Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Measurement of microstructural strain in cortical bone

It is well known that mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Current theories suggest that bone modeling and remodeling is controlled at the cellular level through signals mediated by osteocytes. The objective of this study was to investigate how macroscopically applied bone strains similar in magnitude to those that occur in vivo are manifest at the microscopic level in the bone matrix. Using a digital image correlation strain measurement technique, experimentally determined bone matrix strains around osteocyte lacuna resulting from macroscopic strains of approximately 2,000 microstrain (0.2%) reach levels of over 30,000 microstrain (3%) over fifteen times greater than the applied macroscopic strain. Strain patterns were highly heterogeneous and in some locations similar to observed microdamage around osteocyte lacuna indicating the resulting strains may represent the precursors to microdamage. This information may lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Microstructural strain near osteocyte lacuna in cortical bone in vitro

Mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Two proposed mechanical signals are stress-generated fluid flow forces acting on cells and bone matrix deformation itself. A prominent current theory is that bone cells are more responsive to fluid flow than to mechanical strain. Recent experiments support this conclusion: bone cells increase their production of osteopontin (OPN) mRNA, prostaglandin (PGE(2)), and nitric oxide (NO) in response to fluid flow in contrast to cells stimulated by mechanical strain levels similar to those measured in vivo. However, when cells are subjected to substrate strains levels many times greater than those measured in vivo, increased biological activity again results. We assert that it is neither fluid flow nor matrix deformation per se, but rather the resulting cell deformation that causes cell biological response. Machined specimens of undamaged bovine cortical bone were subjected to increasing levels of macroscopic strain while observed under an optical microscope at 220X. Continuum level strain was measured using a standard foil strain gauge attached to the back of the specimen and ranged from 500 to 6,000 microstrain. Images of the specimen surface at each strain level were captured. To determine the level of osteocyte deformation that results from fluid flow in vitro, MLO-Y4 cells were cultured on collagen coated 190 cm2 plastic sheets and subjected to steady fluid flow at 16 dynes/cm(2). Images representing the initial undisturbed cell configuration and the configuration of the cells after ten minutes of fluid flow were acquired from a videotape of the flow experiment. The captured unloaded vs. loaded image pairs were analyzed to determine the local deformation and strain fields using a digital stereoimaging system. When subjected to a nominal continuum strain level approximately equal to that measured in humans in vivo during rigorous activity (2,000 microstrain), the local, osteocyte level strains can be as high as 12,000 to 15,000 microstrain (1.2% to 1.5%). Average osteocyte strains due to fluid flow in vitro increase from 7,972 microstrains after 16 seconds of flow to 22,856 microstrains after 64 seconds of flow. In contrast, maximum strains measured in vivo are approximately 1,800 microstrain in humans and up to 3,000 microstrain in other species. These data may help to explain why bone cells are more sensitive to fluid flow than substrate strain; fluid forces result in cell deformations much higher than those considered to be "physiological".     

Mechanical properties of single bovine trabeculae are unaffected by strain rate

For a better understanding of traumatic bone fractures, knowledge of the mechanical behavior of bone at high strain rates is required. Importantly, it needs to be clarified how quasistatic mechanical testing experiments relate to real bone fracture. This merits investigating the mechanical behavior of bone with an increase in strain rate. Various studies examined how cortical and trabecular bone behave at varying strain rates, but no one has yet looked at this question using individual trabeculae. In this study, three-point bending tests were carried out on bovine single trabeculae excised from a proximal femur to test the trabecular material's strain rate sensitivity. An experimental setup was designed, capable of measuring local strains at the surface of such small specimens, using digital image correlation. Microdamage was detected using the bone whitening effect. Samples were tested through two orders of magnitude, at strain rates varying between 0.01 and 3.39 s(-1). No linear relationship was observed between the strain rate and the Young's modulus (1.13-16.46 GPa), the amount of microdamage, the maximum tensile strain at failure (14.22-61.65%) and at microdamage initiation (1.95-12.29%). The results obtained in this study conflict with previous studies reporting various trends for macroscopic cortical and trabecular bone samples with an increase in strain rate. This discrepancy might be explained by the bone type, the small sample geometry, the limited range of strain rates tested here, the type of loading and the method of microdamage detection. Based on the results of this study, the strain rate can be ignored when modeling trabecular bone.     

Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone

Strain measurement is an essential tool in the study of trabecular bone structure-function relationships. Digital volume correlation (DVC) is a measurement technique that quantifies strains throughout the interior of a specimen, rather than simply those on the surface. DVC relies on tracking the movement of microstructural features, and as such, the accuracy and precision of this technique may depend on trabecular structure. This study quantified displacement and strain measurement errors in six types of trabecular bone that spanned a wide range of volume fraction and trabecular architecture. Accuracy and precision were compared across bone type and also across three DVC methods. Both simulated and real displacement fields were analyzed using micro-computed tomography images of specimens from the bovine distal femur, bovine proximal tibia, rabbit distal femur, rabbit proximal tibia, rabbit vertebra, and human vertebra. Differences as large as three-fold in accuracy and precision of the displacements and strains were found among DVC methods and among bone types. The displacement precision and the strain accuracy and precision were correlated with measures of trabecular structure such as structural model index. These results demonstrate that the performance of the DVC technique can depend on trabecular structure. Across all bone types, the displacement and strain errors ranged 1.86-3.39 microm and 345-794 microepsilon, respectively. For specimens from the human vertebra and bovine distal femur, the measurement errors were approximately 20 times smaller than the yield strain. In these cases, DVC is a viable technique for measuring pre- and post-yield strains throughout trabecular bone specimens and the trabecular compartment of whole bones.     

Quantification of a rat tail vertebra model for trabecular bone adaptation studies

A feedback controlled loading apparatus for the rat tail vertebra was developed to deliver precise mechanical loads to the eighth caudal vertebra (C8) via pins inserted into adjacent vertebrae. Cortical bone strains were recorded using strain gages while subjecting the C8 in four cadaveric rats to mechanical loads ranging from 25 to 100 N at 1 Hz with a sinusoidal waveform. Finite element (FE) models, based on micro computed tomography, were constructed for all four C8 for calculations of cortical and trabecular bone tissue strains. The cortical bone strains predicted by FE models agreed with strain gage measurements, thus validating the FE models. The average measured cortical bone strain during 25-100 N loading was between 298 +/- 105 and 1210 +/- 297 microstrain (muepsilon). The models predicted average trabecular bone tissue strains ranging between 135 +/- 35 and 538 +/- 138 mu epsilon in the proximal region, 77 +/- 23-307 +/- 91 muepsilon in the central region, and 155 +/- 36-621 +/- 143 muepsilon in the distal region for 25-100 N loading range. Although these average strains were compressive, it is also interesting that the trabecular bone tissue strain can range from compressive to tensile strains (-1994 to 380 mu epsilon for a 100 N load). With this novel approach that combines an animal model with computational techniques, it could be possible to establish a quantitative relationship between the microscopic stress/strain environment in trabecular bone tissue, and the biosynthetic response and gene expression of bone cells, thereby study bone adaptation.     

Using digital image correlation to determine bone surface strains during loading and after adaptation of the mouse tibia

Previous models of cortical bone adaptation, in which loading is imposed on the bone, have estimated the strains in the tissue using strain gauges, analytical beam theory, or finite element analysis. We used digital image correlation (DIC), tracing a speckle pattern on the surface of the bone during loading, to determine surface strains in a murine tibia during compressive loading through the knee joint. We examined whether these surface strains in the mouse tibia are modified following two weeks of load-induced adaptation by comparison with contralateral controls. Results indicated non-uniform strain patterns with isolated areas of high strain (0.5%), particularly on the medial side. Strain measurements were reproducible (standard deviation of the error 0.03%), similar between specimens, and in agreement with strain gauge measurements (between 0.1 and 0.2% strain). After structural adaptation, strains were more uniform across the tibial surface, particularly on the medial side where peak strains were reduced from 0.5% to 0.3%. Because DIC determines local strains over the entire surface, it will provide a better understanding of how strain stimulus influences the bone response during adaptation.     

