Arena surface vertical impact forces vary with surface compaction

Mechanical properties of arena surfaces are extrinsic factors for musculoskeletal injury. Vertical impact forces of harrowed and compacted cushion were measured at five locations on 12 arena surfaces (five dirt, seven synthetic [dirt and fiber]). Eight variables related to impact force, displacement, and acceleration were calculated. Surface temperature, cushion depth and moisture content were also measured. The effects of surface material type (dirt/synthetic) and cushion compaction (harrowed/compacted) on vertical impact properties were assessed using an analysis of variance. Relationships of manageable surface properties with vertical impact forces were examined through correlations. Compacted cushion exhibited markedly higher vertical impact force and deceleration with lower vertical displacement than harrowed cushion (P < 0.001), and the effect was greater on dirt than synthetic surfaces (P = 0.039). Vertical displacement (P = 0.021) and soil rebound (P = 0.005) were the only variables affected by surface type. Surface compaction (harrowed, compacted) had a significantly greater effect on vertical impact forces than surface type (dirt, synthetic). By reducing surface compaction through harrowing, extrinsic factors related to musculoskeletal injury risk are reduced. These benefits were more pronounced on dirt than synthetic surfaces. These results indicate that arena owners should regularly harrow surfaces, particularly dirt surfaces.

Shear ground reaction force variation among equine arena surfaces

Shear forces at the surface-hoof interface affect hoof slide, surface grip, forces transferred to the limb, and injury risk. However, the variation in shear forces among surfaces with different compositions have not been quantified. Shear ground reaction forces were measured on five dirt and seven synthetic arena surfaces. Cohesion/adhesion and angle of internal friction/coefficient of friction were calculated. Surface composition, surface temperature, cushion depth, and moisture content were also measured. The effects of surface material (dirt/synthetic) on shear properties were assessed using analysis of variance (ANOVA; P < 0.05). The relationships between surface composition or management properties and shear properties were analyzed using linear correlation. Shear properties were not different between dirt and synthetic surface categories; however, surface fiber content was correlated with adhesion and coefficient of friction. These correlations predict that more fiber will decrease soil adhesion (r = -0.75; P < 0.01) and increase the coefficient of friction (r = 0.81; P < 0.01). Furthermore, maximum shear force was significantly correlated with cushion depth (r = 0.61; P < 0.01) and moisture content (r = 0.57; P < 0.01), where shear force was greater on surfaces with thicker cushion layers or higher moisture content. The findings suggest that shear mechanical behavior is more dependent on surface composition than surface material categories (dirt/synthetic) and also indicate that arena owners can influence shear forces by adjusting either surface composition or management.

Modelling the effect of race surface and racehorse limb parameters on in silico fetlock motion and propensity for injury

BACKGROUND

The metacarpophalangeal joint (fetlock) is the most commonly affected site of racehorse injury, with multiple observed pathologies consistent with extreme fetlock dorsiflexion. Race surface mechanics affect musculoskeletal structure loading and injury risk because surface forces applied to the hoof affect limb motions. Race surface mechanics are a function of controllable factors. Thus, race surface design has the potential to reduce the incidence of musculoskeletal injury through modulation of limb motions. However, the relationship between race surface mechanics and racehorse limb motions is unknown.

OBJECTIVE

To determine the effect of changing race surface and racehorse limb model parameters on distal limb motions.

STUDY DESIGN

Sensitivity analysis of in silico fetlock motion to changes in race surface and racehorse limb parameters using a validated, integrated racehorse and race surface computational model.

METHODS

Fetlock motions were determined during gallop stance from simulations on virtual surfaces with differing average vertical stiffness, upper layer (e.g. cushion) depth and linear stiffness, horizontal friction, tendon and ligament mechanics, as well as fetlock position at heel strike.

RESULTS

Upper layer depth produced the greatest change in fetlock motion, with lesser depths yielding greater fetlock dorsiflexion. Lesser fetlock changes were observed for changes in lower layer (e.g. base or pad) mechanics (nonlinear), as well as palmar ligament and tendon stiffness. Horizontal friction and fetlock position contributed less than 1° change in fetlock motion.

MAIN LIMITATIONS

Simulated fetlock motions are specific to one horse's anatomy reflected in the computational model. Anatomical differences among horses may affect the magnitude of limb flexion, but will likely have similar limb motion responses to varied surface mechanics.

CONCLUSIONS

Race surface parameters affected by maintenance produced greater changes in fetlock motion than other parameters studied. Simulations can provide evidence to inform race surface design and management to reduce the incidence of injury.

The importance of intrinsic damage properties to bone fragility: a finite element study

As the average age of the population has increased, the incidence of age-related bone fracture has also increased. While some of the increase of fracture incidence with age is related to loss of bone mass, a significant part of the risk is unexplained and may be caused by changes in intrinsic material properties of the hard tissue. This investigation focused on understanding how changes to the intrinsic damage properties affect bone fragility. We hypothesized that the intrinsic (μm) damage properties of bone tissue strongly and nonlinearly affect mechanical behavior at the apparent (whole tissue, cm) level. The importance of intrinsic properties on the apparent level behavior of trabecular bone tissue was investigated using voxel based finite element analysis. Trabecular bone cores from human T12 vertebrae were scanned using microcomputed tomography (μCT) and the images used to build nonlinear finite element models. Isotropic and initially homogenous material properties were used for all elements. The elastic modulus (E(i)) of individual elements was reduced with a secant damage rule relating only principal tensile tissue strain to modulus damage. Apparent level resistance to fracture as a function of changes in the intrinsic damage properties was measured using the mechanical energy to failure per unit volume (apparent toughness modulus, W(a)) and the apparent yield strength (σ(ay), calculated using the 0.2% offset). Intrinsic damage properties had a profound nonlinear effect on the apparent tissue level mechanical response. Intrinsic level failure occurs prior to apparent yield strength (σ(ay)). Apparent yield strength (σ(ay)) and toughness vary strongly (1200% and 400%, respectively) with relatively small changes in the intrinsic damage behavior. The range of apparent maximum stresses predicted by the models was consistent with those measured experimentally for these trabecular bone cores from the experimental axial compressive loading (experimental: σ(max) = 3.0-4.3 MPa; modeling: σ(max) = 2-16 MPa). This finding differs significantly from previous studies based on nondamaging intrinsic material models. Further observations were that this intrinsic damage model reproduced important experimental apparent level behaviors including softening after peak load, microdamage accumulation before apparent yield (0.2% offset), unload softening, and sensitivity of the apparent level mechanical properties to variability of the intrinsic properties.

Stress-whitening occurs in demineralized bone

INTRODUCTION

The incidence of age-related bone fracture is increasing with average population age. Bone scatters more light (stress-whitens) during loading, immediately prior to failure, in a manner visually similar to polymer crazing. We wish to understand the stress-whitening process because of its possible effect on bone toughness. The goals of this investigation were a) to establish that stress-whitening is a property of the demineralized organic matrix of bone rather than only a property of mineralized tissue and that stress whitening within the demineralized bone is dependent upon both b) hydrogen bonding and, c) the orientation of loading.

METHODS

Demineralized cortical bone specimens were loaded in tension to failure (0.08 strain/s). The effect of hydrogen bonding on mechanical properties and the stress-whitening process was probed by altering the Hansen's hydrogen bonding parameter (δh) of the immersing solution.

RESULTS

Stress-whitening occurred in the demineralized bone. Stress-whitening was negatively correlated with δh (R(2)=0.81, p<0.0001). Stress-whitening was significantly lower (p<0.0001) in specimens loaded orthogonally compared to those loaded parallel to the long (strong) axis.

