Material Properties Of Cancellous Bone Research Articles

Influence of interface crack and non-uniform cement thickness on mixed-mode stress intensity factor and prediction of interface failure of cemented acetabular cup

The goal is to determine the influence of interface crack and non-uniform cement thickness on mixed-mode stress intensity factors (SIF) and the prediction of interface failure of the cemented cup. Nine three-dimensional (3D) finite element (FE) models of implanted pelvic bone were developed having the uniform and non-uniform cement thickness based on computed tomography (CT) dataset. Physiological loading conditions and location-dependent material properties of cancellous bone were considered for the present analysis. In order to understand the influence of crack at cement-bone and implant-cement interfaces, two-dimensional (2D) cracked models were generated and solved using the element free Galerkin method (EFGM). For cracked analysis, a rectangular section was considered at both the interfaces in the superior, inferior, anterior, and posterior anatomic locations to determine the SIF. The average stress values obtained from 3D FE analysis was transferred at the cut boundary of the rectangular section and considered as a mixed-mode loading condition to understand the influence of crack and non-uniform cement thickness on interface failure. The results of the present study indicated that the cement thickness plays an important role in interface failure. SIF increases as the cement thickness decreases. Anterior location is more prone to failure as compared to other anatomic locations. The chance of cement-bone interface failure is more as compared to the implant-cement interface. The present study also indicated that the chance of interface failure is more for the generation of edge crack as compared to center crack.

A novel approach to estimate trabecular bone anisotropy from stress tensors.

Continuum finite element (FE) models of bones and bone-implant configurations are usually based on clinical CT scans. In virtually all of these models, material properties assigned to the bone elements are chosen as isotropic. It has been shown, however, that cancellous bone can be highly anisotropic and that its elastic behavior is best described as orthotropic. Material models have been proposed to derive the orthotropic elastic constants from measurements of density and a fabric tensor. The use of such relationships in FE models derived from CT scans, however, is hampered by the fact that the measurement of such a fabric tensor is not possible from clinical CT images since the resolution of such images is not good enough to resolve the trabecular micro-architecture. In this study, we explore an alternative approach that is based on the paradigm that bone adapts its micro-architecture to the loading conditions, hence that fabric and stress tensors should be aligned and correlated. With this approach, the eigenvectors and eigenvalues of the element continuum-level stress tensor are used as an estimate of the element fabric tensor, from which the orthotropic material properties then are derived. Using an iterative procedure, element orthotropic material properties and fabric tensors are updated until a converged situation is reached. The goals of this study were to investigate the feasibility and accuracy of such an iterative approach to derive orthotropic material properties for a human proximal femur and to investigate whether models derived in this way can provide more accurate results than isotropic models. Results were compared to those obtained from models of the same femurs for which the fabric was measured from micro-CT scans. It was found that the iterative approach could well estimate the orientation of the fabric principal directions. When comparing the stress/damage values in the models with material properties based on estimated and measured fabric tensors, the differences were not significant, suggesting that the material properties based on the estimated fabric tensor well reflected those based on the measured fabric tensor. Errors were less than those obtained when using isotropic models. It is concluded that this novel approach can provide a reasonable estimate of anisotropic material properties of cancellous bone. We expect that this approach can lead to more accurate results in particular for models used to study implants, which are usually anchored in highly anisotropic cancellous bone regions.

Finite element modeling to estimate the apparent material properties of trabecular bone

The in-vivo micro-structure and corresponding material property of trabecular bone is important to simulate the mechanical behavior of macroscopic bone structure. In order to simulate the mechanical behavior of bone numerically, the apparent Young’s modulus of trabecular bone should be available. Generally a high-resolution finite-element model based on micro-CT-images could be was used to estimate this value. However, all the previous works regarding this issue have employed either eight-noded voxel elements or four-noded tetrahedral elements, which usually produces large amount of error in estimating an apparent material property. Therefore, rigorous studies on the accuracy of element type for predicting the material properties of cancellous bone have been made in this paper. Micro-CT-data were extracted from a femoral neck to construct three-dimensional finite-element models with three different element types and compression analyses were performed numerically (up to 1.3% strain) to estimate the apparent modulus. Compression tests using the specimens extracted from a cadaver were also performed to validate the simulated apparent material properties using different element types. As a result, ten-noded tetrahedral elements are recommended to obtain reliable material properties of cancellous bone instead of eight-noded voxel elements or four-noded tetrahedral elements.