A three-dimensional digital image correlation technique for strain measurements in microstructures

A three-dimensional digital image correlation technique is presented for strain measurements in open-cell structures such as trabecular bone. The technique uses high-resolution computed tomography images for displacement measurements in the solid structure. In order to determine the local strain-state within single trabeculae, a tetrahedronization method is used to fill the solid structure with tetrahedrae. Displacements are calculated at the nodes of the tetrahedrae. The displacement data is subsequently converted to a deformation tensor in each of the tetrahedral element centers with a least-squares estimation method. Because the trabeculae are represented by a mesh, it is possible to deform this mesh according to the deformation tensor and, at the same time, visualize the calculated local strain in the deformed mesh with a finite element post-processing tool. In this way, the deformation of a single trabecula from an aluminum foam sample was determined and validated with rendered images of the three-dimensional sample. A precision analysis showed that a rigid translation or rotation does not affect the accuracy. Typical values for the standard deviation in the displacement and strain components are 2.0 microm and 0.01, respectively. Presently, the precision limits the technique to strain measurements beyond the yield strain.     

Do microcracks decrease or increase fatigue resistance in cortical bone?

Fatigue of cortical bone produces microcracks; it has been hypothesized that these cracks are analogous to those occurring in engineered composite materials and constitute a similar mechanism for fatigue resistance. However, the numbers of these linear microcracks increase substantially with age, suggesting that they contribute to increased fracture incidence among the elderly. To test these opposing hypotheses, we fatigued 20 beams of femoral cortical bone from elderly men and women in load-controlled four point bending having initial strain ranges of 3000 or 5000 microstrain. Loading was stopped at fracture or 10(6) cycles, whichever occurred first, and microcrack density and length were measured in the loaded region and in a control region that was not loaded. We studied the dependence of fatigue life and induced microdamage on initial microdamage, cortical region, subject gender and age, and several other variables. When the effect of modulus variability was controlled, longer fatigue life was associated with higher rather than lower initial crack density, particularly in the medial cortex. The increase in crack density following fatigue loading was greater in specimens from older individuals and those initially having longer microcracks. Crack density increased as much in specimens fatigued short of the failure point as in those that fractured, and microcracks were, on average, shorter in specimens with greater numbers of resorption spaces, a measure of remodeling rate.     

Measurement of the microstructural fracture toughness of cortical bone using indentation fracture

The purpose of this work is to investigate the use of indentation fracture as a method of measuring toughness at the microscale in cortical bone. Indentation fracture employs sharp indenters to initiate cracks, whose length can be used to calculate the toughness of the material. Only a cube corner indenter tip is found to initiate cracks at a suitable size scale for microstructural measurement. Cracks from 7 to 56 microm in length are produced using loads from 0.05 to 3N. Preliminary data predicts rising toughness with increasing crack length (rising R-curve behaviour) at the microscale. This technique provides a new insight into fracture in cortical bone since it allows the investigator to observe mechanisms and measure toughness at a size scale at which in vivo damage is known to exist.     

