Poroelastic finite element analysis of a bone specimen under cyclic loading

It had been suggested that the fluid embodied in bone lacunar-canalicular porosity may play an important role in bone remodelling [Weinbaum et al., 1994. Journal of Biomechanics 27, 339-360]. In this paper a finite element model of a poroelastic prismatic solid of rectangular cross-section is considered to simulate bone behaviour, precisely as in the previous work by Zhang and Cowin [Zhang and Cowin, 1994. Journal of Mechanical Physics of Solids 42, 1575-1599]. This solid is subject to combined cyclic axial and bending loads at its end. The objectives of the study are: (1) to verify the accuracy of the simplifying hypotheses underlying the analytical solutions established by the above authors; (2) to provide further insight into the behaviour of that solid; (3) to test the advantages in generality and versatility and the computing costs of general-purpose finite element codes in poroelastic analysis. The study is parametric with respect to the fluid leakage coefficient, to the ratio of the bending moment and axial load, and to the ratio of the characteristic relaxation time of the pore pressure over the excitation period. Results show that, for all the cases considered, the pore pressure distribution along the section height of the poroelastic beam exhibits a very good matching with previous analytical results. Stresses transversal with respect to the beam axis (assumed as constant or zero in previous analytical solutions) are evaluated. The analysis pointed out that: (1) the effects due to end-loads with zero resultants practically extinguish within a distance from the beam end almost equal to a typical length of the cross-section; (2) cross-sections remain plane above that distance; (3) the transversal total stresses are three orders of magnitude lower than axial stress.     

Skeletal adaptation to intramedullary pressure-induced interstitial fluid flow is enhanced in mice subjected to targeted osteocyte ablation

Interstitial fluid flow (IFF) is a potent regulatory signal in bone. During mechanical loading, IFF is generated through two distinct mechanisms that result in spatially distinct flow profiles: poroelastic interactions within the lacunar-canalicular system, and intramedullary pressurization. While the former generates IFF primarily within the lacunar-canalicular network, the latter generates significant flow at the endosteal surface as well as within the tissue. This gives rise to the intriguing possibility that loading-induced IFF may differentially activate osteocytes or surface-residing cells depending on the generating mechanism, and that sensation of IFF generated via intramedullary pressurization may be mediated by a non-osteocytic bone cell population. To begin to explore this possibility, we used the Dmp1-HBEGF inducible osteocyte ablation mouse model and a microfluidic system for modulating intramedullary pressure (ImP) to assess whether structural adaptation to ImP-driven IFF is altered by partial osteocyte depletion. Canalicular convective velocities during pressurization were estimated through the use of fluorescence recovery after photobleaching and computational modeling. Following osteocyte ablation, transgenic mice exhibited severe losses in bone structure and altered responses to hindlimb suspension in a compartment-specific manner. In pressure-loaded limbs, transgenic mice displayed similar or significantly enhanced structural adaptation to Imp-driven IFF, particularly in the trabecular compartment, despite up to ～50% of trabecular lacunae being uninhabited following ablation. Interestingly, regression analysis revealed relative gains in bone structure in pressure-loaded limbs were correlated with reductions in bone structure in unpressurized control limbs, suggesting that adaptation to ImP-driven IFF was potentiated by increases in osteoclastic activity and/or reductions in osteoblastic activity incurred independently of pressure loading. Collectively, these studies indicate that structural adaptation to ImP-driven IFF can proceed unimpeded following a significant depletion in osteocytes, consistent with the potential existence of a non-osteocytic bone cell population that senses ImP-driven IFF independently and potentially parallel to osteocytic sensation of poroelasticity-derived IFF.     

On computational predictions of fluid flow and its effects on bone healing in dental implant treatments: an investigation of spatiotemporal fluid flow in cyclic loading

Biomechanics and Modeling in Mechanobiology - Fluid flow in (porous) bone plays an important role in its maintenance, adaptation, and healing after an injury. Experimental and computational studies...     

