and Volkmann's canals) and the lacunar-canalicular porosity of live cortical bone. It is estimated that the peak pore water pressure will be 19 percent of the applied axial stress in the vascular porosity and 12 percent of the applied axial stress in the lacunar-canalicular porosity for an impulsive step loading. However, the estimated relaxation time for the vascular porosity (1.36 microseconds) is three orders of magnitude faster than that estimated for the lacunar-canalicular porosity (4.9 ms). Thus, under physiological loading, which has a stress rise time generally larger than 1 ms, pressures higher than the vascular pressure cannot be sustained in the vascular porosity due to the swift pressure relaxation in this porosity (unless the fluid drainage through the boundary is obstructed). The model also predicts a slight hydraulic stiffening of the bulk modulus due to longer draining time of the lacunar-canalicular porosity. The undrained bulk modulus is 6 percent higher than the drained bulk modulus in this case.     

Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.     

Influence of vascular porosity on fluid flow and nutrient transport in loaded cortical bone

Load-induced fluid flow is a key factor in triggering bone modeling and remodeling processes that maintain bone mass and architecture. To provide an enhanced understanding of fluid flow in bone, unique computational models of a tibial section were developed. The purpose of the study was to examine the effects of incorporating vascular porosity on pore fluid pressure and resulting lacunocanalicular flow and to determine the role of load-induced fluid flow in tracer transport. Simulations revealed large local pressure gradients surrounding the vascular canals that were dependent on the magnitude and state (i.e., compressive or tensile) of the stress. Fluid velocity magnitudes were increased by over an order of magnitude in the dual-porosity model, relative to the single-porosity model. Fluid flow had a marked effect on tracer perfusion within the cortex. After 10 loading cycles, a 9-fold increase in tracer concentration, relative to diffusion alone, was observed in the compressive region where fluid exchange was greatest between the lacunocanalicular porosity and the vascular canals. Agreement was achieved between computational results and experimental investigations of electrokinetic phenomenon, tracer transport, cellular stimulation, and functional adaptation. The models produced substantial improvements in bone fluid flow simulation and underscored the significance of incorporating vascular porosity in models designed to quantify fluid pressure and flow characteristics within mechanically loaded cortical bone.     

Interfacial Strength of Cement Lines in Human Cortical Bone

In human cortical bone, cement lines (or reversal lines) separate osteons from the interstitial bone tissue, which consists of remnants of primary lamellar bone or fragments of remodeled osteons. There have been experimental evidences of the cement line involvement in the failure process of bone such as fatigue and damage. However, there are almost no experimental data on interfacial properties of cement lines in human cortical bone. The objective of this study is to design and assemble a precision and computer controlled osteon pushout microtesting system, and to experimentally determine the interfacial strength of cement lines in human cortical bone by performing osteon pushout tests. Thirty specimens were prepared from humeral diaphyses of four human subjects. Twenty specimens were tested under the condition of a small hole in the supporting plate, in which the cement line debonding occurred. The cement line interfacial strength ranged from 5.38 MPa to 10.85 MPa with an average of 7.31±1.73 MPa. On the other hand, ten specimens were tested under the condition of a large hole in the supporting plate, in which the shear failure inside osteons was observed. The specimens tested under the condition of the large hole resulted in an average shear strength of 73.71±15.06 MPa, ranging from 45.97 MPa to 93.74 MPa. Therefore, our results suggest that the cement line interface between osteon and interstitial bone tissue is weaker than that between bone tissue lamellae.     

Influence of cortical canal architecture on lacunocanalicular pore pressure and fluid flow

Bone is a dynamic tissue that undergoes structural modification in response to its mechanical environment, but how bone cells sense and respond to loading conditions remains incompletely understood. Current theories focus on strain-induced fluid flow for the primary means of mechanotransduction. To examine the influence of age-related cortical rarefaction on lacunocanalicular fluid characteristics, coupled fluid flow and mechanical computational models of bone specimens representing young, mid-age and aged samples were derived artificially from the same original micro-computed tomography image data. Simulated mechanical loading was applied to the bone models to induce pressure-driven interstitial fluid flow. Results demonstrated a decrease in pore pressure and fluid velocity magnitudes with age as a result of increased cortical porosity. Mean canal separation, as opposed to canal size, was implicated as a primary factor affecting age-related fluid dynamics. Future investigations through refinement of the model may implicate fluid stasis or inadequate nutrient transport experienced by osteocytes as a key factor in the initiation of cortical remodelling events.     