CONCLUSION

The stress-whitening observed was consistent with increased Mie scattering. We suggest that the change in Mie scattering was due to collagen fibril dehydration driven by the externally applied stress. The presence of stress-whitening in demineralized bone suggests that this process may be a property of the collagenous matrix and hence may be present in other collagenous tissues rather than an emergent property of the bone composite.

Polymer Mechanics as a Model for Short-Term and Flow-Independent Cartilage Viscoelasticity

Articular cartilage is the load bearing soft tissue that covers the contacting surfaces of long bones in articulating joints. Healthy cartilage allows for smooth joint motion, while damaged cartilage prohibits normal function in debilitating joint diseases such as osteoarthritis. Knowledge of cartilage mechanical function through the progression of osteoarthritis, and in response to innovative regeneration treatments, requires a comprehensive understanding of the molecular nature of interacting extracellular matrix constituents and interstitial fluid. The objectives of this study were therefore to (1) examine the timescale of cartilage stress-relaxation using different mechanistic models and (2) develop and apply a novel (termed "sticky") polymer mechanics model to cartilage stress-relaxation based on temporary binding of constituent macromolecules. Using data from calf cartilage samples, we found that different models captured distinct timescales of cartilage stress-relaxation: monodisperse polymer reptation best described the first second of relaxation, sticky polymer mechanics best described data from ∼1-100 seconds of relaxation, and a model of inviscid fluid flow through a porous elastic matrix best described data from 100 seconds to equilibrium. Further support for the sticky polymer model was observed using experimental data where cartilage stress-relaxation was measured in either low or high salt concentration. These data suggest that a complete understanding of cartilage mechanics, especially in the short time scales immediately following loading, requires appreciation of both fluid flow and the polymeric behavior of the extracellular matrix.

Volume effects on yield strength of equine cortical bone

Volume effects are a fundamental determinant of structural failure. A material exhibits a volume effect if its failure properties are dependent on the specimen volume. Many brittle ceramics exhibit volume effects due to loading a structure in the presence of "critical" flaws. The number of flaws, their locations, and the effect of stress field within the stressed volume play a role in determining the structure's failure properties. Since real materials are imperfect, structures composed of large volumes of material have higher probabilities of containing a flaw than do small volumes. Consequently, large material volumes tend to fail at lower stresses compared to smaller volumes when tested under similar conditions. Volume effects documented in brittle ceramic and composite structures have been proposed to affect the mechanical properties of bone. We hypothesized that for cortical bone material, (1) small volumes have greater yield strengths than large volumes and (2) that compared to microstructural features, specimen volume was able to account for comparable amounts of variability in yield strength. In this investigation, waisted rectangular, equine third metacarpal diaphyseal specimens (n=24) with nominal cross sections of 3 x 4 mm and gage lengths of either 10.5, 21, or 42 mm, were tested monotonically in tension to determine the effect of specimen volume on their yield strength. Yield strength was greatest in the smallest volume group compared to the largest volume group. Within each group of specimens the logarithm of yield strength was positively correlated with the cumulative failure probability, indicating that the data follow the two-parameter Weibull distribution. Additionally, log yield strength was negatively correlated with log volume, supporting the hypothesis that small stressed volumes of cortical bone possess greater yield strength than similarly tested large stressed volumes.

On sampling bones for microcracks

This paper addresses the problem of designing experiments to measure microcrack density in cortical bone. Microcracks are relatively scarce in bone cross-sections, and their size requires microscope settings having small fields of view. Thus, substantial time is required to count cracks in each cross-section. Consequently, most studies evaluate a relatively small cross-sectional area from each specimen, the chance of finding a crack in any given field is small, and there is a significant chance of not finding even one crack in the specimens representing a particular subject. Therefore, a statistical model for microcrack counting was created to develop guidelines for sampling bones for microcracks. Three questions were addressed. 1) What are the relationships of sample size to variability in microcrack density results and the probability of crackless specimens? 2) How can sample size be chosen a priori so as to reduce the probability of crackless specimens and the associated variability in the data to an acceptable level? 3) What are the confidence intervals for the mean density of microcracks measured using microscopic counting? Using a Poisson model for the distribution of microcracks within microscope fields the total area (mm(2)) that should be examined for each specimen is given by A(s)=-ln(F)/Cr.Dn, where Cr.Dn is the expected microcrack density for an individual sample and F is the desired probability (expressed as a fraction) that the individual sample will contain no microcracks. This equation is validated against 8 results from three different experiments.

Volume effects on fatigue life of equine cortical bone

Materials, including bone, often fail due to loading in the presence of critical flaws. The relative amount, location, and interaction of these flaws within a stressed volume of material play a role in determining the failure properties of the structure. As materials are generally imperfect, larger volumes of material have higher probabilities of containing a flaw of critical size than do smaller volumes. Thus, larger volumes tend to fail at fewer cycles compared with smaller volumes when fatigue loaded to similar stress levels. A material is said to exhibit a volume effect if its failure properties are dependent on the specimen volume. Volume effects are well documented in brittle ceramics and composites and have been proposed for bone. We hypothesized that (1) smaller volumes of cortical bone have longer fatigue lives than similarly loaded larger volumes and (2) that compared with microstructural features, specimen volume was able to explain comparable amounts of variability in fatigue life. In this investigation, waisted rectangular specimens (n=18) with nominal cross-sections of 3x4 mm and gage lengths of 10.5, 21, or 42 mm, were isolated from the mid-diaphysis of the dorsal region of equine third metacarpal bones. These specimens were subjected to uniaxial load controlled fatigue tests, with an initial strain range of 4000 microstrain. The group having the smallest volume exhibited a trend of greater log fatigue life than the larger volume groups. Each volume group exhibited a significant positive correlation between the logarithm of fatigue life and the cumulative failure probability, indicating that the data follow the two-parameter Weibull distribution. Additionally, log fatigue life was negatively correlated with log volume, supporting the hypothesis that smaller stressed volumes of cortical bone possess longer fatigue lives than similarly tested larger stressed volumes.

Summary--Measuring "bone quality"

The idea of bone quality is well-established in the literature and represents a real conundrum in the treatment of osteoporosis. On the one hand, there are measurements for patients that predict fracture risk for the population as a whole, but between individual patients, one will fracture but another will not, despite the fact that all of the technical measurements we use to predict fracture risk are the same. There are, of course, many aspects of bone mechanical properties that cannot yet be measured in patients. The session began with a discussion of what bone quality is, then the speakers presented work on novel aspects of bone properties that could help explain why fracture prediction in vivo is inexact.

Comparison of the Linear Finite Element Prediction of Deformation and Strain of Human Cancellous Bone to 3D Digital Volume Correlation Measurements

The mechanical properties of cancellous bone and the biological response of the tissue to mechanical loading are related to deformation and strain in the trabeculae during function. Due to the small size of trabeculae, their motion is difficult to measure. To avoid the need to measure trabecular motions during loading the finite element method has been used to estimate trabecular level mechanical deformation. This analytical approach has been empirically successful in that the analytical models are solvable and their results correlate with the macroscopically measured stiffness and strength of bones. The present work is a direct comparison of finite element predictions to measurements of the deformation and strain at near trabecular level. Using the method of digital volume correlation, we measured the deformation and calculated the strain at a resolution approaching the trabecular level for cancellous bone specimens loaded in uniaxial compression. Smoothed results from linearly elastic finite element models of the same mechanical tests were correlated to the empirical three-dimensional (3D) deformation in the direction of loading with a coefficient of determination as high as 97% and a slope of the prediction near one. However, real deformations in the directions perpendicular to the loading direction were not as well predicted by the analytical models. Our results show, that the finite element modeling of the internal deformation and strain in cancellous bone can be accurate in one direction but that this does not ensure accuracy for all deformations and strains.

