Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment.

When bone is mechanically loaded, bone fluid flow induces shear stresses on bone cells that have been proposed to be involved in bone's mechanosensory system. To investigate bone fluid flow and strain-generated potentials, several theoretical models have been proposed to mimic oscillatory four-point bending experiments performed on thin bone specimens. While these previous models assume that the bone fluid relaxes across the specimen thickness, we hypothesize that the bone fluid relaxes primarily through the vascular porosity (osteonal canals) instead and develop a new poroelastic model that integrates the microstructural details of the lacunar-canalicular porosity, osteonal canals, and the osteonal cement lines. Local fluid pressure profiles are obtained from the model, and we find two different fluid relaxation behaviors in the bone specimen, depending on its microstructure: one associated with the connected osteonal canal system, through which bone fluid relaxes to the nearby osteonal canals; and one associated with the thickness of a homogeneous porous bone specimen (approximately 1 mm in our model), through which bone fluid relaxes between the external surfaces of the bone specimen at relatively lower loading frequencies. Our results suggest that in osteonal bone specimens the fluid pressure response to cyclic loading is not sensitive to the permeability of the osteonal cement lines, while it is sensitive to the applied loading frequency. Our results also reveal that the fluid pressure gradients near the osteonal canals (and thus the fluid shear stresses acting on the nearby osteocytes) are significantly amplified at higher loading frequencies.     

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.     

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.     

A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone

Interstitial fluid flow through the lacunocanalicular cavities of mechanically loaded bone provides the biophysical basis for a number of postulates regarding mechanotransduction in bone. Recently, the existence of load-induced fluid flow and its influence on molecular transport through bone has been confirmed using tracer methods to visualize fluid flow induced by in vivo four-point-bending of rat tibiae. In this paper, we present a theoretical two-stage approach for the calculation of load-induced flow fields and for the evaluation of their influence on molecular transport in bone loaded in four-point bending, analogous to the aforementioned experimental model. In the first stage, the fluid velocities are calculated using a three-dimensional, poroelastic finite element model. In the second stage, mass transport analysis, this calculated fluid flow serves as a forced convection flow and its contribution to the total transport potential is determined. Based on this combined approach, the overall tracer concentration in the loaded bone is significantly higher than that in the unloaded bone. Furthermore, augmentation of mass transport through convective flow is more pronounced in the tension band of the tissue, as compared to the compression band. In general, augmentation of tracer concentration via convective mechanisms is most pronounced in areas corresponding to lowest fluid velocities, which is indicative of fluid flow direction and areas of increased "dwell time" or accumulation during the loading cycle. This theoretical model, in combination with the corresponding experimental model, provides unique insight into the role of mechanical loads in modulating local flow distributions and concentration gradients within bone tissue.     

Experimental and numerical identification of cortical bone permeability

Bone is a complex system, and could be modeled as a poroelastic media. The aim of this paper is to identify the macroscopic value of the cortical bone permeability coefficient. A simple experimental method was designed in order to determine the permeability coefficient. Two bone samples taken from different ox femurs were filled with water, to place them under internal pressure. The measurements gave both the fluid flow through the lateral surfaces and the internal pressure. The originality of this work is the coupling between an experimental process and a structural computation performed with a finite element method. The mean cortical bone permeability coefficient identified was about k=1.1x10(-13)m(2). This value tends to confirm other values found in the literature, obtained by different methods and often at macroscopic scale. It confirms also the domination of vascular permeability (Haversian and Volkmann's canals).     

An ex vivo model to study transport processes and fluid flow in loaded bone

Load-induced fluid flow has been postulated to provide a mechanism for the transmission of mechanical signals (e.g. via shear stresses, enhancement of molecular transport, and/or electrical effects) and the subsequent elicitation of a functional adaptation response (e.g. modeling, remodeling, homeostasis) in bone. Although indirect evidence for such fluid flow phenomena can be found in the literature pertaining to strain generated potentials, actual measurement of fluid displacements in cortical bone is inherently difficult. This problem motivated us to develop and introduce an ex vivo perfusion model for the study of transport processes and fluid flow within bone under controlled mechanical loading conditions. To this end, a closed-loop system of perfusion was established in the explanted forelimb of the adult Swiss alpine sheep. Immediately prior to mechanical loading, a bolus of tracer was introduced intraarterially into the system. Thereafter, the forelimb of the left or right side (randomized) was loaded cyclically, via Schanz screws inserted through the metaphyses, producing a peak compressive strain of 0.2% at the middiaphysis of the anterior metacarpal cortex. In paired experiments with perfusion times totalling 2, 4, 8 and 16 min, the concentration of tracer measured at the middiaphysis of the cortex in cross section was significantly higher in the loaded bone than in the unloaded contralateral control. Fluorometric measurements of procion red concentration in the anterior aspect alone showed an enhancement in transport at early stages of loading (8 cycles, 2 min) but no effect in transport after higher number of cycles or increased perfusion times, respectively. This reflects both the small size of the molecular tracer, which would be expected to be transported rapidly by way of diffusive mechanisms alone, as well as the loading mode to which the anterior aspect was exposed. Thus, using our new model it could be shown that load-induced fluid flow represents a powerful mechanism to enhance molecular transport within the lacunocanalicular system of compact bone tissue. Based on these as well as previous studies, it appears that the degree of this effect is dependent on tracer size as well as the mechanical loading mode to which a given area of tissue is exposed.     