Influence of cortical canal architecture on lacunocanalicular pore pressure and fluid flow

Bone is a dynamic tissue that undergoes structural modification in response to its mechanical environment, but how bone cells sense and respond to loading conditions remains incompletely understood. Current theories focus on strain-induced fluid flow for the primary means of mechanotransduction. To examine the influence of age-related cortical rarefaction on lacunocanalicular fluid characteristics, coupled fluid flow and mechanical computational models of bone specimens representing young, mid-age and aged samples were derived artificially from the same original micro-computed tomography image data. Simulated mechanical loading was applied to the bone models to induce pressure-driven interstitial fluid flow. Results demonstrated a decrease in pore pressure and fluid velocity magnitudes with age as a result of increased cortical porosity. Mean canal separation, as opposed to canal size, was implicated as a primary factor affecting age-related fluid dynamics. Future investigations through refinement of the model may implicate fluid stasis or inadequate nutrient transport experienced by osteocytes as a key factor in the initiation of cortical remodelling events.     

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.     

Micromechanics fracture in osteonal cortical bone: a study of the interactions between microcrack propagation, microstructure and the material properties

A two-dimensional micromechanical fibre reinforced composite materials model for osteonal cortical bone is presented. The interstitial bone is modelled as a matrix, the osteons are modelled as fibres, and the cement line is presented as interface tissue. The interaction between osteons and microcracks is evaluated by linear elastic fracture mechanics theory, followed by a determination of the stress intensity factor at the vicinity of the microcrack tips. The results indicate that bone microstructural heterogeneity greatly influences fracture parameters. Furthermore, microstructural morphology and loading conditions affect growth trajectories, the microcrack propagation trajectory deviates from the osteon under tensile loading, and osteon penetration is observed under compressive loads.     

Shear stress inhibits while disuse promotes osteocyte apoptosis

Cell apoptosis operates as an organizing mechanism in biology in addition to removing effete cells. We have recently proposed that during bone remodeling, osteocyte apoptosis steers osteonal alignment in relation to mechanical loading of the whole bone [J. Biomech. 36 (2003) 1453]. Here we present evidence that osteocyte apoptosis in cell culture is modulated by shear stress. Under static culture conditions, serum starved osteocytes exposed phosphatidylserine (PS) on their cell membrane 6x more often than periosteal fibroblasts and 3x more often than osteoblasts. Treatment with shear stress reduced the number of osteocytes that exposed PS by 90%, but did not affect the other cell types. Fluid shear stress of increasing magnitude, dose-dependently stimulated Bcl-2 mRNA expression in human bone cells, while shear stress did not change Bax expression. These data suggest that disuse promotes osteocyte apoptosis, while mechanical stimulation by fluid shear stress promotes osteocyte survival, by modulating the Bcl-2/Bax expression ratio.     

Nitric oxide production by bone cells is fluid shear stress rate dependent

Shear stress due to mechanical loading-induced flow of interstitial fluid through the lacuno-canalicular network is a likely signal for bone cell adaptive responses. Moreover, the rate (determined by frequency and magnitude) of mechanical loading determines the amount of bone formation. Whether the bone cells' response to fluid shear stress is rate dependent is unknown. Here we investigated whether bone cell activation by fluid shear stress is rate dependent. MC3T3-E1 osteoblastic cells were subjected for 15 min to fluid shear stress of varying frequencies and amplitudes, resulting in peak fluid shear stress rates ranging from 0 to 39.6 Pa-Hz. Nitric oxide production, a parameter for bone cell activation, was found to be linearly dependent on the fluid shear stress rate; the slope was steepest at 5 min (0.11 Pa-Hz(-1)) and decreased to 0.03 Pa-Hz(-1) at 15 min. We conclude that the fluid shear stress rate is an important parameter for bone cell activation.     

Influence of interstitial bone microcracks on strain-induced fluid flow

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.     