Osteocytes subjected to pulsating fluid flow regulate osteoblast proliferation and differentiation

Osteocytes are thought to orchestrate bone remodeling, but it is unclear exactly how osteocytes influence neighboring bone cells. Here, we tested whether osteocytes, osteoblasts, and periosteal fibroblasts subjected to pulsating fluid flow (PFF) produce soluble factors that modulate the proliferation and differentiation of cultured osteoblasts and periosteal fibroblasts. We found that osteocyte PFF conditioned medium (CM) inhibited bone cell proliferation, and osteocytes produced the strongest inhibition of proliferation compared to osteoblasts and periosteal fibroblasts. The nitric oxide (NO) synthase inhibitor N(G)-nitro-L-arginine methyl ester (L-NAME) attenuated the inhibitory effects of osteocyte PFF CM, suggesting that a change in NO release is at least partially responsible for the inhibitory effects of osteocyte PFF CM. Furthermore, osteocyte PFF CM stimulated osteoblast differentiation measured as increased alkaline phosphatase activity, and l-NAME decreased the stimulatory effects of osteocyte PFF CM on osteoblast differentiation. We conclude that osteocytes subjected to PFF inhibit proliferation but stimulate differentiation of osteoblasts in vitro via soluble factors and that the release of these soluble factors was at least partially dependent on the activation of a NO pathway in osteocytes in response to PFF. Thus, the osteocyte appears to be more responsive to PFF than the osteoblast or periosteal fibroblast with respect to the production of soluble signaling molecules affecting osteoblast proliferation and differentiation.     

Regulation of tumor invasion by interstitial fluid flow

The importance of the tumor microenvironment in cancer progression is undisputed, yet the significance of biophysical forces in the microenvironment remains poorly understood. Interstitial fluid flow is a nearly ubiquitous and physiologically relevant biophysical force that is elevated in tumors because of tumor-associated angiogenesis and lymphangiogenesis, as well as changes in the tumor stroma. Not only does it apply physical forces to cells directly, but interstitial flow also creates gradients of soluble signals in the tumor microenvironment, thus influencing cell behavior and modulating cell-cell interactions. In this paper, we highlight our current understanding of interstitial fluid flow in the context of the tumor, focusing on the physical changes that lead to elevated interstitial flow, how cells sense flow and how they respond to changes in interstitial flow. In particular, we emphasize that interstitial flow can directly promote tumor cell invasion through a mechanism known as autologous chemotaxis, and indirectly support tumor invasion via both biophysical and biochemical cues generated by stromal cells. Thus, interstitial fluid flow demonstrates how important biophysical factors are in cancer, both by modulating cell behavior and coupling biophysical and biochemical signals.     

Length scale parameter of single trabecula in cancellous bone

Biomechanics and Modeling in Mechanobiology - In this paper, the material length scale parameter of the modified couple stress theory for trabecular bones is studied. For this reason, experimental...     

A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone

Targeted remodeling is activated by fatigue microcracks and plays an important role in maintaining bone integrity. It is widely believed that fluid flow-induced shear stress plays a major role in modulating the mechanotransduction process. Therefore, it is likely that fluid flow-induced shear stress plays a major role in the initiation of the repair of fatigue damage. Since no in vivo measurements of fluid flow within bone exist, computational and mathematical models must be employed to investigate the fluid flow field and the shear stress occurring within cortical bone. We developed a computational fluid dynamic model of cortical bone to examine the effect of a fatigue microcrack on the fluid flow field. Our results indicate that there are alterations in the fluid flow field as far as 150 microm away from the crack, and that at distances farther than this, the fluid flow field is similar to the fluid flow field of intact bone. Through the crack and immediately above and below it, the fluid velocity is higher, while at the lateral edges it is lower than that calculated for the intact model, with a maximum change of 29%. Our results suggest that the presence of a fatigue microcrack can alter the shear stress in regions near the crack. These alterations in shear stress have the potential to significantly alter mechanotransduction and may play a role in the initiation of the repair of fatigue microcracks.     

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.     

Bone tissue engineering: the role of interstitial fluid flow

It is well established that vascularization is required for effective bone healing. This implies that blood flow and interstitial fluid (ISF) flow are required for healing and maintenance of bone. The fact that changes in bone blood flow and ISF flow are associated with changes in bone remodeling and formation support this theory. ISF flow in bone results from transcortical pressure gradients produced by vascular and hydrostatic pressure, and mechanical loading. Conditions observed to alter flow rates include increases in venous pressure in hypertension, fluid shifts occurring in bedrest and microgravity, increases in vascularization during the injury-healing response, and mechanical compression and bending of bone during exercise. These conditions also induce changes in bone remodeling. Previously, we hypothesized that interstitial fluid flow in bone, and in particular fluid shear stress, serves to mediate signal transduction in mechanical loading- and injury-induced remodeling. In addition, we proposed that a lack or decrease of ISF flow results in the bone loss observed in disuse and microgravity. The purpose of this article is to review ISF flow in bone and its role in osteogenesis.     