Long-term ovariectomy decreases ovine compact bone viscoelasticity

Changes in bone mineral density associated with estrogen depletion in humans do not account for all of the associated change in fracture risk, and it is possible that some of this variation may lie in changes of other aspects of bone quality. The purpose of this study was to investigate changes in viscoelastic behavior of compact bone that may be associated with estrogen depletion. Changes in compact bone viscoelastic properties associated with three years of ovariectomy were investigated with dynamic mechanical analysis (low-amplitude 3-point bending at frequencies of 1-20 Hz) using beams milled from the diaphysis of the ovine radius. The viscoelastic storage modulus was significantly (5.2%) lower at the higher frequencies for the ovariectomized animals. The general anatomic variation in storage modulus, in which cranial sectors had higher values than caudal sectors, did not change with ovariectomy. The loss tangent (tandelta, a measure of damping) was also greatly decreased (up to 83%) at high frequencies in the ovariectomized animals. Anatomic variation in tandelta at low (6-12 Hz) frequencies (cranial and caudal sectors having higher values than lateral or medial sectors) was enhanced with ovariectomy. Changes in viscoelastic properties associated with long-term estrogen depletion could be responsible for a significant reduction in the toughness or strength of a bone without concomitant changes in screening modalities used to evaluate bone quality (e.g., DXA, QCT, QUA).

Matrix concentration of insulin-like growth factor I (IGF-I) is negatively associated with biomechanical properties of human tibial cancellous bone within individual subjects

Insulin-like growth factor-I (IGF-I), abundant in bone matrix, is believed to play an important role during bone development and remodeling. To our knowledge, however, few studies have addressed the relationship between the concentration of IGF-I in bone matrix and the biomechanical properties of bone tissue. In this study, forty-five cylindrical specimens of cancellous bone were harvested from six human tibiae and scanned using micro-computed tomography (microCT). The bone volume fraction (BV/TV) was calculated from three-dimensional (3D) microCT images. Mechanical tests were then performed on a servohydraulic testing system to determine the strength and stiffness of cancellous bone. Following mechanical testing, the concentration of IGF-I in bone matrix was measured by using an enzyme-linked immunoabsorbent assay (ELISA). Within each subject, the concentration of IGF-I in bone matrix had significant (P<0.01) negative correlations with the bone volume fraction, strength, and stiffness of cancellous bone. In particular, the anterior quadrant of the proximal tibia was significantly (P<0.02) greater in IGF-I matrix concentration and marginally significantly lower in strength (P=0.053) and stiffness (P=0.059) than the posterior quadrant. The negative correlations between the cancellous bone matrix concentration of IGF-I and cancellous bone biomechanical properties within subjects found in this study may help us understand the variation of the biomechanical properties of cancellous bone in proximal human tibiae.

Determinants of ovine compact bone viscoelastic properties: effects of architecture, mineralization, and remodeling

Significant decreases in ovine compact bone viscoelastic properties (specifically, stress-rate sensitivity, and damping efficiency) are associated with three years of ovariectomy and are particularly evident at higher frequencies [Proc. Orthop. Res. Soc. 27 (2002) 89]. It is unclear what materials or architectural features of bone are responsible for either the viscoelastic properties themselves, or for the changes in those properties that were observed with estrogen depletion. In this study, we examined the relationship between these viscoelastic mechanical properties and features involving bone architecture (BV/TV), materials parameters (ash density, %mineralization), and histologic evidence of remodeling (%remodeled, cement line interface). The extent of mineralization was inversely proportional to the material's efficiency in damping stress oscillations. The damping characteristics of bone material from ovariectomized animals were significantly more sensitive to variation in mineralization than was bone from control animals. At low frequencies (6 Hz or less), increased histologic evidence of remodeling was positively correlated with increased damping efficiency. However, the dramatic decreases in stress-rate sensitivity that accompanied 3-year ovariectomy were seen throughout the bone structure and occurred even in areas with little or no secondary Haversian remodeling as well as in areas of complete remodeling. Taken together, these data suggest that, while the mineral component may modify the viscoelastic behavior of bone, the basic mechanism underlying bone viscoelastic behavior, and of the changes in that behavior with estrogen depletion, reside in a non-mineral component of the bone that can be significantly altered in the absence of secondary remodeling.

Polymer dynamics as a mechanistic model for the flow-independent viscoelasticity of cartilage

The initial, rapid, flow independent, apparent stress relaxation of articular cartilage disks deformed by unconfined compressive displacement is shown to be consistent with the theory of polymer dynamics. A relaxation function for polymers based upon a mechanistic model of molecular interaction (reptation) appropriately approximated early, flow independent relaxation of stress. It is argued that the theory of polymer dynamics, with its reliance on mechanistic models of molecular interaction, is an appropriate technique for application to and the understanding of rapid, flow independent, stress relaxation in cartilage.

Effects of vertebral bone fragility and bone formation rate on the mineralization levels of cancellous bone from white females

Back-scattered electron microscopy was used to study mineralization levels of human iliac cancellous bone of white females (N = 49). Mineralization levels were assessed by converting bone pixel grayscale levels to atomic number (Z) using known calibration standards. The data set consisted of bone biopsies from normal and vertebral fracture subjects that had either high or low values for bone formation rate (BFR(s)) within their respective groups (fracture/low BFR(s), N = 12; fracture/high BFR(s), N = 10; normal/low BFR(s), N = 12; normal/high BFR(s), N = 15). The following three measures of mineralization were quantitatively determined for each specimen: an overall mean mineralization (Z(mean)), the mineralization of trabecular packets deep within the interior of trabeculae (Z(deep)), and the mineralization of superficial exterior packets (Z(superficial)). Two-way analysis of variance revealed that the high BFR(s) group had a significantly lower Z(superficial) than the low BFR(s) group [mean (SD) 10.383 (0.270) vs. 10.563 (0.289)], and there was no significant interaction. BFR(s) had no effect on Z(mean) or Z(deep). For the pooled data, Z(deep) was significantly higher than Z(superficial) [10.866 (0.242) vs. 10.471 (0.291)]. There was no significant difference in Z(mean), Z(deep), or Z(superficial) between normals and those with vertebral fracture, but the standard deviations of the mineralization measures in the fracture group were at least double that of the normal group. Frequency histograms show that the two groups have fundamentally different mineralization distributions. The normal group demonstrates typical Gaussian distributions centered around the mean, and the distributions of the fracture group are bimodal, with peaks occurring at either the high or low tails of the distributions of the normal group. We hypothesize that both low and high patterns of mineralization might detrimentally affect bone material properties, with low mineralization levels causing reduced stiffness and strength and high mineralization resulting in reduced fracture toughness. The degree to which the mineralization differences may affect strength and stiffness of individual elements is estimated. The higher standard deviations of mineralization measures in the fracture group may reflect an inability to properly regulate trabecular level stress and strain. Forward stepwise regression analysis showed significant relationships between Ob.S/OS and both Z(superficial) and Z(mean), suggesting that the osteoblast may play an important role in regulating mineralization.

Determination of bone volume by osteocyte population

During development and growth, biological tissues and organisms can control their size and mass by regulating cell number (Raff, 1992; Conlon and Raff, 1999). Later in life both cell number and organ mass decrease (Buetow, 1985). We demonstrate that the number density of bone cells buried in the calcified matrix (osteocyte lacunar density) predicts extracellular matrix volume for both cancellous and cortical bone in a broad cross-section of the population (males and females, age range 23-91 years, r(2) = 0.98). Our hypothesis is that bone mass is determined by the control of osteocyte number, and that this is a particular instance of the control of organ size through the social controls on cell survival and death (Raff, 1992; Conlon and Raff, 1999).