Permeability study of vertebral cancellous bone using micro-computational fluid dynamics

Understanding of cancellous bone permeability is lacking despite its importance in designing tissue engineering scaffolds for bone regeneration and orthopaedic surgery that relies on infiltration of bone cement into porous cancellous bone. We employed micro-computational fluid dynamics to investigate permeability for 37 cancellous bone specimens, eliminating stringent technical requirements of bench-top testing. Microarchitectural parameters were also determined for the specimens and correlated, using uni-variate and multi-variate regression analyses, against permeability. We determined that bone surface density, trabecular pattern factor, structure model index and trabecular number are other possible predictors of permeability (with R values of 0.47, 0.44, 0.40 and 0.33), in addition to the commonly used porosity parameter (R value of 0.38). Pooling these parameters and performing multi-variate linear regression analysis improved yield the R-value of 0.50, indicating that porosity alone is a poor predictor of cancellous bone permeability and, therefore, other parameters should be included for a better and improved linear model.     

Deformation behaviour and damage accumulation of cortical bone specimens from the equine tibia under cyclic loading

Despite its clinical importance, the fatigue behaviour of cortical bone has not been examined as widely as its static behaviour. In the present study, specimens from the tibiae of horses have been subjected to load-controlled single step tests. The cyclic deformation behaviour was described by the development of stress-strain hysteresis parameters over the lifetime. The fatigue behaviour of bone is characterised by cyclic softening which is most distinctive towards the end of the lifetime. The microstructural damage accumulated during cyclic loading results in a loss of stiffness, asymmetrical deformation of the bone in tension and compression in cyclic creep. As shown by light and scanning electron microscopy, microcrack formation and growth is the main damage mechanism. The crack growth behaviour is strongly influenced by the microstructure, the stress components and the absolute value of the local stresses. Lower local stresses and/or compressive mean stresses lead to a dominant influence of the shear stress components with shear failure at inner interfaces. With increasing crack length, that is, higher local stress amplitudes, or tensile mean stresses, the microstructure is more and more ignored and failure occurs primarily under the influence of the normal stress components. This can be clearly seen on the fracture and specimen surfaces.     

Permeability study of vertebral cancellous bone using micro-computational fluid dynamics

Understanding of cancellous bone permeability is lacking despite its importance in designing tissue engineering scaffolds for bone regeneration and orthopaedic surgery that relies on infiltration of bone cement into porous cancellous bone. We employed micro-computational fluid dynamics to investigate permeability for 37 cancellous bone specimens, eliminating stringent technical requirements of bench-top testing. Microarchitectural parameters were also determined for the specimens and correlated, using uni-variate and multi-variate regression analyses, against permeability. We determined that bone surface density, trabecular pattern factor, structure model index and trabecular number are other possible predictors of permeability (with R values of 0.47, 0.44, 0.40 and 0.33), in addition to the commonly used porosity parameter (R value of 0.38). Pooling these parameters and performing multi-variate linear regression analysis improved yield the R-value of 0.50, indicating that porosity alone is a poor predictor of cancellous bone permeability and, therefore, other parameters should be included for a better and improved linear model.     

The fate of mechanically induced cartilage in an unloaded environment.

According to mechanobiologic theories, persistent intermittent mechanical stimulation is required to maintain differentiated cartilage. In a rat model for bone repair, we studied the fate of mechanically induced cartilage after unloading. In three groups of rats, regenerating mesenchymal tissue was submitted to different loading conditions in bone chambers. Two groups were immediately killed after loading periods of 3 or 6 weeks (the 3-group and the 6-group). The third group was loaded for 3 weeks and then kept unloaded for another 3 weeks (the (3 + 3)-group). Cartilage was found in all loaded groups. Without loading, cartilage does not appear in this model. In the 3-group there was no clear ongoing endochondral ossification, the 6-group showed ossification in 2 out of 5 cartilage containing specimens, and in the (3 + 3)-group all cartilage was undergoing ossification. These results suggest a tendency of the cartilage to be maintained also under unloaded conditions until it is reached by bone that can replace it through endochondral ossification.Additional measurements showed less amount of new bone in the loaded specimens. In most of the loaded specimens in the 3-group, necrotic bone fragments were seen embedded in the fibrous tissue layer close to the loading piston, indicating that bone tissue had been resorbed due to the hydrostatic compressive load. In some specimens, a continuous cartilage layer covered the end of the specimen and seemed to protect the underlying bone from pressure-induced resorption. We suggest that one of the functions of the cartilage forming in the compressive loaded parts of a bone callus is to protect the surrounding bone callus from pressure-induced fluid flow leading to resorption.