Nanostructure and elastic modulus of single trabecula in bovine cancellous bone

We aimed to investigate the elastic modulus of trabeculae using tensile tests and assess the effects of nanostructure at the hydroxyapatite (HAp) crystal scale on the elastic modulus. In the experiments, 18 trabeculae that were at least 3 mm in length in the proximal epiphysis of three adult bovine femurs were used. Tensile tests were conducted using a small tensile testing device coupled with microscopy under air-dried condition. The c-axis orientation of HAp crystals and the degree of orientation were measured by X-ray diffraction. To observe the deformation behavior of HAp crystals under tensile loading, the same tensile tests were conducted in X-ray diffraction measurements. The mineral content of specimens was evaluated using energy dispersive X-ray spectrometry. The elastic modulus of a single trabecula varied from 4.5 to 23.6 GPa, and the average was 11.5±5.0 GPa. The c-axis of HAp crystals was aligned with the trabecular axis and the crystals were lineally deformed under tensile loading. The ratio of the HAp crystal strain to the tissue strain (strain ratio) had a significant correlation with the elastic modulus (r=0.79; P<0.001). However, the mineral content and the degree of orientation did not vary widely and did not correlate with the elastic modulus in this study. It suggests that the strain ratio may represent the nanostructure of a single trabecula and would determine the elastic modulus as well as mineral content and orientation.     

Fibroblast alignment under interstitial fluid flow using a novel 3-D tissue culture model

Interstitial flow is an important component of the microcirculation and interstitial environment, yet its effects on cell organization and tissue architecture are poorly understood, in part due to the lack of in vitro models. To examine the effects of interstitial flow on cell morphology and matrix remodeling, we developed a tissue culture model that physically supports soft tissue cultures and allows microscopic visualization of cells within the three-dimensional matrix. In addition, pressure-flow relationships can be continuously monitored to evaluate the bulk hydraulic resistance as an indicator of changes in the overall matrix integrity. We observed that cells such as human dermal fibroblasts aligned perpendicular to the direction of interstitial flow. In contrast, fibroblasts in static three-dimensional controls remained randomly oriented, whereas cells subjected to fluid shear as a two-dimensional monolayer regressed. Also, the dynamic measurements of hydraulic conductivity suggest reorganization toward a steady state. These primary findings help establish the importance of interstitial flow on the biology of tissue organization and interstitial fluid balance.     

Differential proteomic analysis of renal cell carcinoma tissue interstitial fluid

Renal cell carcinoma (RCC), the most common type of kidney cancer, currently has no biomarker of clinical utility. The present study utilized a mass spectrometry-based proteomics workflow for identifying differentially abundant proteins in RCC by harvesting shed and secreted proteins from the tumor microenvironment through sampling tissue interstitial fluid (TIF) from radical nephrectomies. Matched tumor and adjacent normal kidney (ANK) tissues were collected from 10 patients diagnosed with clear cell RCC. One-hundred thirty-eight proteins were identified with statistically significant differential abundances derived by spectral counting in tumor TIF when compared to ANK TIF. Among those proteins with elevated abundance in tumor TIF, nicotinamide n-methyltransferase (NNMT) and enolase 2 (ENO2) were verified by Western blot and selected reaction monitoring (SRM). The presence of ENO2 and thrombospondin-1 (TSP1) were verified as present and at elevated abundance in RCC patient serum samples as compared to a pooled standard control by enzyme-linked immunosorbent assay (ELISA), recapitulating the relative abundance increase in RCC as compared with ANK TIF.     

Modeling actin filament reorganization in endothelial cells subjected to cyclic stretch

Hemodynamic forces affect endothelial cell morphology and function. In particular, circumferential cyclic stretch of blood vessels, due to pressure changes during the cardiac cycle, is known to affect the endothelial cell shape, mediating the alignment of the cells in the direction perpendicular to stretch. This change in cell shape proceeds a drastic reorganization at the internal level. The cellular scaffolding, mainly composed of actin filaments, reorganize in the direction which later becomes the cell’s long axis. How this external mechanical stimulus is ’sensed’ and transduced into the cell is still unknown. Here, we develop a mathematical model depicting the dynamics of actin filaments, and the influence of the cyclic stretch of the substratum based on the experimental evidence that external stimuli may be transduced inside the cell via transmembrane proteins which are coupled with actin filaments on the cytoplasmic side. Based on this view, we investigate two approaches describing the formulation of the transduction mechanisms involving the coupling between filaments and the membrane proteins. As a result, we find that the mechanical stimulus could cause the experimentally observed reorganization of the entire cytoskeleton simply by altering the dynamics of the filaments connected with the integral membrane proteins, as described in our model. Comparison of our results with previous studies of cytoskeletal dynamics reveals that the cytoskeleton, which, in the absence of the effect of stretch would maintain its isotropic distribution, slowly aligns with the precise direction set by the external stimulus. It is found that even a feeble stimulus, coupled with a strong internal dynamics, is sufficient to align actin filaments perpendicular to the direction of stretch.     

