Quantification of Bone Microarchitecture with the Structure Model Index

The deterioration of cancellous bone structure due to aging and disease is characterized by a conversion from plate elements to rod elements. Consequently the terms “rod-like” and “plate-like” are frequently used for a subjective classification of cancellous bone. In this work a new morphometric parameter called Structure Model Index (SMI) is introduced, which makes it possible to quantify the characteristic form of a three-dimensionally described structure in terms of the amount of plates and rod composing the structure. The SMI is calculated by means of three-dimensional image analysis based on a differential analysis of the triangulated bone surface. For an ideal plate and rod structure the SMI value is 0 and 3, respectively, independent of the physical dimensions. For a structure with both plates and rods of equal thickness the value lies between 0 and 3, depending on the volume ratio of rods and plates. The SMI parameter is evaluated by examining bone biopsies from different skeletal sites. The bone samples were measured three-dimensionally with a micro-CT system. Samples with the same volume density but varying trabecular architecture can uniquely be characterized with the SMI. Furthermore the SMI values were found to correspond well with the perceived structure type.     

Quantification of Bone Microarchitecture with the Structure Model Index

The deterioration of cancellous bone structure due to aging and disease is characterized by a conversion from plate elements to rod elements. Consequently the terms "rod-like" and "plate-like" are frequently used for a subjective classification of cancellous bone. In this work a new morphometric parameter called Structure Model Index (SMI) is introduced, which makes it possible to quantify the characteristic form of a three-dimensionally described structure in terms of the amount of plates and rod composing the structure. The SMI is calculated by means of three-dimensional image analysis based on a differential analysis of the triangulated bone surface. For an ideal plate and rod structure the SMI value is 0 and 3, respectively, independent of the physical dimensions. For a structure with both plates and rods of equal thickness the value lies between 0 and 3, depending on the volume ratio of rods and plates. The SMI parameter is evaluated by examining bone biopsies from different skeletal sites. The bone samples were measured three-dimensionally with a micro-CT system. Samples with the same volume density but varying trabecular architecture can uniquely be characterized with the SMI. Furthermore the SMI values were found to correspond well with the perceived structure type.     

Dependence of mechanical compressive strength on local variations in microarchitecture in cancellous bone of proximal human femur

Human cancellous bone is a heterogeneous material. Despite this, most of the published studies report correlations between mechanical properties and morphometric parameters averaged on the whole specimen. This work investigated whether local variations in morphometric parameters were linked to the localized failure regions of cancellous bone. Additionally, it was examined whether local values of morphometric parameters can predict the ultimate stress better than the average bone volume fraction (BV/TV). Cylindrical cancellous bone specimens extracted along the primary compressive group of human femoral heads were studied. These were microCT-imaged to assess the morphometric parameters, compressed to determine the ultimate stress, and rescanned by microCT to visualize the failure region. Failure involved slightly less than half of the free height of the specimens. Significant differences were found in the morphometric parameters calculated in the failure and in the non-failure regions. The cross-sections containing minimum BV/TV values were those most often located inside the failure region (83%, p<0.001). Regression analysis confirmed that variations in BV/TV best describe variations in ultimate stress (R2=0.84) out of the averaged morphometric parameters. The prediction of ultimate stress increased when minimum or maximum values of the morphometric parameters were taken, with the highest prediction found by considering the minimum BV/TV (R2=0.95). In conclusion, due to the heterogeneity of cancellous bone, there may exist regions characterized by a different microarchitecture, where the bone is weaker and consequently is more likely to fail. These regions mostly contain minimum values in BV/TV, which were found to predict ultimate stress better than average BV/TV.     

Morphometric comparison of the lumbar cancellous bone of sheep, deer, and humans

To investigate the feasibility of using deer and sheep as animal models for the human spine, we compared the microarchitectural dimensions of the deer and sheep spines and with human data. To this end, we adopted the traditional bone tissue morphometric method, using figure analysis software for quantitative analysis of 2D images of bone tissue. Compared with those of humans, the lumbar cancellous bone of deer and sheep has higher microarchitectural indices, more densely packed bone trabeculae, lower porosity, and higher bone mass. Despite specific differences in various morphologic indices, the anisotropy of lumbar cancellous bone in deer and sheep shows the same trend as that in humans.     