Effect of oscillating fluid flow stimulation on osteocyte mRNA expression

Structural adaptation of the bone tissue is mediated by loading-induced interstitial fluid flow within the bone microstructure. Within this framework, osteocytes fulfill the central mechanotransductive role in the bone remodeling process. While osteocytes have been demonstrated to be exquisitely sensitive to various forms of fluid flow stimulus in vitro, the effect of different oscillating fluid flow (OFF) parameters on osteocyte activity has yet to be systematically characterized. In this study, we investigate the effect of three OFF parameters on osteocyte activity in vitro and hypothesize that COX-2, RANKL, and OPG mRNA expression in osteocytes are sensitive to the OFF parameters: peak shear stress amplitude (0.5 Pa, 1 Pa, 2 Pa, and 5 Pa), oscillating frequency (0.5 Hz, 1 Hz, and 2 Hz), and total flow duration (1 h, 2 h, and 4 h). Our findings demonstrate that COX-2 mRNA levels are elevated in osteocytes subjected to higher peak shear stress amplitudes and longer flow durations, while RANKL/OPG mRNA levels decreased to a minimum threshold in response to higher peak shear stress amplitudes, faster oscillating frequencies, and longer flow durations. These findings suggest that dynamic fluid flow with higher peak shear stress amplitudes, faster oscillating frequencies, and longer loading durations provide the best conditions for promoting bone formation.     

Numerical simulation of streaming potentials due to deformation-induced hierarchical flows in cortical bone

Bone is a very dynamic tissue capable of modiA,fing its composition, microstructure, and overall geometry in response to the changing biomechanical needs. Streaming potential has been hypothesized as a mechanotransduction mechanism that may allow osteocytes to sense their biomechanical environment. A correct understanding of the mechanism for streaming potential will illuminate our understanding of bone remodeling, such as the remodeling associated with exercise hypertrophy, disuse atrophy, and the bone remodeling arounid implants. In the current research, a numerical model based on the finite element discretization is proposed to simulate the fluid flows through the complicated hierarchical flow system and to calculate the concomitant stress generated potential (SGP) as a result of applied mechanical loading. The lacunae-canaliculi and the matrix microporosity are modeled together as discrete one-dimensional flow channels superposed in a biphasic poroelastic matrix. The cusplike electric potential distribution surrounding the Haversian canal that was experimentallv observed and reported in the literature earlier was successfully reproduced by the current numerical calculation.     

Mechanobiological modeling of endochondral ossification: an experimental and computational analysis

Long bone formation starts early during embryonic development through a process known as endochondral ossification. This is a highly regulated mechanism that involves several mechanical and biochemical factors. Because long bone development is an extremely complex process, it is unclear how biochemical regulation is affected when dynamic loads are applied, and also how the combination of mechanical and biochemical factors affect the shape acquired by the bone during early development. In this study, we develop a mechanobiological model combining: (1) a reaction–diffusion system to describe the biochemical process and (2) a poroelastic model to determine the stresses and fluid flow due to loading. We simulate endochondral ossification and the change in long bone shapes during embryonic stages. The mathematical model is based on a multiscale framework, which consisted in computing the evolution of the negative feedback loop between Ihh/PTHrP and the diffusion of VEGF molecule (on the order of days) and dynamic loading (on the order of seconds). We compare our morphological predictions with the femurs of embryonic mice. The results obtained from the model demonstrate that pattern formation of Ihh, PTHrP and VEGF predict the development of the main structures within long bones such as the primary ossification center, the bone collar, the growth fronts and the cartilaginous epiphysis. Additionally, our results suggest high load pressures and frequencies alter biochemical diffusion and cartilage formation. Our model incorporates the biochemical and mechanical stimuli and their interaction that influence endochondral ossification during embryonic growth. The mechanobiochemical framework allows us to probe the effects of molecular events and mechanical loading on development of bone.     

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.     

A discrete model for streaming potentials in a single osteon

A mathematical model for streaming potentials in an osteon is proposed, taking into account the microstresses in the vicinity of the Haversian Canal. With the help of the finite element method, a boundary problem for the fluid pressure amplitude in the osteon is investigated when the bone sample is subjected to harmonic loading. A numerical analysis of the intra-osteonal potential is performed. It is found that there exists an azimuthal asymmetry which increases with the enlargement of the Haversian Canal. The results of the numerical modeling of the intra-osteonal potential are in accordance with the available experimental data.     