Interference between wave modes may contribute to the apparent negative dispersion observed in cancellous bone

Previous work has shown that ultrasonic waves propagating through cancellous bone often exhibit a linear-with-frequency attenuation coefficient, but a decrease in phase velocity with frequency (negative dispersion) that is inconsistent with the causality-imposed Kramers-Kronig relations. In the current study, interfering wave modes similar to those observed in bone are shown to potentially contribute to the observed negative dispersion. Biot theory, the modified Biot-Attenborogh model, and experimental results are used to aid in simulating multiple-mode wave propagation through cancellous bone. Simulations entail constructing individual wave modes exhibiting a positive dispersion using plausible velocities and amplitudes, and then summing the individual modes to create mixed-mode output wave forms. Results of the simulations indicate that mixed-mode wave forms can exhibit negative dispersion when analyzed conventionally under the assumption that only one wave is present, even when the individual interfering waves exhibit positive dispersions in accordance with the Kramers-Kronig relations. Furthermore, negative dispersion is observed when little or no visual evidence of interference exists in the time-domain data. Understanding the mechanisms responsible for the observed negative dispersion could aid in determining the true material properties of cancellous bone, as opposed to the apparent properties measured using conventional data analysis techniques.

Regional differences in mechanical and material properties of femoral head cancellous bone in health and osteoarthritis.

Osteoarthritis (OA) is a debilitating condition common among the aging population. In this study we have determined mechanical and material properties of cancellous bone cores from two differently loaded regions of femoral heads obtained from healthy subjects and those with end-stage osteoarthritis. Densitometric properties were determined prior to compression testing for Young's modulus (EC) and yield strength (sigma(y)), after which bones were powdered for analysis of collagen and mineral content. In both OA and normal cancellous bone, volumetric bone mineral density (BMDv), apparent density (rhoA), E(C), and sigma(y) were systematically greater in the superior than in the inferior region (P<0.05). In the OA inferior region, median BMDv (0.434 g-cm(-3)) and rA (0.426 g-cm(-3)) were significantly greater than in normals (0.329 and 0.287 g-cm(-3), respectively, both P<0.05) reflecting an increased amount of tissue. The mineral:collagen ratio was decreased in OA, but this was only significant in the superior region (P<0.008). Relationships between EC and both BMDv and rho(A) were weaker in OA bone cores (r(2) = 0.66 and r(2) = 0.59) than in normals (r(2) = 0.86 and r(2) = 0.77, respectively). Likewise, sigma(y) and both BMDv and rho(A) were weaker in OA (r(2) = 0.74 and r(2) = 0.70) than in normals (r(2) = 0.83 and r(2) = 0.77, respectively). For the same value of density measure, EC and sigma(y) tended to be lower in OA bone when compared with normal bone. In conclusion, femoral head cancellous bone mass in end-stage osteoarthritis is increased but undermineralized, and is neither stiffer nor stronger than normal cancellous bone.

Predictive value of Singh index and bone mineral density measured by quantitative computed tomography in determining the local cancellous bone quality of the proximal femur