Fatigue damage-fracture mechanics interaction in cortical bone

Fatigue loading causes accumulation of damage that may lead to the initiation of a macrocrack and result in a catastrophic failure of bone. The objective of this study was to examine the influence of fatigue damage on crack growth parameters in bovine cortical bone. Nineteen rectangular beam specimens (4 x 4 x 48 mm) were machined from bovine tibiae. The long axis of the beams was aligned with the long axis of bones. Using a four-point bending fatigue setup, ten specimens were fatigue-damaged to different levels as indicated by stiffness loss. A through-thickness notch was machined at the center of each damaged and undamaged beam. The notched specimens were then monotonically loaded beyond failure using a three-point bending protocol. Critical stress intensity factor, K(I), and work to critical load, W(Q), were significantly lower in the damaged group than in the undamaged group (p < 0.03). When the undamaged specimens were assigned a percent stiffness loss of zero and pooled with the damaged group, significant negative correlations of percent stiffness loss with K(I) (R = 0.58, p < 0.01), W(Q) (R = 0.54, p < 0.02), maximum load, P(max) (R = 0.59, p < 0.008), deflection at maximum load, Delta(max) (R = 0.48, p < 0.04), structural stiffness, S(max) (R = 0.53, p < 0.02), W(max) (R = 0.55, p < 0.02), and load at 1.4 mm deflection (a value beyond failure but without complete fracture), P(1.4) (R = 0.47, p < 0.05), were found. Post hoc analysis revealed that the average load-deflection curve from the damaged group was transformable into that from the undamaged group through a special shift on the load-deflection plane. Fatigue damage reduces bone stiffness and resistance to crack initiation, maximum load-carrying capacity, and deflection before and after failure in cortical bone. The data suggest there is a single rule that governs the overall effect of fatigue damage on the fracture behavior of cortical bone.

Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions

Strong correspondence between the uniaxial apparent strength and stiffness of cancellous bone allows the use of stiffness as a predictor of bone strength. Measured values of mechanical properties in cancellous bone can be different between experiments due to different experimental conditions. In the current study, bone volume fraction, experimentally determined and finite element (FE) predicted stiffness were examined as predictors of cancellous bone ultimate strength in two different groups each of which was tested using a different end constraint. It is demonstrated that, although always significant, the relationships of strength with bone volume fraction and experimentally determined stiffness are different between test groups. Apparent stiffness, estimated by FE modeling, predicts the ultimate strength of human cancellous bone consistently for all examined experimental protocols.

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.

Shear stress distribution in the trabeculae of human vertebral bone

The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV = A + B exp(-x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.

Estimation of bone matrix apparent stiffness variation caused by osteocyte lacunar size and density

The role of osteocyte lacunar size and density on the apparent stiffness of bone matrix was predicted using a mechanical model from the literature. Lacunar size and lacunar density for different bones from different gender and age groups were used to predict the range of matrix apparent stiffness values for human cortical and cancellous tissue. The results suggest that bone matrix apparent stiffness depends on tissue type (cortical versus cancellous), age, and gender, the magnitudes of the effects being significant but small in all cases. Males had a higher predicted matrix apparent stiffness than females for vertebral cancellous bone (p< I0(-7)) and the difference increased with age (p =0.0007). In contrast, matrix apparent stiffness was not different between males and females forfemoral cortical bone and increased with age in both males (p < 0.0001) and females (p < 0.0364). Osteocyte lacunar density and size may cause significant gender and age-related variations in bone matrix apparent stiffness. The magnitude of variations in matrix apparent stiffness was small within the physiological range of lacunar size and density for healthy bone, whereas the variations can be profound in certain pathological cases. It was proposed that the mechanical effects of osteocyte density be uncoupled from their biological effects by controlling lacunar size in normal bone.

Influence of nonenzymatic glycation on biomechanical properties of cortical bone

In this study, the influence of nonenzymatic glycation (NEG) on the mechanical properties of bone and bone collagen were investigated. Bovine cortical bone specimens were incubated in ribose to cause collagen cross-links in vitro, and nondestructive mechanical testing was used to determine tensile and compressive elastic modulus as a function of incubation time. Mechanical properties associated with yield, postyield, and final fracture of bone were determined at the end of the incubation period. The stiffness of the collagen network was measured using stress relaxation tests of demineralized bone cylinders extracted periodically throughout the incubation period. It was found that accumulation of nonenzymatic glycation end-products in cortical bone caused stiffening of the type I collagen network in bone (r2 = 0.92; p < 0.001) but did not significantly affect the overall stiffness of the mineralized bone (p = 0.98). The ribosylated group had significantly more NEG products and higher yield stress and strain than the control group (p < 0.05). Postyield properties including postyield strain and strain energy were lower in the ribosylated group but were not significantly different from the control group (p = 0.24). Compared with the control group, the ribosylated group was characterized by significantly higher secant modulus and lower damage fraction (p < 0.05). Taken together, the results of this study suggest that collagen in bone is susceptible to the same NEG-mediated changes as collagen in other connective tissues and that an increased stiffness of the collagen network in bone due to NEG may explain some of the age-related increase in skeletal fragility and fracture risk.

Femoral structure and stiffness in patients with femoral neck fracture

Bone morphological characteristics may relate to the risk of hip fracture. We applied finite element modeling to radiologic data for two groups of women in vivo to address two questions: (a) Do individuals who have just sustained a femoral neck fracture exhibit reduced three-dimensional structural stiffness? and (b) Are victims of hip fracture disproportionately more susceptible to loads sustained in a fall than to stance-type loads? Ten white women (age: 64-76 years) who had just sustained a femoral neck fracture and 18 female volunteers (age: 65-76 years), matched as groups for race, age. and body mass index, were evaluated. From quantitative computed tomography scans, femoral morphometric and volumetric cancellous density measurements were obtained and a finite element model was constructed. Two load conditions were simulated: single-stance phase and lateral fall. Global stiffness values were determined for each model. The cancellous bone density was significantly lower at the femoral neck and the femoral neck and head diameters were significantly larger in the women in the fracture group than in those in the control group. The stiffness of the proximal femur did not differ significantly between the groups for either load condition. An apparently linear relationship was found for stiffness at stance load compared with stiffness at fall load (r = 0.84, p < 0.001). and slopes did not differ significantly between the groups. Although cancellous density was reduced at the fracture site in patients with femoral neck fractures. this did not result in a reduction in the predicted bone stiffness. Previous studies have established a very strong relationship between the stiffness and strength of bone. Since these modeling methods were thoroughly validated ex vivo, we conclude that although decreased bone density at the femoral neck may predict where fracture initiates, the risk of hip fracture per se may be more strongly dependent on issues such as the risk of falling and fall biomechanics than on the structural characteristics of bone.

Short term in vivo precision of proximal femoral finite element modeling

As more therapies are introduced to treat osteoporosis, precise in vivo methods are needed to monitor response to therapy and to estimate the gains in bone strength that result from treatment. A method for evaluating the strength of the proximal femur was developed and its short term reproducibility, or precision, was determined in vivo. Ten volunteer subjects aged 51-62 years (mean 55.6 years), eight women and two men, were examined using a quantitative computed tomography (QCT) protocol. They were positioned, scanned, repositioned and re-scanned. The QCT images were registered in three-dimensional space, and finite element (FE) models were generated and processed to simulate a stance phase load configuration. Stiffness was computed from each FE model, and strength was computed using a regression equation between FE stiffness and fracture load for a small set (n = 6) of experimental specimens. The coefficients of variation (COV) and repeatability (COR= 2.23* 42*COV) were determined. The COV for the FE fracture load computed was 1.85%, and the detectable limit (coefficient of repeatability) for serial measurements was 5.85%. That is, if a change of 5.85% or more in computed FE fracture load is observed, it will be too large to be consistent with measurement variation, but instead can be interpreted as a real change in the strength of the bone. The detectable limit of this method makes it suitable for serial research studies on changes in femoral bone strength in vivo.

