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.     

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.     

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.     

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.     

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.     

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.     

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.     

Evidence for bulk flow of brain interstitial fluid: significance for physiology and pathology

This review surveys evidence for the flow of brain interstitial fluid (ISF) via preferential pathways through the brain, and its relation to cerebrospinal fluid (CSF). Studies over >100 years have raised several controversial points, not all of them resolved. Recent studies have usefully combined a histological and a mathematical approach. Taken together the evidence indicates an ISF bulk flow rate of 0.1-0.3 microl min(-1) g(-1) in rat brain along preferential pathways especially perivascular spaces and axon tracts. The main source of this fluid is likely to be the brain capillary endothelium, which has the necessary ion transporters, channels and water permeability to generate fluid at a low rate, c1/100th of the rate per square centimeter of CSF secretion across choroid plexus epithelium. There is also evidence that a proportion of CSF may recycle from the subarachnoid space into arterial perivascular spaces on the ventral surface of the brain, and join the circulating ISF, draining back via venous perivascular spaces and axon tracts into CSF compartments, and out both through arachnoid granulations and along cranial nerves to the lymphatics of the neck. The bulk flow of ISF has implications for non-synaptic cell:cell communication (volume transmission); for drug delivery, distribution, and clearance; for brain ionic homeostasis and its disturbance in brain edema; for the immune function of the brain; for the clearance of beta-amyloid deposits; and for the migration of cells (malignant cells, stem cells).     

An analysis of the flow of a power law fluid due to ciliary motion in an infinite channel

The propulsion mechanics of cilia-induced flow is studied through a mathematical model. The problem of two-dimensional motion of a power law fluid inside a channel with ciliated walls is considered. The characteristics of ciliary systems are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Solutions for the longitudinal, transverse, and resultant velocities are obtained. The pressure gradient and volume flow rate for different values of the power law index are also calculated. The flow properties for the power law fluid are determined as a function of the cilia and metachronal wave velocity. The viscous and power law fluid are compared and discussed graphically.     

Lengthening of a single-loop tibialis tendon graft construct after cyclic loading: a study using Roentgen stereophotogrammetric analysis

Although single-loop tibialis tendon allografts have increased in popularity owing to their many advantages over patellar tendon and double-loop hamstring tendon autografts, some percentage of the patient population do not have clinically stable knees following anterior cruciate ligament reconstruction with single-loop tibialis tendon allografts. Therefore, it would be advantageous to determine the causes of increased anterior laxity which ultimately must be traced to lengthening of the graft construct. One objective of this study was to demonstrate the feasibility of using Roentgen stereophotogrammetric analysis (RSA) to determine the causes of lengthening of a single-loop graft construct subjected to cyclic loading. A second objective was to determine which cause(s) contributes most to an increase in length of this graft construct. Radio-opaque markers were inserted into ten grafts to measure the lengthening at the sites of the tibial and femoral fixations and between the sites of fixation. Each graft was passed through a tibial tunnel in a calf tibia, looped around a rigid cross-pin, and fixed to the tibia with a Washerloc fixation device. The grafts were cyclically loaded for 225,000 cycles from 20 to 170 N. Prior to and at intervals during the cyclic loading, simultaneous radiographs were taken. RSA was used to determine the three-dimensional coordinates of the markers from which the lengthening at the sites of fixation and between the sites of fixation was computed at each interval. The sites of the femoral and tibial fixations were the largest contributors to the increase in length of the graft construct, with maximum average values of 0.68 and 0.55 mm, respectively, after 225,000 cycles. The graft substance between the sites of fixation contributed least to lengthening of the graft, with a maximum average value of 0.31 mm. Ninety percent of the maximum average values occurred before 100,000 cycles of loading for the largest contributors. RSA proved to be a useful method for measuring lengthening due to all three causes. Lengthening of the graft construct at the sites of both fixations is sufficiently large that the combined contributions may manifest as a clinically important increase in anterior laxity.     

A numerical model of expired flow in a monoalveolar lung model subjected to pressure ramps

A numerical investigation of pulmonary flow properties was carried out in a monoalveolar model composed of a balloon and a compliant tube in series, subjected to pressure ramps. The flow is shown to become quickly limited by a wave-speed mechanism, occurring at the peak flow. The critical point then travels upstream, while the main part of the exit flow rate is provided by the tube collapse. After the critical flow period, the flow becomes subcritical and viscous effects are predominant in the deeply collapsed tube.