Analysis of microstructural and mechanical alterations of trabecular bone in a simulated three-dimensional remodeling process

Bone remodeling is a complex dynamic process, which modulates both bone mass and bone microstructure. In addition to bone mass, bone microstructure is an important contributor to bone quality in osteoporosis and fragility fractures. However, the quantitative knowledge of evolution of three-dimensional (3D) trabecular microstructure in adaptation to the external forces is currently limited. In this study, a new 3D simulation method of remodeling of human trabecular bone was developed to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to different external loading conditions. The morphological features of trabecular plate and rod, such as thickness and number density in different orientations were monitored during the remodeling process using a novel imaging analysis technique, namely Individual Trabecula Segmentation (ITS). We showed that the volume fraction and microstructures of trabecular bone including, trabecular type and orientation, were determined by the applied mechanical load. Particularly, the morphological parameters of trabecular plates were more sensitive to the applied load, indicating that they played the major role in the mechanical properties of the trabecular bone. Reducing the applied load caused severe microstructural deteriorations of trabecular bone, such as trabecular plate perforation, rod breakage, and a conversion from plates to rods.     

An effective-diffusivity model of pulmonary capillary exchange: General theory, limiting cases, and sensitivity analysis

A family of possible models of capillary-tissue exchange useful for interpreting multiple-tracer data from the pulmonary circulation was derived from the convective-diffusion equation. The models are simplifications of a uniform-transit-time model with two serial diffusion layers outside of the capillary. Modifications of this four-parameter model were derived, and the importance of simplifying assumptions were compared using moment analysis and transform-domain equivalence. A permeability-diffusion model was derived by assuming that the layer nearer the capillary contributed a constant resistance to tracer movement. Using sensitivity analysis, we found that the three parameters of this permeability-diffusion model could not be determined independently, and that further model simplification was highly desirable. Two distinct paths of further simplification were explored.The Sangren-Sheppard model was considered as one path. An alternative path of simplification led to a new model of tracer behavior which we have called an effective-diffusivity model. Moment matching was used to determine the relationships among these models. Sensitivity analysis of the Sangren-Sheppard and effective-diffusivity models showed that the parameters of both of these models were more easily identified. However, the sensitivity analysis also showed that these two models had quite different sensitivities to their respective volume parameters. The Sangren-Sheppard model prediction was affected at all times by a change in the extravascular volume parameter, while the effective-diffusivity model prediction was affected only at the longest times. We concluded that the effective-diffusivity model may be a better alternative to the Sangren-Sheppard model under some conditions. The parameters of the effective-diffusivity model provide a more reliable index of the physiology of capillary-tissue exchange as small molecules as measured by the multiple tracer method in the pulmonary circulation.     

Cellular automaton simulation of tumour growth -- equivocal relationships between simulation parameters and morphologic pattern features.

OBJECTIVE: To develop an interpretation procedure which estimates simulation parameters (tumour cell motility, tumour cell adhesion, autocrine and paracrine growth control, stroma destruction) of simulated patterns solely based on morphometric features of the morphologic pattern. METHODS: A cellular automaton computer simulation program was developed which produces morphologic patterns by growth of a seed of tumour cells. At the beginning of each simulation run certain simulation parameters are assigned to the tumour cells. After the run has been completed, the resulting pattern is evaluated by a set of morphometric features. Simulation parameters and resulting morphometric features of 27,800 simulations were stored in a database and were used for the evaluation of potential relationships. RESULTS: Correlation analysis showed highly significant correlations between morphometric features on the one hand and the preset simulation parameters (tumour cell motility, tumour cell adhesion, autocrine and paracrine growth control, stroma destruction) on the other. Correlation coefficients, however, varied from 0.72 to 0.99. When only one simulation parameter varied while all others were kept constant, morphometric features yielded a highly reliable estimate of the particular simulation parameter. When variability was extended to 4 simulation parameters, morphometric features were less effective in estimating the setting of the parameters. Though in all patterns tested several possible simulation parameter constellations could be ruled out, morphometric features were usually compatible with more than one set of simulation parameters thus preventing a straightforward interpretation. CONCLUSIONS: Though simulation parameters significantly and reproducibly influence the resulting morphologic pattern as characterized by morphometric features, estimates of the simulation parameters based on morphometric features yield equivocal results.     