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.     

Time-dependent deformations in bone cells exposed to fluid flow in vitro: investigating the role of cellular deformation in fluid flow-induced signaling

Numerous experiments have shown fluid flow to be a potent stimulator of bone cells in vitro, suggesting that fluid flow is an important physical signal in bone mechanotransduction. In fluid flow experiments, bone cells are exposed to both time-dependent (e.g., oscillating or pulsing) and time-independent (e.g., steady) flow profiles. Interestingly, the signaling response of bone cells shows dependence on loading frequency and/or rate that has been postulated to be due to viscoelastic behavior. Thus, the objective of this study was to investigate the time-dependent deformations of bone cells exposed to fluid flow in vitro. Specifically, our goal was to characterize the mechanical response of bone cells exposed to oscillatory flow from 0.5 to 2.0 Hz and steady flow, since these flow profiles have previously been shown to induce different morphological and biochemical responses in vitro. By tracking cell-bound sulfate and collagen coated fluorescent beads of varying sizes, we quantified the normalized peak deformation (peak displacement normalized by the maximum peak displacement observed for all frequencies) and phase lag in bone cells exposed to 1.0 Pa oscillating flow at frequencies of 0.5-2.0 Hz. The phase lag was small (3-10 degrees ) and frequency dependent, while the normalized peak displacements decreased as a weak power law of frequency ( approximately f(-0.2)). During steady flow, the cells exhibited a nearly instantaneous deformation, followed by creep. Our results suggest that while substantial viscous deformation may occur during steady flow (compared to oscillating flow at approximately 1 Hz), bone cells behave primarily as elastic bodies when exposed to flow at frequencies associated with habitual loading.     

The influence of load repetition in bone mechanotransduction using poroelastic finite-element models: the impact of permeability

Experimental evidence suggests that interstitial fluid flow is a stimulus for mechanoadaptation in bone. Bone adaptation is sensitive to the frequency of loading and rest insertion between load cycles. We investigated the effects of permeability, frequency and rest insertion on fluid flow in bone using finite-element models to understand how these parameters affect the mechanical stimulus. A simplified 3D poroelastic finite-element model of a beam in bending was developed, in order to simulate the behavior of interstitial fluid flow in the lacunar-canalicular system of mouse cortical bone. Two different load sets were considered: (1) a continuous haversine sinusoid, with frequency ranging from 1 to 30 Hz, and (2) a 10 Hz haversine with rest-insertion times ranging from 0 to 10 s. For both load sets, a range of intrinsic permeability from $10^{-23}$ to $10^{-18}\, \mathrm m^2 $ was tested, and fluid flow was determined. Models with permeabilities down to $10^{-21}\, \mathrm m^2 $ follow a dose–response relationship between fluid flow and sinusoidal frequency. Smaller orders of magnitude of permeability proved to be relatively insensitive to frequency. Our results also suggest that there is a minimum time of rest between load cycles that is required to maximize fluid motion, which depends on the order of magnitude of the intrinsic permeability. We show that frequency and rest insertion may be optimized to deliver maximal mechanical stimulus as a function of permeability.     

Tendon exhibits complex poroelastic behavior at the nanoscale as revealed by high-frequency AFM-based rheology

Tendons transmit load from muscle to bone by utilizing their unique static and viscoelastic tensile properties. These properties are highly dependent on the composition and structure of the tissue matrix, including the collagen I hierarchy, proteoglycans, and water. While the role of matrix constituents in the tensile response has been studied, their role in compression, particularly in matrix pressurization via regulation of fluid flow, is not well understood. Injured or diseased tendons and tendon regions that naturally experience compression are known to have alterations in glycosaminoglycan content, which could modulate fluid flow and ultimately mechanical function. While recent theoretical studies have predicted tendon mechanics using poroelastic theory, no experimental data have directly demonstrated such behavior. In this study, we use high-bandwidth AFM-based rheology to determine the dynamic response of tendons to compressive loading at the nanoscale and to determine the presence of poroelastic behavior. Tendons are found to have significant characteristic dynamic relaxation behavior occurring at both low and high frequencies. Classic poroelastic behavior is observed, although we hypothesize that the full dynamic response is caused by a combination of flow-dependent poroelasticity as well as flow-independent viscoelasticity. Tendons also demonstrate regional dependence in their dynamic response, particularly near the junction of tendon and bone, suggesting that the structural and compositional heterogeneity in tendon may be responsible for regional poroelastic behavior. Overall, these experiments provide the foundation for understanding fluid-flow-dependent poroelastic mechanics of tendon, and the methodology is valuable for assessing changes in tendon matrix compressive behavior at the nanoscale.     