A fiber matrix model for interstitial fluid flow and permeability in ligaments and tendons

Collagen fibrils in ligaments and tendons are highly organized into parallel arrays which influence interstitial fluid transport. Finite element (FE) models were developed analogous to the fibrillar arrays in ligaments and tendons to investigate interstitial fluid flow and tissue permeability as a function of interfibrillar spacing and fluid properties. Collagen fibrils were assumed to be a periodic square array of impermeable cylinders. A two-dimensional FE model was used to study transverse fluid flow and a three-dimensional model was used to study flow parallel to the collagen fibrils. Parametric FE analysis provided data to formulate empirical expressions for permeability (kappa) as a function of porosity (phi). Results show that longitudinal permeability (kappa = 1.1.10(-15)phi 2.5[1 - phi]-0.333) can be up to 50 times higher than transverse permeability (kappa = 1.2.10(-15)phi 0.5[phi - phi min]2.5) in a compact array. Maximum fluid shear stresses occur at the narrowest zones of adjacent fibrils (1.21 Pa or 12.1 dyn/cm2 at 10 microns/s of average transverse influx). If interstitial fluid is highly non-Newtonian, the permeability should be considered as flow (shear)-dependent. The computational results suggest that tissue permeability in ligaments and tendons is highly anisotropic, porosity-dependent, and can be estimated by analytic expressions.     

Effects of abnormal posture on capsular ligament elongations in a computational model subjected to whiplash loading

Although considerable biomechanical investigations have been conducted to understand the response of the cervical spine under whiplash (rear impact-induced postero-anterior loading to the thorax), studies delineating the effects of initial spinal curvature are limited. This study advanced the hypothesis that abnormal curvatures (straight or kyphotic) of the cervical column affect spinal kinematics during whiplash loading. Specifically, compared to the normal lordotic curvature, abnormal curvatures altered facet joint ligament elongations. The quantifications of these elongations were accomplished using a validated mathematical model of the human head-neck complex that simulated three curvatures. The model was validated using companion experiments conducted in our laboratory that provided facet joint kinematics as a function of cervical spinal level. Regional facet joint ligament elongations were investigated as a function of whiplash loading in the four local anatomic regions of each joint. Under the normal posture, greatest elongations occurred in the dorsal anatomic region at the C2-C3 level and in the lateral anatomic region from C3-C4 to C6-C7 levels. Abnormal postures increased elongation magnitudes in these regions by up to 70%. Excessive ligament elongations induce laxity to the facet joint, particularly at the local regions of the anatomy in the abnormal kyphotic posture. Increased laxity may predispose the cervical spine to accelerated degenerative changes over time and lead to instability. Results from the present study, while providing quantified level- and region-specific kinematic data, concur with clinical findings that abnormal spinal curvatures enhance the likelihood of whiplash injury and may have long-term clinical and biomechanical implications.     

Development of a fluorescent light technique for evaluating microdamage in bone subjected to fatigue loading.

A new method using fluorescent light microscopy has been developed to visualize and evaluate bone microdamage. We report the findings of two different experiments with a common aim of comparing the fluorescent light technique to the brightfield method for quantifying microdamage in bone. In Experiment 1, 36 canine femurs were tested in four-point cyclic bending until they had lost between 5 and 43% of their stiffness. The loaded portion of the bone was stained en bloc with basic fuchsin for the presence of damage. Standard point counting techniques were used to calculate fractional damaged area (Dm.Ar = Cr.Ar/B.Ar, mm2/mm2) under brightfield and fluorescent microscopy. In Experiment 2, bone microdamage adjacent to endosseous implants, subjected to fatigue loading (150,000 cycles, 2 Hz and 37 degrees C) ex vivo was examined. The bone around the implant was either allowed to heal (adapted specimen) for 12 weeks after placement in dog mid-femoral diaphyses prior to testing or was loaded immediately to simulate non-healed bone surrounding endosseous implants (non-adapted). Crack numerical density (Cr.Dn = Cr.N/B.Ar, #/mm2), crack surface density (Cr.S.Dn = Tt.Cr.Le/B.Ar, mm/mm2) and fractional damaged area were calculated separately by both techniques in the adapted and non-adapted specimens. In both Experiments 1 and 2, significantly more microdamage was detected by the fluorescent technique than by the brightfield method. Also, there was a trend towards higher intraobserver repeatability when using the fluorescent method. These results suggest that the brightfield technique underestimates microdamage accumulation and that the fluorescent technique better represents the actual amounts of microdamage present. The results demonstrate that the fluorescent method provides an accurate and precise approach for bone microdamage evaluation, and that it improves the prediction of stiffness loss from damage accumulation.     