New Fluorescence Parameters for the Determination of QA Redox State and Excitation Energy Fluxes

A number of useful photosynthetic parameters are commonly derived from saturation pulse-induced fluorescence analysis. We show, that q(P), an estimate of the fraction of open centers, is based on a pure 'puddle' antenna model, where each Photosystem (PS) II center possesses its own independent antenna system. This parameter is incompatible with more realistic models of the photosynthetic unit, where reaction centers are connected by shared antenna, that is, the so-called 'lake' or 'connected units' models. We thus introduce a new parameter, q(L), based on a Stern-Volmer approach using a lake model, which estimates the fraction of open PS II centers. We suggest that q(L) should be a useful parameter for terrestrial plants consistent with a high connectivity of PS II units, whereas some marine species with distinct antenna architecture, may require the use of more complex parameters based on intermediate models of the photosynthetic unit. Another useful parameter calculated from fluorescence analysis is Phi(II), the yield of PS II. In contrast to q(L), we show that the Phi(II) parameter can be derived from either a pure 'lake' or pure 'puddle' model, and is thus likely to be a robust parameter. The energy absorbed by PS II is divided between the fraction used in photochemistry, Phi(II), and that lost non-photochemically. We introduce two additional parameters that can be used to estimate the flux of excitation energy into competing non-photochemical pathways, the yield induced by downregulatory processes, Phi(NPQ), and the yield for other energy losses, Phi(NO).     

Sperm head morphometry in ejaculates of adult marmosets (Callithrix jacchus): A model for studying sperm subpopulations and among-donor variations

In humans and other mammals, sperm morphology has been considered one of the most important predictive parameters of fertility. The objective was to determine the presence and distribution of sperm head morphometric subpopulations in a nonhuman primate model (Callithrix jacchus), using an objective computer analysis system and principal component analysis (PCA) methods to establish the relationship between the subpopulation distribution observed and among-donor variation. The PCA method revealed a stable number of principal components in all donors studied, that represented more than 85% of the cumulative variance in all cases. After cluster analysis, a variable number (from three to seven) sperm morphometric subpopulations were identified with defined sperm dimensions and shapes. There were differences in the distribution of the sperm morphometric subpopulations (P < 0.001) in all ejaculates among the four donors analyzed. In conclusion, in this study, computerized sperm analysis methods combined with PCA cluster analyses were useful to identify, classify, and characterize various head sperm morphometric subpopulations in nonhuman primates, yielding considerable biological information. In addition, because all individuals were kept in the same conditions, differences in the distribution of these subpopulations were not attributed to external or management factors. Finally, the substantial information derived from subpopulation analyses provided new and relevant biological knowledge which may have a practical use for future studies in human and nonhuman primate ejaculates, including identifying individuals more suitable for assisted reproductive technologies.     

Methods for comparison of parameters from longitudinal rhythmometric models with multiple components

Multiple components linear least-squares methods have been proposed for the detection of periodic components in nonsinusoidal longitudinal time series. However, a proper test for comparison of parameters obtained from this method for two or more time series is not yet available. Accordingly, we propose two methods, one parametric and one nonparametric, to compare parameters from rhythmometric models with multiple components. The parametric method is based on techniques commonly and generally employed in linear regression analysis. The comparison of parameters among two or more time series is accomplished by the use of so-called dummy variables. The nonparametric method is based on bootstrap techniques. This approach basically tests if the difference in any given parameter obtained by fitting a model with the same periods to two different longitudinal time series differs from zero. This method calculates a confidence interval for the difference in the tested parameter. If this interval does not contain zero, it can be concluded that the parameters obtained from the two time series are different with high probability. An estimation of the p-value for the corresponding test can also be calculated. By the use of similar bootstrap techniques, confidence intervals can also be obtained for any parameter derived from the multiple component fit of several periods to nonsinusoidal longitudinal time series, including the orthophase (peak time), bathyphase (trough time), and global amplitude (difference between the maximum and the minimum) of the fitted model waveform. These methods represent a valuable tool for the comparison of rhythm parameters obtained by multiple component analysis, and they render this approach as a generally applicable one for waveform representation and detection of periodicities in nonsinusoidal, sparse, and noisy longitudinal time series sampled with either equidistant or unequidistant observations.     