Micromechanics modeling of Haversian cortical bone properties.

A finite-element micromechanics model for Haversian cortical bone tissue has been developed and studied. The model is an extension of two-dimensional micromechanics techniques for fiber-reinforced composite materials. Haversian systems, or secondary osteons, are considered to be the fiber component, and interstitial lamellar bone the matrix material. The cement line is included as an 'interphase' component along the fiber/matrix interface. The model assumes a regular repeatable spacing of the longitudinally aligned continuous fibers and is, therefore, restricted to approximating Haversian cortical bone in its present form. Haversian porosity is modeled explicitly by incorporating a hollow fiber to represent the Haversian canal. Solutions have been obtained by applying uniform macroscopic stresses to the boundaries of the repeating unit cell model. Macroscopic mechanical property predictions correspond reasonably well with the experimental data for cortical bone, but are necessarily dependent on the input properties for each constituent, which are not well established. The predicted variation in the elastic modulus with porosity is not as sensitive as that observed experimentally. Stresses within the constituents can also be modeled with this method and are demonstrated to deviate from the macroscopic applied stress levels.     

Evidence for increased de novo synthesis of NAD in immune-activated RAW264.7 macrophages: a self-protective mechanism?

Chondrogenesis in cartilage development and repair and cartilage degeneration in arthritis can be regulated by mechanical-load-induced physical factors such as tissue deformation, interstitial fluid flow and pressure, and electrical fields or streaming potentials. Previous animal and tissue explant studies have shown that time-varying dynamic tissue loading can increase the synthesis and deposition of matrix molecules in an amplitude-, frequency-, and spatially dependent manner. To provide information on the cell-level physical factors which may stimulate chondrocytes to increase production and export of aggrecan, the main proteoglycan component of the cartilage matrix, we characterized local changes in aggrecan synthesis within cyclically loaded tissue explant disks and compared those changes to values of predicted local physical factors. Aggrecan synthesis following a 23-h compression/radiolabel protocol was measured with a spatial resolution of approximately 0.1 mm across the 1.5-mm radius of explanted disks using a quantitative autoradiography method. A uniform stimulation of aggrecan synthesis was observed at an intermediate frequency of 0.01 Hz, while, at a higher frequency of 0.1 Hz, stimulation was only seen at peripheral radial positions. Profiles of radial solid matrix deformation and interstitial fluid pressure and velocity predicted to be occurring across the radius of the disk during sinusoidal loading were estimated using a composite poroelastic model. Tissue regions experiencing high interstitial fluid velocities corresponded to those displaying increased aggrecan synthesis. These results reinforce the role of load-induced flow of interstitial fluid in the stimulation of aggrecan production during dynamic loading of cartilage.     

Fluid shear stress stimulates prostaglandin and nitric oxide release in bone marrow-derived preosteoclast-like cells

Bone is a porous tissue that is continuously perfused by interstitial fluid. Fluid flow, driven by both vascular pressure and mechanical loading, may generate significant shear stresses through the canaliculi as well as along the bone lining at the endosteal surface. Both osteoblasts and osteocytes produce signaling factors such as prostaglandins and nitric in response to fluid shear stress (FSS); however, these humoral agents appear to have more profound affects on osteoclast activity at the endosteal surface. We hypothesized that osteoclasts and preosteoclasts may also be mechanosensitive and that osteoclast-mediated autocrine signaling may be important in bone remodeling. In this study, we investigated the effect of FSS on nitric oxide (NO), prostaglandin E(2) (PGE(2)), and prostacyclin (PGI(2)) release by neonatal rat bone marrow-derived preosteoclast-like cells. These cells were tartrate-resistant acid phosphatase (TRAP) positive, weakly nonspecific esterase (NSE) positive, and capable of fusing into calcitonin-responsive, bone-resorbing, multinucleated cells. Bone marrow-derived preosteoclast-like cells exposed for 6 h to a well-defined FSS of 16 dynes/cm(2) produced NO at a rate of 7.5 nmol/mg protein/h, which was 10-fold that of static controls. This response was completely abolished by 100 microM N(G)-amino-L-arginine (L-NAA). Flow also stimulated PGE(2) production (3.9 microg/mg protein/h) and PGI(2) production (220 pg/mg protein/h). L-NAA attenuated flow-induced PGE(2) production by 30%, suggesting that NO may partially modulate PGE(2) production. This is the first report demonstrating that marrow derived cells are sensitive to FSS and that autocrine signaling in these cells may play an important role in load-induced remodeling and signal transduction in bone.     

Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a dimensionless ratio h / lambda(v), in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to be met: (1) h / lambda(v) < 2, where h is the distance between the plates and lambda(v) is the viscous penetration depth; and (2) f(0) < f(c) / m, where the critical frequency f(c) is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f(0) is the fundamental frequency of fluid flow.