Development of a cell culture system loading cyclic mechanical strain to chondrogenic cells

Mechanical stimulation is considered to be one of the major epigenetic factors regulating the metabolism, proliferation, survival and differentiation of cells in the skeletal tissues. It is generally accepted that the cytoskeleton can undergo remodeling in response to mechanical stimuli such as tensile strain or fluid flow. Mechanically induced cell deformation is one of the possible mechanotransduction pathways by which chondrocytes sense and respond to changes in their mechanical environment. Mechanical strain has a variety of effects on the structure and function of their cells in the skeletal tissues, such as chondrocytes, osteoblasts and fibroblasts. However, little is known about the effect of the quality and quantity of mechanical strain and the timing of mechanical loading on the differentiation of these cells. The present study was designed to investigate the effect of the deformation of chondrogenic cells, and cyclic compression using a newly developed culture device, by analyzing mechanobiological response to the differentiating chondrocytes. Cyclic compression between 0 and 22% strains, at 23 microHz was loaded on chondrogenic cell line ATDC5 by seeding in a mass mode on PDMS membrane, assuming direct transfer of cyclic deformation from the membrane to the cells at the same frequency. The compressive strain, induced within the membrane, was characterized based on the analysis of the finite element modeling (FEM). The results showed that the tensile strain inhibits the chondrogenic differentiation of ATDC5 cells, whereas the compressive strain enhances the chondrogenic differentiation, suggesting that the differentiation of the chondrogenic cells could be controlled by the amount and the mode of strain. In conclusion, we have developed a unique strain loading culture system to analyze the effect of various types of mechanical stimulation on various cellular activities.     

Estimations of lipid bilayer geometry in fluid lamellar phases

The excess water bilayer thickness, d(l,0), and molecular area, A(0), of lipid amphiphiles in the fluid lamellar phases of dioleoylphosphatidylcholine (DOPC) and dipalmitoleoylphosphatidylcholine (DPolPC) have been estimated between 15 and 50 degrees C and for dimyristoylphosphatidylcholine (DMPC) between 25 and 50 degrees C. These determinations have been made from X-ray measurements on samples of known water composition. With respect to temperature, T, d(l,0) and A(0) are well fitted to a linear equation. We find d(l,0) (A)=(35.68+/-0.02)-(0.0333+/-0.0006)T (degrees C) and A(0) (A(2))=(70.97+/-0.05)+(0.136+/-0.001)T (degrees C) for DOPC, d(l,0) (A)=(35.2+/-0.1)-(0.068+/-0.003)T (degrees C) and A(0) (A(2))=(59.7+/-0.2)+(0.210+/-0.006)T (degrees C) for DMPC, and d(l,0) (A)=(34.54+/-0.03)-(0.0531+/-0.0009)T (degrees C) and A(0) (A(2))=(67.12+/-0.09)+(0.173+/-0.003)T (degrees C) for DPolPC. The accuracy of these estimates depends largely on how accurately the excess water point is determined. Ideally, reliable X-ray and compositional data will be available around the excess water and it may be found by simple inspection, but this is the exception rather than the rule, since samples close to water excess normally sequester sizeable amounts of water in defects, which lead to an underestimate of d(l,0). and overestimate of A(0). In this paper, we report a methodology for identifying and removing such data points and fitting the remaining data in order to determine the excess water point.     

Mechanical behaviour of in-situ chondrocytes subjected to different loading rates: a finite element study

Experimental findings indicate that in-situ chondrocytes die readily following impact loading, but remain essentially unaffected at low (non-impact) strain rates. This study was aimed at identifying possible causes for cell death in impact loading by quantifying chondrocyte mechanics when cartilage was subjected to a 5% nominal tissue strain at different strain rates. Multi-scale modelling techniques were used to simulate cartilage tissue and the corresponding chondrocytes residing in the tissue. Chondrocytes were modelled by accounting for the cell membrane, pericellular matrix and pericellular capsule. The results suggest that cell deformations, cell fluid pressures and fluid flow velocity through cells are highest at the highest (impact) strain rate, but they do not reach damaging levels. Tangential strain rates of the cell membrane were highest at the highest strain rate and were observed primarily in superficial tissue cells. Since cell death following impact loading occurs primarily in superficial zone cells, we speculate that cell death in impact loading is caused by the high tangential strain rates in the membrane of superficial zone cells causing membrane rupture and loss of cell content and integrity.