The Measurement of Local Variation in Shape

Geometric morphometrics comprises tools for measuring and analyzing shape as captured by an entire set of landmark configurations. Many interesting questions in evolutionary, genetic, and developmental research, however, are only meaningful at a local level, where a focus on ??parts?? or ??traits?? takes priority over properties of wholes. To study variational properties of such traits, current approaches partition configurations into subsets of landmarks which are then studied separately. This approach is unable to fully capture both variational and spatial characteristics of these subsets because interpretability of shape differences is context-dependent. Landmarks omitted from a partition usually contain information about that partition??s shape. We present an interpolation-based approach that can be used to model shape differences at a local, infinitesimal level as a function of information available globally. This approach belongs in a large family of methods that see shape differences as continuous ??fields?? spanning an entire structure, for which landmarks serve as reference parameters rather than as data. We show, via analyses of simulated and real data, how interpolation models provide a more accurate representation of regional shapes than partitioned data. A key difference of this interpolation approach from current morphometric practice is that one must assume an explicit interpolation model, which in turn implies a particular kind of behavior of the regions between landmarks. This choice presents novel methodological challenges, but also an opportunity to incorporate and test biomechanical models that have sought to explain tissue-level processes underlying the generation of morphological shape.     

Foot kinematics during walking measured using bone and surface mounted markers

The aim was to compare kinematic data from an experimental foot model comprising four segments ((i) heel, (ii) navicular/cuboid (iii) medial forefoot, (iv) lateral forefoot), to the kinematics of the individual bones comprising each segment. The foot model was represented using two different marker attachment protocols: (a) markers attached directly to the skin; (b) markers attached to rigid plates mounted on the skin. Bone data were collected for the tibia, talus, calcaneus, navicular, cuboid, medial cuneiform and first and fifth metatarsals (n=6). Based on the mean differences between the three data sets during stance, the differences between any two of the three kinematic protocols (i.e. bone vs skin, bone vs plate, skin vs plate) were >3 degrees in only 35% of the data and >5 degrees in only 3.5% of the data. However, the maximum difference between any two of the three protocols during stance was >3 degrees in 100% of the data, >5 degrees in 73% of the data and >8 degrees in 23% of the data. Differences were greatest for motion of the combined navicular/cuboid relative to the calcaneus and the medial forefoot segment relative to the navicular/cuboid. The differences between the data from the skin and plate protocols were consistently smaller than differences between either protocol and the kinematic data for each bone comprising the segment. The pattern of differences between skin and plate protocols and the actual bone motion showed no systematic pattern. It is unlikely that one rigid body foot model and marker attachment approach is always preferable over another.     

Assessing the accuracy of high-resolution X-ray computed tomography of primate trabecular bone by comparisons with histological sections

Different lines of evidence suggest that trabecular bone architecture contains a functional signal related to an organism's locomotor behavior. An understanding of the interspecific and intraspecific variation in extant nonhuman primate trabecular structure is needed to evaluate its usefulness as a tool to reconstruct the locomotor habits of extinct primates. High-resolution X-ray computed tomography (HRXCT) is a new imaging approach with a resolution in the tens of microns that allows nondestructive access to the internal structure of bony elements. Previous studies indicate that such resolution is necessary to accurately quantify structural parameters of trabecular bone. The primary goal of this study was to test the accuracy of HRXCT by comparing stereological measurements from HRXCT images and histological thin sections of cancellous bone taken from the proximal femur and humerus of baboons. To this end, 11 bone samples were scanned on an HRXCT scanner and then thin-sectioned to reveal the scanned plane. HRXCT images were thresholded using a modified half-maximum height protocol. The stereological measurements included bone volume fraction (BV/TV), trabecular number (Tb.N), bone surface to volume ratio (BS/BV), trabecular thickness (Tb.Th), and trabecular spacing (Tb.Sp). The measurement errors on the HRXCT images were 10.90% for BV/TV, 6.06% for Tb.N, 14.19% for BS/BV, 14.33% for Tb.Th, and 7.09% for Tb.Sp, but none of these measurements were significantly different from the histological standards (alpha = 0.05). A second goal of this study was to examine the influence of thresholding, a necessary step in any morphometric study using computed tomography, on the accuracy of the quantitative morphometry. Threshold values derived from a modified half-maximum height protocol showed that parameters derived from the region of interest (area in which stereological measurements were later taken) produced better reconstructions of the actual bone structure than threshold values derived from more inclusive areas of bone. We conclude that HRXCT can accurately reconstruct the complex architecture of trabecular bone, and that thresholding is a nontrivial step in trabecular bone studies, with even slight changes in the protocol greatly affecting the morphometric data. HRXCT represents a valuable analytical tool that should be of interest to a great many researchers in physical anthropology because it allows nondestructive access to internal morphology, thereby preserving valuable and limited skeletal collections.     