Decline in osteocyte lacunar density in human cortical bone is associated with accumulation of microcracks with age

Despite osteocytes' ideal position to sense the local environment and thereby influence bone remodeling, the function of osteocytes in bone remains controversial. In this study, histomorphometric examination of male and female femoral middiaphyseal cortical bone was conducted to determine if bone's remodeling response, indicated by tissue porosity and accumulation of damage, is associated with osteocyte lacunar density (number of osteocyte lacunae per bone area). The results support the sensory role of the osteocyte network as the decline in osteocyte lacunar density in human cortical bone is associated with the accumulation of microcracks and increase in porosity with age. Porosity and microcrack density increased exponentially with a decline in osteocyte lacunar density indicating that a certain minimum number of osteocytes is essential for an "operational" network. No gender-related differences were found in the relationship of osteocyte lacunar density to age, porosity, or microcrack density. The coefficient of variation of osteocyte lacunar density increased linearly with age, indicating that aging bone tissue is characterized by increased heterogeneity in the spatial organization of osteocytes. Osteocyte lacunar density, porosity, and microcrack density exhibited the same exponential probability density distribution in the donor population, indicating their regulation by similar biological phenomena.

In vivo diffuse damage in human vertebral trabecular bone

Accumulation of microdamage in vivo may lead to loss of bone quality. Until recently, linear microcracks were the only known form of in vivo microdamage, but through the use of confocal microscopy an additional level of damage (diffuse damage) has been identified. In this study, in vivo diffuse damage was characterized and quantified in human vertebral trabecular bone as a function of tissue morphology, age, race, gender, and previously quantified in vivo linear microcracks. Presence of diffuse damage in human vertebral tissue was confirmed and validated by simultaneous use of polarized, ultraviolet, and laser confocal microscopy. Diffuse damage was found to occur preferentially within trabecular packets rather than in interstitial bone (p < 0.05). It was consistently higher in men compared with women (p < 0.05), but was not different by race or age group. Diffuse damage did not correlate with linear microcracks, but both exhibited the same probability distribution in which the percentage of individuals having a particular amount of damage decreased exponentially as damage content increased. These findings suggest that diffuse damage accumulation and repair are governed by the same biological phenomena as microcracks, but diffuse damage contributes independently to the microdamage content of bone.

Bone stiffness predicts strength similarly for human vertebral cancellous bone in compression and for cortical bone in tension

The yield strength and ultimate strength of cortical and cancellous bone tissue are very highly correlated to bone stiffness. For samples of human vertebral cancellous bone in compression and for bovine cortical bone in tension, the coefficient of determination (r2) for regression between ultimate strength and stiffness was 0.89 and 0.92, and between yield strength and stiffness it was 0.94 and 0.93, respectively. The slope of the regression for human vertebral cancellous bone ultimate strength predicted by stiffness was not statistically different from similar regressions for cortical bone in tension in either a bovine sample or in published data from multiple species. We believe that the observed correlation results from the evolutionary need to build sufficiently strong bones using cells that are sensitive to deformation and that directly control bone stiffness, but not strength. The practical significance of this work is that an in vivo estimate of bone stiffness (e.g., from ultrasound measurement) may be a surrogate for bone strength.

Variations in three-dimensional cancellous bone architecture of the proximal femur in female hip fractures and in controls

Cubes of cancellous bone were obtained from proximal femora of women with hip fractures (n = 26) and from female cadaveric controls (n = 32) to compare architecture and mechanics between groups. Specimens were scanned on a microcomputed tomography system. Stereologic algorithms and model-based estimates were applied to the data to characterize the three-dimensional cancellous microstructure. Cubes were mechanically tested to failure to obtain mechanical properties. Specimens from control subjects had significantly higher bone volume fraction, trabecular number, and connectivity than specimens from patients with hip fractures; no difference in trabecular thickness was observed between groups. Both maximum modulus and ultimate stress were significantly higher in the control than in the fracture group, consistent with the higher bone volume found in the control group. No statistical differences in any of these architectural or mechanical variables were found when groups were matched for bone volume. Specimens from both patients with hip fractures and controls demonstrated strong relationships between trabecular number and bone volume fraction that were statistically equivalent, suggesting that for a given bone mass, both groups have the same overall number of trabeculae. However, there was an architectural difference between fracture and control groups in terms of the three-dimensional spatial arrangement of trabeculae. Fracture specimens had a significantly more anisotropic (oriented) structure than control specimens, with proportionately fewer trabecular elements transverse to the primary load axis, even when matched for bone volume. Relationships between mechanical and architectural parameters were significantly different between groups, suggesting that fracture and control groups have different structure-mechanics relationships, which we hypothesize may be a consequence of the altered three-dimensional structure between groups.

NACOB presentation to ASB Young Scientist Award: Postdoctoral. The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modeling. North American Congress on Biomechanics

The apparent properties of cancellous bone are determined by a combination of both hard tissue properties and microstructural organization. A method is desired to extract the underlying hard tissue properties from simple mechanical tests, free from the complications of microstructure. It has been suggested that microCT voxel-based large-scale finite element models could be employed to accomplish this goal (van Rietbergen et al., 1995, Journal of Biomechanics, 28, 69-81). This approach has recently been implemented and it is becoming increasingly popular as finite element models increase in size and sophistication (Fyhrie et al., 1997, Proceedings of the 43rd Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, p. 815; van Rietbergen et al., 1997, Proceedings of the 43rd Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, p. 62). However, no direct quantitative measurements of the accuracy of this method applied to porous structures such as cancellous bone have been made. This project demonstrates the feasibility of this approach by quantifying its best-case accuracy in determining the trabecular hard tissue modulus of analogues fabricated of a material with known material properties determined independently by direct testing. In addition we were able to assess the impact of mesh size and boundary conditions on accuracy. We found that the assumption of a frictionless boundary condition in the parallel plate compression loading configuration was a significant source of error that could be overcome with the use of rigid end-caps similar to those used by Keaveny et al. (1997 Journal of Orthopaedic Research, 15(1), 101-110). In conclusion, we found that this approach is an effective method for determining the average trabecular hard tissue properties of human cancellous bone with an expected practical accuracy level better than 5%.

NACOB presentation Keynote lecture. Cancellous bone biomechanics. North American Congress on Biomechanics

Cancellous bone is both a biological and a mechanical structure. The interaction between these two aspects of cancellous bone is sufficiently strong that understanding the mechanical properties of the tissue is not possible without consideration of the biology. This manuscript is a mathematical expansion of a portion of the first author's Keynote lecture at the 1998 NACOB presentation. The cellular activity of cancellous bone proceeds in part by the transport of metabolites between trabecular hard tissue and marrow. The anatomical observation is that human trabeculae are seldom internally served by a blood supply, suggesting that the transport mechanisms for trabecular survival are diffusion and a collection of mechanisms for active transport of metabolites independent of blood flow. It will be demonstrated that metabolite transport by diffusion can explain two notable empirical relationships for bone: (a) the close relationship between the bone surface and the bone volume, and (b) the exponential decline in the bone volume fraction during periods of mechanical disuse. A mathematical model is also developed showing how mechanical loading can effect bone volume fraction by increasing metabolite transport between the tissue compartments.