Mechanical properties of porcine femoral cortical bone measured by nanoindentation

This study uses a nanoindentation technique to examine variations in the local mechanical properties of porcine femoral cortical bone under hydrated conditions. Bone specimens from three age groups (6, 12 and 42 months), representing developing bone, ranging from young to mature animals, were tested on the longitudinal and transverse cross-sectional surfaces. Elastic modulus and hardness of individual lamellae within bone's microstructure: laminar bone, interstitial bone, and osteons, were measured. Both the elastic modulus and hardness increased with age. However, the magnitudes of these increases were different for each microstructural component. The longitudinal moduli were higher than the transverse moduli. Dehydrated samples were also tested to allow a comparison with hydrated samples and these resulted in higher moduli and hardness than the hydrated samples. Again, the degree of variation was different for each microstructural component. These results indicate that the developmental changes in bone have different rates of mechanical change within each microstructural component.     

Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing

A new quantitative tissue differentiation theory which relates the local tissue formation in a fracture gap to the local stress and strain is presented. Our hypothesis proposes that the amounts of strain and hydrostatic pressure along existing calcified surfaces in the fracture callus determine the differentiation of the callus tissue. The study compares the local strains and stresses in the callus as calculated from a finite element model with histological findings from an animal fracture model. The hypothesis predicts intramembranous bone formation for strains smaller approximately +/- 5% and hydrostatic pressures smaller than +/- 0.15 MPa. Endochondral ossification is associated with compressive pressures larger than about -0.15 MPa and strains smaller than +/- 15%. All other conditions seemed to lead to connective tissue or fibrous cartilage. The hypothesis enables a better understanding of the complex tissue differentiation seen in histological images and the mechanical conditions for healing delayed healing or nonunions.     

Quantifying the strain history of bone: spatial uniformity and self-similarity of low-magnitude strains

We hypothesize that when a broad spectrum of bone strain is considered, strain history is similar for different bones in different species. Using a data collection protocol with a fine resolution, mid-diaphyseal strains were measured in vivo for both weightbearing and non-weightbearing bones in three species: dog, sheep, and turkey, with strain information collected continuously while the animals performed their natural daily activities. The daily strain history was quantified by both counting cyclic strain events (to quantify the distribution of strains of different magnitudes) and by estimating the average spectral characteristics of the strain (to quantify the frequency content of the strain signals). Counting of the daily (12-24 h) strain events show that large strains (> 1000 microstrain) occur relatively few times a day, while very small strains (< 10 microstrain) occur thousands of times a day. The lower magnitude strains (< approximately 200 microstrain) are found to be more uniform around the bone cross-section than the higher magnitude, peak strains. Strain dynamics are found to be well described by a power-law relationship and exhibit self-similar characteristics. These data lead to the suggestion that the organization of bone tissue is driven by the continual barrage of activity spanning a wide but consistent range of frequency and amplitude, and until the mechanism of bone's mechanosensory system is fully understood, all portions of bone's strain history should be considered to possibly play a role in bone adaptation.     

Age-related properties at the microscale affect crack propagation in cortical bone

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.     

Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

Spatial correlations of trabecular bone microdamage with local stresses and strains using rigid image registration

Although microdamage is known to accumulate in trabecular bone with overloading and aging, the tissue-level stresses and strains associated with local bone failure are not well known. Local correlation of microdamage with microstructural stresses and strains requires methods to accurately register histological sections with micro-computed tomography (micro-CT) based finite element models. In addition, the resolution of correlation (i.e., grid size) selected for analysis may affect the observed results. Therefore, an automated, repeatable, and accurate image registration algorithm was developed to determine the range of local stresses and strains associated with microdamage initiation. Using a two-dimensional rigid registration algorithm, bone structures from histology and micro-CT imaging were aligned. Once aligned, microdamaged regions were spatially correlated with local stresses and strains obtained from micro-CT based finite element analysis. Using this more sophisticated registration technique, we were able to analyze the effects of varying spatial grid resolution on local stresses and strains initiating microdamage. The results indicated that grid refinement to the individual pixel level (pixel-by-pixel method) more precisely defined the range of microdamage initiation compared to manually selected individual damaged and undamaged trabeculae. Using the pixel-by-pixel method, we confirmed that trabecular bone from younger cows sustained higher local strains prior to microdamage initiation compared to older bone.     