Covariation between forelimb muscle anatomy and bone shape in an Australian scratch-digging marsupial: Comparison of morphometric methods

The close association between muscle and bone is broadly intuitive; however, details of the covariation between the two has not been comprehensively studied. Without quantitative understanding of how muscle anatomy influences bone shape, it is difficult to draw conclusions of the significance of many morphological traits of the skeleton. In this study, we investigated these relationships in the Quenda (Isoodon fusciventer), a scratch-digging marsupial. We quantified the relationships between forelimb muscle anatomy and bone shape for animals representing a range of body masses (124–1,952 g) using two-block partial least square analyses. Muscle anatomy was quantified as muscle mass and physiological cross-sectional area (PCSA), and we used two morphometric methods to characterize bone shape: seven indices of linear bone proportions, and landmarks analysis. Bone shape was significantly correlated with body mass, reflecting allometric bone growth. Of the seven bone indices, only shoulder moment index (SMI) and ulna robustness index (URI) showed a significant covariation with muscle anatomy. Stronger relationships between muscle anatomy and forelimb bone shape were found using the landmark coordinates: muscle mass and PCSA were correlated with the geometric shape of the scapula, humerus, and third metacarpal, but to a lesser extent with shape of the ulna. Overall, our data show that landmark coordinates are more sensitive than bone indices to capturing shape changes evident throughout ontogeny, and is therefore a more appropriate method to investigate covariation with forelimb muscle anatomy. Single-species studies investigating ontogeny require refined methods to accurately develop understanding of the important relationships between muscle force generation and bone shape remodeling. Landmark analyses provide such a method.     

Optimal experiment selection for parameter estimation in biological differential equation models

ABSTRACT: BACKGROUND: Parameter estimation in biological models is a common yet challenging problem. In this work we explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection. RESULTS: A minimization formulation is used to find the parameter values that best fit the experiment data. When the data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show that selecting a new experiment based on the local Fisher Information of one local minimum generates additional data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices are roughly independent of which local minima is used to calculate the local Fisher Information. CONCLUSIONS: We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.     

Structure-function relationships in the pulmonary arterial tree

Knowledge of the relationship between structure and function ofthe normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of thevascular remodeling that accompanies pulmonary vascular diseases. In aneffort to provide a means for relating the measurable vascular geometryand vessel mechanics data to the mean pressure-flow relationship andlongitudinal pressure profile, we present a mathematical model of thepulmonary arterial tree. The model is based on the observation that thenormal pulmonary arterial tree is a bifurcating tree in which theparent-to-daughter diameter ratios at a bifurcation and vesseldistensibility are independent of vessel diameter, and although theactual arterial tree is quite heterogeneous, the diameter of eachroute, through which the blood flows, tapers from the arterial inlet toessentially the same terminal arteriolar diameter. In the model theaverage route is represented as a tapered tube through which the bloodflow decreases with distance from the inlet because of the diversion offlow at the many bifurcations along the route. The taper and flowdiversion are expressed in terms of morphometric parameters obtainedusing various methods for summarizing morphometric data. To help putthe model parameter values in perspective, we applied one such methodto morphometric data obtained from perfused dog lungs. Modelsimulations demonstrate the sensitivity of model pressure-flowrelationships to variations in the morphometric parameters. Comparisonsof simulations with experimental data also raise questions as to the"hemodynamically" appropriate ways to summarize morphometric data.     