Femoral strength is better predicted by finite element models than QCT and DXA

Clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in-vivo were available. A group of 51 human femurs (age range 21-93; 23 females, 28 males) were evaluated for bone density and geometry using quantitative computed tomography (QCT) and dual energy X-ray absorptiometry (DXA). Regional bone density and dimensions obtained from QCT and DXA were used to develop statistical models to predict femoral strength ex vivo. The QCT data also formed the basis of a three-dimensional finite element (FE) models to predict structural stiffness. The femurs were separated into two groups; a model training set (n = 25) was used to develop statistical models to predict ultimate load, and a test set (n = 26) was used to validate these models. The main goal of this study was to test the ability of DXA, QCT and FE techniques to predict fracture load non-invasively, in a simple load configuration which produces predominantly femoral neck fractures. The load configuration simulated the single stance phase portion of normal gait; in 87% of the specimens, clinical appearing sub-capital fractures were produced. The training/test study design provided a tool to validate that the predictive models were reliable when used on specimens with "unknown" strength characteristics. The FE method explained at least 20% more of the variance in strength than the DXA models. Planned refinements of the FE technique are expected to further improve these results. Three-dimensional FE models are a promising method for predicting fracture load, and may be useful in monitoring strength changes in vivo.

A comparative analysis of the microarchitecture of cortical membranous and cortical endochondral onlay bone grafts in the craniofacial skeleton

Previous work in this laboratory established that an onlay bone graft's survival is determined primarily by its relative cortical and cancellous composition rather than its embryologic origin. A volumetric analysis of external bone graft resorption, however, does not explain the internal microarchitectural changes that may be occurring as these grafts become incorporated. To expand the knowledge of bone graft dynamics beyond volumetric parameters, a better understanding of the internal processes of bone graft remodeling is needed. In this comparative study of cortical onlay bone graft microarchitecture, the authors propose to show that cortical onlay bone grafts undergo measurable internal microarchitectural changes as they become incorporated into the surrounding craniofacial skeleton. In addition, the authors propose to further demonstrate similarities between the internal microarchitecture of cortical onlay bone grafts of different embryologic origin over time. Twenty-five adult New Zealand White rabbits were used for this study. They were divided into two groups of eight animals and one group of nine. The groups were killed at 3, 8, and 16 weeks. Cortical membranous and endochondral bone grafts were placed subperiosteally onto each rabbit's cranium. In addition, five ungrafted cortical endochondral and membranous bone specimens were used as controls. Microcomputed tomography (MCT) scanning and histomorphometric analysis were performed on all of the specimens to obtain detailed information regarding the microarchitecture of the cortical bone grafts. The parameters of bone volume fraction, bone surface area to volume, mean trabecular number, and anisotropy were used to give quantitative information about a bone's micro-organization. The results showed that there is no statistically significant difference between the cortical endochondral and the cortical membranous bone grafts for bone volume fraction, bone surface to volume, mean trabecular number, and anisotropy measurements for all time points. There were, however, statistically significant differences when comparing the control and 3-week groups to the 16-week group for all parameters. The advanced MCT technology and histomorphometric techniques proved to be effective in providing a qualitative and quantitative ultrastructural comparison of cortical endochondral and membranous onlay bone grafts over time. In this study, a statistically significant change in the internal microarchitecture of cortical onlay bone grafts of different embryologic origins was seen as they were remodeled and resorbed at all time points. Specifically, the onlay cortical bone grafts developed a less dense, more trabecular, and less organized internal ultrastructure. In addition, no difference in the three-dimensional ultrastructure of cortical endochondral and membranous bone was found. These results challenge some of the currently accepted theories of bone-graft dynamics and may eventually lead to a change in the way clinicians approach bone-graft selection for craniofacial surgery.

Human vertebral body apparent and hard tissue stiffness

Cancellous bone apparent stiffness and strength are dependent upon material properties at the tissue level and trabecular architecture. Microstructurally accurate, large-scale finite element (LS-FE) models were used to predict the experimental apparent stiffness of human vertebral cancellous bone and to estimate the trabecular hard tissue stiffness. Twenty-eight LS-FE models of cylindrical human vertebral cancellous bone specimens (8 mm in diameter, 9.5 mm in height, one each from twenty-eight individuals) were generated directly from microcomputed tomography images and solved by a special purpose iterative finite element program. The experimental apparent stiffness and strength of the specimens were determined by mechanical testing to failure in the infero superior direction. Morphometric measurements including bone volume fraction (BV/TV), three eigenvalues of the fabric tensor and average P(L) were also calculated. The finite element estimate of apparent stiffness explained much of the variance in both experimental apparent stiffness (r2=0.89) and experimental apparent strength (r2=0.87). Stepwise linear regression analysis demonstrated that the LS-FE estimated apparent stiffness was the only significant predictor of experimental apparent stiffness and strength when it was included with all measured morphometric values. Hard tissue stiffness was quite variable between individuals (mean, 5.7 GPa; S.D. 1.6 GPa), but was not significantly related to age, sex, race, weight or morphometric measures for this sample.

Intracortical remodeling in adult rat long bones after fatigue loading

Intracortical remodeling in the adult skeleton removes and replaces areas of compact bone that have sustained microdamage. Although studies have been performed in animal species in which there is an existing baseline of remodeling activity, laboratory rodents have been considered to have limited suitability as models for cortical bone turnover processes because of a lack of haversian remodeling activity. Supraphysiological cyclic axial loading of the ulna in vivo was used to induce bending with consequent fatigue and microdamage. Right ulnae of adult Sprague-Dawley rats were fatigue-loaded to a prefailure stopping point of 30% decrease in ulnae whole bone stiffness. Ten days after the first loading, left ulnae were fatigued in the same way. Ulnae were harvested immediately to allow comparison of the immediate response of the left ulna to the fatigue loads, and the biological response of the right leg to the fatigue challenge. Histomorphometry and confocal microscopy of basic fuchsin-stained bone sections were used to assess intracortical remodeling activity, microdamage, and osteocyte integrity. Bone microdamage (linear microcracks, as well as patches of diffuse basic fuchsin staining within the cortex) occurred in fatigue-loaded ulnar diaphyses. Ten days after fatigue loading, intracortical resorption was activated in ulnar cortices. Intracortical resorption occurred in preferential association with linear-type microcracks, with microcrack number density reduced almost 40% by 10 days after fatigue. Resorption spaces were also consistently observed within areas of the cortex in which no bone matrix damage could be detected. Confocal microscopy studies showed alterations of osteocyte and canalicular integrity around these resorption spaces. These studies reveal that: (1) rat bone undergoes intracortical remodeling in response to high levels of cyclic strain, which induce microdamage in the cortex; and (2) intracortical resorption is associated both with bone microdamage and with regions of altered osteocyte integrity. From these studies, we conclude that rats can initiate haversian remodeling in long bones in response to fatigue, and that osteocyte death or damage may provide one of the stimuli for this process.