Trabecular bone microdamage and microstructural stresses under uniaxial compression

The balance between local remodeling and accumulation of trabecular bone microdamage is believed to play an important role in the maintenance of skeletal integrity. However, the local mechanical parameters associated with microdamage initiation are not well understood. Using histological damage labeling, micro-CT imaging, and image-based finite element analysis, regions of trabecular bone microdamage were detected and registered to estimated microstructural von Mises effective stresses and strains, maximum principal stresses and strains, and strain energy density (SED). Bovine tibial trabecular bone cores underwent a stepwise uniaxial compression routine in which specimens were micro-CT imaged following each compression step. The results indicate that the mode of trabecular failure observed by micro-CT imaging agreed well with the polarity and distribution of stresses within an individual trabecula. Analysis of on-axis subsections within specimens provided significant positive relationships between microdamage and each estimated tissue stress, strain and SED parameter. In a more localized analysis, individual microdamaged and undamaged trabeculae were extracted from specimens loaded within the elastic region and to the apparent yield point. As expected, damaged trabeculae in both groups possessed significantly higher local stresses and strains than undamaged trabeculae. The results also indicated that microdamage initiation occurred prior to apparent yield at local principal stresses in the range of 88-121 MPa for compression and 35-43 MPa for tension and local principal strains of 0.46-0.63% in compression and 0.18-0.24% in tension. These data provide an important step towards understanding factors contributing to microdamage initiation and establishing local failure criteria for normal and diseased trabecular bone.     

A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

Stereoscopically observed deformations of a compliant abdominal aortic aneurysm model

A new experimental setup has been implemented to precisely measure the deformations of an entire model abdominal aortic aneurysm (AAA). This setup addresses a gap between the computational and experimental models of AAA that have aimed at improving the limited understanding of aneurysm development and rupture. The experimental validation of the deformations from computational approaches has been limited by a lack of consideration of the large and varied deformations that AAAs undergo in response to physiologic flow and pressure. To address the issue of experimentally validating these calculated deformations, a stereoscopic imaging system utilizing two cameras was constructed to measure model aneurysm displacement in response to pressurization. The three model shapes, consisting of a healthy aorta, an AAA with bifurcation, and an AAA without bifurcation, were also evaluated with computational solid mechanical modeling using finite elements to assess the impact of differences between material properties and for comparison against the experimental inflations. The device demonstrated adequate accuracy (surface points were located to within 0.07?mm) for capturing local variation while allowing the full length of the aneurysm sac to be observed at once. The experimental model AAA demonstrated realistic aneurysm behavior by having cyclic strains consistent with reported clinical observations between pressures 80 and 120?mm Hg. These strains are 1-2%, and the local spatial variations in experimental strain were less than predicted by the computational models. The three different models demonstrated that the asymmetric bifurcation creates displacement differences but not cyclic strain differences within the aneurysm sac. The technique and device captured regional variations of strain that are unobservable with diameter measures alone. It also allowed the calculation of local strain and removed rigid body motion effects on the strain calculation. The results of the computations show that an asymmetric aortic bifurcation created displacement differences but not cyclic strain differences within the aneurysm sac.     

About the inevitable compromise between spatial resolution and accuracy of strain measurement for bone tissue: A 3D zero-strain study

The accurate measurement of local strain is necessary to study bone mechanics and to validate micro computed tomography (µCT) based finite element (FE) models at the tissue scale. Digital volume correlation (DVC) has been used to provide a volumetric estimation of local strain in trabecular bone sample with a reasonable accuracy. However, nothing has been reported so far for µCT based analysis of cortical bone. The goal of this study was to evaluate accuracy and precision of a deformable registration method for prediction of local zero-strains in bovine cortical and trabecular bone samples. The accuracy and precision were analyzed by comparing scans virtually displaced, repeated scans without any repositioning of the sample in the scanner and repeated scans with repositioning of the samples.