East Greenland and Barents Sea polar bears (Ursus maritimus): adaptive variation between two populations using skull morphometrics as an indicator of environmental and genetic differences

A morphometric study was conducted on four skull traits of 37 male and 18 female adult East Greenland polar bears (Ursus maritimus) collected 1892-1968, and on 54 male and 44 female adult Barents Sea polar bears collected 1950-1969. The aim was to compare differences in size and shape of the bear skulls using a multivariate approach, characterizing the variation between the two populations using morphometric traits as an indicator of environmental and genetic differences. Mixture analysis testing for geographic differentiation within each population revealed three clusters for Barents Sea males and three clusters for Barents Sea females. East Greenland consisted of one female and one male cluster. A principal component analysis (PCA) conducted on the clusters defined by the mixture analysis, showed that East Greenland and Barents Sea polar bear populations overlapped to a large degree, especially with regards to females. Multivariate analyses of variance (MANOVA) showed no significant differences in morphometric means between the two populations, but differences were detected between clusters from each respective geographic locality. To estimate the importance of genetics and environment in the morphometric differences between the bears, a PCA was performed on the covariance matrix derived from the skull measurements. Skull trait size (PC1) explained approx. 80% of the morphometric variation, whereas shape (PC2) defined approx. 15%, indicating some genetic differentiation. Hence, both environmental and genetic factors seem to have contributed to the observed skull differences between the two populations. Overall, results indicate that many Barents Sea polar bears are morphometrically similar to the East Greenland ones, suggesting an exchange of individuals between the two populations. Furthermore, a subpopulation structure in the Barents Sea population was also indicated from the present analyses, which should be considered with regards to future management decisions.     

An interfacial approach to regional segregation of two competing species mediated by a predator

We consider the problem of coexistence of two competing species mediated by the presence of a predator. We employ a reaction-diffusion model equation with Lotka-Volterra interaction, and speculate that the possibility of coexistence is,enhanced by differences in the diffusion rates of the prey and their predator. In the limit where the diffusion rate of the prey tends to zero, a new equation is derived and the dynamics of spatial segregation is discussed by means of the interfacial dynamics approach. Also, we show that spatial segregation permits periodic and chaotic dynamics for certain parameter ranges.     

Model-based workflow for scale-up of process strategies developed in miniaturized bioreactor systems

Miniaturized bioreactor (MBR) systems are routinely used in the development of mammalian cell culture processes. However, scale-up of process strategies obtained in MBR- to larger scale is challenging due to mainly non-holistic scale-up approaches. In this study, a model-based workflow is introduced to quantify differences in the process dynamics between bioreactor scales and thus enable a more knowledge-driven scale-up. The workflow is applied to two case studies with antibody-producing Chinese hamster ovary cell lines. With the workflow, model parameter distributions are estimated first under consideration of experimental variability for different scales. Second, the obtained individual model parameter distributions are tested for statistical differences. In case of significant differences, model parametric distributions are transferred between the scales. In case study I, a fed-batch process in a microtiter plate (4 ml working volume) and lab-scale bioreactor (3750 ml working volume) was mathematically modeled and evaluated. No significant differences were identified for model parameter distributions reflecting process dynamics. Therefore, the microtiter plate can be applied as scale-down tool for the lab-scale bioreactor. In case study II, a fed-batch process in a 24-Deep-Well-Plate (2 ml working volume) and shake flask (40 ml working volume) with two feed media was investigated. Model parameter distributions showed significant differences. Thus, process strategies were mathematically transferred, and model predictions were simulated for a new shake flask culture setup and confirmed in validation experiments. Overall, the workflow enables a knowledge-driven evaluation of scale-up for a more efficient bioprocess design and optimization.     

Tensile strength of bovine trabecular bone

Data on the tensile and compressive properties of trabecular bone are needed to define input parameters and failure criteria for modeling total joint replacements. To help resolve differences in reports comparing tensile and compressive properties of trabecular bone, we have developed new methods, based on porous foam technology, for tensile testing of fresh/frozen trabecular bone specimens. Using bovine trabecular bone from an isotropic region from the proximal humerus as a model material, we measured ultimate strengths in tension and compression for two groups of 24 specimens each. The average ultimate strength in tension was 7.6 +/- 2.2 (95% C.I.) MPa and in compression was 12.4 +/- 3.2 MPa. This difference was statistically significant (p = 0.013) and was not related to density differences between the test groups (p = 0.28). Strength was related by a power-law function of the local apparent density, but, even accounting for density influences, isotropic bovine trabecular bone exhibits significantly lower strengths in tension than in compression.