Effect of fatiguing exercise on longitudinal bone strain as related to stress fracture in humans

Muscular fatigue in the training athlete or military recruit has been hypothesized to cause increased bone strain that may contribute to the development of a stress fracture. Under normal circumstances, muscles exert a protective effect by contracting to reduce bending strains on cortical bone surfaces. In vivo strain studies in dogs show that muscle fatigue following strenuous exercise elevates bone strain and changes strain distribution. However, a similar experiment has yet to be performed in humans. The purpose of this work was to test the hypothesis in humans that strenuous fatiguing exercise causes an elevation in bone strain. It was also hypothesized that this elevation is greater in younger people than in older people due to the decline in muscle strength and endurance that normally occurs with age. To test these hypotheses, strain in the tibiae of seven human volunteers was measured during walking before and after a period of fatiguing exercise. Neither hypothesis was sustained. Post-hoc analysis of the strain data suggests that strain rate increases after fatigue with a greater increase in younger as opposed to older persons. Although not conclusive, this suggests that it is strain rate, rather than strain magnitude, that may be causal for stress fracture.

Damage type and strain mode associations in human compact bone bending fatigue

When compact bone is subjected to fatigue loading, it develops matrix microdamage, which reduces the tissue's ability to resist fracture. The relative influence of different strain modes on damage and strength in compact bone has not been characterized, to our knowledge. In this study, the nonuniform strain field produced by four-point bending was used to introduce fatigue damage into tibial bending beam specimens from men 40-49 years old. The specimens were then bulk-stained with basic fuchsin to mark damage surfaces and were examined histologically and with confocal microscopy to describe damage morphologies and position relative to tension and compression-strained regions of the specimen. Histomorphometric methods were used to quantify the amounts of different types of bone microdamage. Three major types were observed. In regions subjected to tensile strains, the bone had focal regions of diffusely increased basic fuchsin staining (i.e., diffuse microdamage). Confocal microscopy of these regions showed them to be composed of extensive networks of fine, ultrastructural-level cracks. In compressive strain regions, the tissue developed linear microcracks in interstitial areas similar to those originally described by Frost. Fine, tearing-type (wispy-appearing) cracks were observed near and in the plane of the neutral axis. The paths of these fine cracks were not influenced by microstructural boundaries. Other minor damage morphologies (sector-stained osteons, delamination of regions of lamellae, and intraosteonal cracking) were observed, but their distribution was unrelated to local strain field. Thus. in fatigue of human compact bone, the principal mechanisms of matrix failure (i.e., linear microcrack, diffuse damage foci, and tearing-type damage) are strongly dependent on local strain type.

The interosseous membrane affects load distribution in the forearm

The role of the interosseous membrane in load sharing was defined by simultaneously quantitating loads in the distal radius and ulna and in the proximal radius and ulna with an axial load to the wrist, before and after transecting the interosseous membrane. With the interosseous membrane intact, the load at the proximal ulna was greater than at the distal ulna and the load at the proximal radius was less than at the distal radius, suggesting that force was transferred from the radius distally to the ulna proximally. The average percentage of the total load in each bone in supination was as follows: distal radius, 68%; distal ulna, 32%; proximal radius, 51%; proximal ulna, 49%. After interosseous membrane division, the proximal and distal load values became equal in each bone, in all forearm positions, demonstrating that without the membrane there was no load transfer between the radius and ulna. The interosseous membrane transfers load from the wrist to the proximal forearm, via fibers that run from the proximal radius to the distal ulna and exert a proximally directed pull on the ulnar shaft.

A cone beam computed tomography system for true 3D imaging of specimens

A system for 3D cone beam computed tomography has been developed, consisting of a microfocus x-ray source and x-ray image intensifier coupled to a CCD camera. Full width at half maximum resolving power has been experimentally measured to be 70 microns when imaging 10 mm diameter objects. The 3D nature of the resulting image data can be used to visualize internal structure and compute parameters such as volume, surface area, and surface/volume orientation.

Gompertzian growth curves in parathyroid tumours: further evidence for the set-point hypothesis

BACKGROUND

Clinical and cell kinetic data in parathyroid tumours show that their rate of growth slows down progressively and that tumour size approaches an asymptotic value. The Gompertz equation has been widely used in oncology to model growth retardation in malignant tumours; we describe its first application to a benign tumour.

METHODS

In 41 patients with radiation associated hyperparathyroidism, individual solutions were derived for the Gompertz equation: Nt = Exp[A/ a(1 - Exp - at)], where A is the rate constant (years-1) for initial exponential growth and a is the rate constant (years-1) for exponential decline in A. Input data comprised three estimates of tumour age at surgery, 100%, 75% and 50% of the time since irradiation, cell number estimated from tumour weight, and current tumour growth rate, representing the difference between current cell birth rate, estimated from the prevalence of mitotic figures, and an assumed mean rate of cell loss of 5%.

RESULTS

With 100% tumour age, geometric mean values were 2.76 for A, 0.134 for a, and 0.87 g for the growth asymptote. As assumed tumour age decreased, the rate constants increased and the growth asymptotes declined from 22% to 9% greater than the geometric mean tumour weight. Depending on assumed tumour age, the rate constants were about 15-45 times smaller than in myeloma and in testicular tumours, and the growth asymptotes about 2500 and about 60 times smaller, respectively. A and a were highly correlated (r2 = 0.993), with a slope of 20.9 and no significant intercept. Depending on assumed tumour age, the geometric mean time from the initial mutation to the first cell division ranged from 39 to 92 days, much longer than in malignant tumours.

CONCLUSIONS

(1) The Gompertz modelling demonstrates that both the nonprogressive clinical course and the slow growth of parathyroid tumours can be accounted for by a single mutation. (2) The extremely low values for A and a, and consequent very long delay before the first cell division, support the notion that the initial mutation does not affect a growth regulatory gene, but increases growth indirectly via an increase in secretory set-point, the clone of mutant cells behaving as if they were in a hypocalcaemic environment until the plasma calcium rises to the new set-point. (3) The clinical characteristics of radiation-induced parathyroid tumours are modelled more closely if there is a substantial delay between time of irradiation and onset of tumour growth. (4) The rate constants A and a are highly correlated because the variability of tumour weight on a logarithmic scale is much lower than the variability of the rate constants.

A method suitable for in vivo measurement of bone strain in humans

Strain gages are the gold-standard for measurement of bone strains in vivo. The use of strain gages in humans, however, is limited by the need for surgery to implant them and by the use of cyanoacrylate adhesives to bond them to bone. Cyanoacrylate adhesives are not FDA approved for implantation in humans, making it difficult to justify their use in experimental procedures. To surmount this difficulty, a method was developed to bond strain gages to bone using an approved substance: polymethylmethacrylate (PMMA). The technique and the validating experiments are presented. The PMMA bonding method gave strain gage readings within an average of 0.25% (range 0-5%) of those found using cyanoacrylate bonding in a side by side comparison on cast acrylic. On bone, the PMMA bonding method produced results comparable to extensometer readings. This method of strain gage application is accurate and straightforward. It is currently being successfully used for in vivo strain measurements in both humans and animals for up to several days following gage application.

Decrease in canine proximal femoral ultimate strength and stiffness due to fatigue damage

Fractures of the proximal femur represent a significant health concern especially in the elderly. Fatigue damage and microfractures have been implicated in the etiology of hip fractures; however, the extent to which these factors are sufficient to bring about significant reductions in proximal femur strength and stiffness is unknown. This study examined the hypothesis that fatigue loading of the proximal femur results in highly correlated decreases in bone stiffness and strength through the accumulation of bone microdamage. One canine femur from each of 10 pairs was monotonically loaded to failure to determine the ultimate strength. The contralateral femur was then cyclically loaded at 50% of the ultimate load value for either 3600 cycles or until a 40% reduction in stiffness was achieved. This femur was then monotonically loaded to failure. For two additional femur pairs, the fatigued femur was histologically processed to reveal bone microdamage. In support of the hypothesis, the data demonstrated a linear relationship between strength loss and stiffness loss (Adj. R2 = 0.79, p < 0.0004) with significant decreases in residual whole bone strength (p < 0.004) following cyclic loading. In addition, damage (microcracks) in the cortical bone and broken trabeculae were observed in the neck and head region of the femur fatigued until its stiffness was reduced by 40% but not fractured subsequent to cyclic loading.

Bone microdamage and skeletal fragility in osteoporotic and stress fractures

The accumulation of bone microdamage has been proposed as one factor that contributes to increased skeletal fragility with age and that may increase the risk for fracture in older women. This paper reviews the current status and understanding of microdamage physiology and its importance to skeletal fragility. Several questions are addressed: Does microdamage exist in vivo in bone? If it does, does it impair bone quality? Does microdamage accumulate with age, and is the accumulation of damage with age sufficient to cause a fracture? The nature of the damage repair mechanism is reviewed, and it is proposed that osteoporotic fracture may be a consequence of a positive feedback between damage accumulation and the increased remodeling space associated with repair.

In vivo trabecular microcracks in human vertebral bone

Human vertebral cancellous bone from white males (N = 19), black males (N = 16), white females (N = 12), and black females (N = 17) was examined histologically for the presence, numerical density, and morphology of in vivo microscopic cracking (microdamage). Two patterns of microcracks, linear and cross-hatched, were observed. Linear microcracks were observed in both the central portion and near surfaces of trabeculae. Those inside trabeculae were usually single microcracks approximately 50 microns in length and were found in both cement lines and in interstitial bone matrix. Linear microcracks near the trabecular surface were usually multiple parallel cracks approximately 80 microns in length. Microcracks with a cross-hatched appearance were less prevalent. They were observed primarily in vertically oriented trabeculae and were often surrounded by an area of diffuse staining. Two-way ANOVA revealed no differences in microcrack density (Cr.Dn; #/mm2) between males and females [mean (SD) 5.13 (5.02) vs. 5.41 (6.26), respectively], but whites had significantly higher microcrack density than blacks [7.00 (5.71) vs. 3.63 (4.98), respectively, p < 0.05]. White males had a significantly higher microcrack density than black males [7.60 (5.56) vs. 2.21 (1.78), respectively, p < 0.05]. Although not statistically significant, white females also had higher microcrack density than black females. In contrast to what has been reported in the femur, regression analysis found no statistically significant relationship between microcrack density in the spine and age for any of the four race-gender groups. However, significant power relationships were found between microcrack density and bone area fraction for all groups except for black females. The difference between axial and appendicular bone remodeling rates, and their implications for microdamage accumulation, are discussed.

Human vertebral cancellous bone surface distribution

The three-dimensional distribution of bone surface and the bone volume fraction (BV/TV) of 110 human vertebral cancellous bone specimens from seven individuals were measured using a three-dimensional radiographic method (microcomputed tomography). The ratios of the three principal projections of bone surface per total volume were found to be relatively constant for specimens examined in this study. The constancy of the projected surface ratios means that the fraction of the total bone surface oriented in any direction does not change markedly with BV/TV. Bone volume fraction was a good predictor of bone surface per total volume (BS/TV) for a one-parameter nonlinear model (r2 = 0.92). The results of this pilot study suggest that the changes in surface distribution which occur during age-related bone loss are largely predetermined rather than adaptive. The results are also consistent with the idea that cancellous bone tends to maintain a constant ratio of trabecular number for the principal directions. If these inferences from the data are correct, the morphogenetic processes which create the initial adult trabecular pattern become of primary interest. A model was developed which explained the strong relationship between BS/TV and BV/TV. The model was used to demonstrate the importance of morphogenetic processes.

The adaptation of bone apparent density to applied load

A phenomenological theory of bone remodeling was developed with improved spatial stability compared to some of the more standard formulations. The improved stability was created by changing the nature of the remodeling differential equation to have an exponential character. As a result, the theoretical predictions are consistent with the experimental observation that changes in bone density during disuse, after hip surgery, during growth and during aging are all consistent with an exponential dependence of density on time. The new theory and the standard theory were both used to model the time course of bone changes in two animal models of bone loss during disuse. The new theory was better able to model the results of the experiments than the standard theory. The basic continuum theory underlying the remodeling theory was presented in some detail. This presentation was used to motivate the development of the new theory, as the standard theories can predict non-smooth distributions of bone density rather than the expected smooth distributions. It was shown that these non-smooth distributions are a violation of the continuum assumption, one of the bases for the theory of finite element stress analysis. The new model's stability was investigated using example problems and shown to be improved compared to the standard model.

Failure mechanisms in human vertebral cancellous bone

Specimens of human vertebral cancellous bone were compressed to well past mechanical failure (15% strain) in the infero-superior direction. The mechanisms of failure were examined microscopically and histologically. The primary mechanism of failure was shown to be microscopic cracking rather than overt failure of the trabecular elements. The morphology of the cracks was consistent with an hypothesis that they were the result of shear stress (or strain) in the tissue. Complete fracture of trabeculae was confined to elements oriented transversely to the direction of loading. The tissue's ultimate strength and residual strength after compressive failure were both strongly correlated to tissue stiffness (R2 = 0.88 and R2 = 0.71, respectively). It is proposed that cancellous bone strength may be a consequence of the adaptation of bone stiffness to applied stresses. With removal of the load, all specimens recovered at least 94% of their original height. Implications of energy dissipation by microcracking for recovery and maintenance of overall trabecular architecture are discussed.

Direct calculation of the surface-to-volume ratio for human cancellous bone

There are many diseases which cause detrimental changes in the trabecular structure of cancellous bone, leading to mechanical failure of the tissue. One approach to understanding the mechanisms of these diseases is to create idealized models that recreate the morphology of the tissue. This paper presents a partial development of such a model. Further histological methods must be developed before a complete definition of morphologically valid models is possible. In a histological section of cancellous bone, the orientation and length of the trabecular surfaces determine how a line drawn across the bone section will intersect the bone-marrow interface. The distribution of the average length between intersections for a set of parallel lines is defined as the mean intercept length distribution. In this paper, the average surface morphology and volume of the average structure of cancellous bone is determined from an examination of the mean intercept length. The average structure of cancellous bone contains a repeated structural element (SE). As a result, the basic bone structure is analogous to a brick wall made from many similar bricks. For a group of 107 specimens, a strong relationship between structural element volume (SE.V) and bone volume fraction (BV/TV) is demonstrated, SE.V = 0.017 kappa (BV/TV)-2.05 mm3, R2 = 0.93, with kappa a model-dependent constant. For the same specimens, the structural element surface (SE.S) showed the relationship, SE.S = 0.144 kappa (BV/TV)-1.35, R2 = 0.92. As a result of the inverse square dependence of structural element volume on bone volume fraction, it is predicted that cancellous bone strength is inversely proportional to structural element volume.

Application of homogenization theory to the study of trabecular bone mechanics

It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hypothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and/or strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible to perform microstructural and continuum analyses separately and then combine them in a systematic manner. Stiffness predictions from two different microstructural models of trabecular bone show reasonable agreement with experimental results, depending on metaphyseal region, (R2 greater than 0.5 for proximal humerus specimens, R2 less than 0.5 for distal femur and proximal tibia specimens). Estimates of both microstructural strain energy density (SED) and apparent SED show that there are large differences (up to 30 times) between apparent SED (as calculated by standard continuum finite element analyses) and the maximum microstructural or tissue SED. Furthermore, a strut and spherical void microstructure gave very different estimates of maximum tissue SED for the same bone volume fraction (BV/TV). The estimates from the spherical void microstructure are between 2 and 20 times greater than the strut microstructure at 10-20% BV/TV.