Objective. The purpose of this study was to assess the predictive value of the Singh index as well as quantitative computed tomography for the in vitro local mechanical competence of the cancellous bone of the proximal femur. Design. An experimental study examining the relation between mechanical properties and bone mineral density of the femoral neck determined in vitro and the clinical estimated Singh index on X-rays. Background. Evaluation of the predictive value of the Singh index, an inexpensive and simple technique for the mechanical properties of the cancellous bone of the proximal femur. Methods. The bone quality of the proximal femur of 34 patients undergoing total hip replacement was estimated by roentgenography using the Singh index. Bone mineral density was quantified by quantitative computed tomography using cylindrical cancellous bone biopsies harvested during the total hip replacement procedure by a new biopsy method. The mechanical properties of the bone specimens (Young's modulus, strength and maximum energy absorption E max) were measured by mechanical testing of the bone biopsies. Results. A strong correlation of the Singh index versus material properties of cancellous bone was noted ( r=0.66 for Young's modulus, r=0.73 for strength and r=0.69 for E max, P<0.0001). The correlations of bone mineral density measured by quantitative computed tomography versus Young's modulus, strength and energy absorption E max were significant. Strength was predicted best ( r=0.82; P<0.0001), followed by E max ( r=0.79; P<0.0001) and Young's Modulus ( r=0.73; P<0.0001). Conclusions. We conclude, that assessment of bone mineral density by quantitative computed tomography is a reliable and precise method for the estimation of cancellous bone material properties. The Singh index provides a rough estimate for the mechanical competence of the proximal femur. It is inexpensive, simply to assess and can in some cases replace the measurement of bone mineral density, notably in cases of marked decrease in bone density. Relevance The judgement of bone strength of the proximal femur is of major importance in clinical practice. The measurement of bone density of the cancellous bone of the proximal femur has been established, however this procedure is expensive and not widely available. The relevance of the Singh-index as a simple and inexpensive Method for the estimation of the cancellous bone quality of the proximal femur in comparison to the measurement of bone density remains to be explored.

Composition and mechanical properties of cancellous bone from the femoral head of patients with osteoporosis or osteoarthritis.

The material properties of cancellous bone from patients with osteoporosis (OP) or osteoarthritis (OA) were determined and compared with normal controls. Samples were selected from defined sites in human femoral heads which are subjected to different loads in vivo. Overall, OP bone had the lowest stiffness and OA the highest, and this same order was reflected in the apparent densities of the bone, with OA being the most dense and OP the least. Normal and OP bone were found to have very similar stiffness-density relationships and composition. However, OA bone differed significantly from normal. The stiffness of OA bone increased more slowly with apparent density and its material density was significantly reduced. These findings were due to an altered composition of the bone in which the mass fraction of mineral is 12% less than normal. There was also greater site variation of both apparent and material density, suggesting an altered sensitivity to applied load. These results support the concept that osteoporosis is a loss of normal bone. They also provide evidence for the hypothesis that osteoarthritis is, at least partly, a bone disease in which proliferation of defective bone results in an increase in bone stiffness.

Analysis of mechanical properties of cancellous bone under conditions of simulated bone atrophy

The mechanical properties of cancellous bone have been shown to depend on bone density and on the anisotropy of the trabecular bone structure. By means of high-resolution quantitative computed tomography (QCT), providing a nominal resolution of 0.17 mm, it became possible to assess both apparent density and trabecular microstructure of intact bones. In order to study the influence of age- and disease-related bone loss on the mechanical properties of cancellous bone, a more phenomenological approach was used to develop a novel bone resorption algorithm, called simulated bone atrophy. The algorithm, which is principlally based on constrained Gauss filtration of segmented data volumes, was applied to create derived microstructural models. The mechanical behavior of the cancellous bone can be expressed as a function of the anisotropic bone properties of the microstructural model on the continuum level. To study the influence of bone atrophy on bone strength we compared three models: the originally noninvasively measured bone biopsy and two derived models simulating moderate and pronounced atrophy. For the comparison of the three models, the apparent Young's moduli in the three orthogonal directions were predicted for each model with the help of three-dimensional finite-element analysis. Realistic results for the apparent Young's moduli were found for the tissue moduli chosen. The results siggest that the prediction of anisotropic material properties of cancellous bone based on noninvasive measurements of trabecular microstructures and the application of simulated bone atrophy may be helpful to understand the influence of age- and disease-related bone loss on bone strength.

Predictive value of proximal femoral bone densitometry in determining local orthogonal material properties

Models which are based on non-invasive bone measurements may in the future be able to successfully identify individual subjects at an increased risk for hip fracture; thus, we designed a study to determine the usefulness of dual-energy X-ray absorptiometry (DXA) and quantitative computed tomography (QCT) in predicting the local material properties of human proximal femoral cancellous bone. There has been some disagreement in the scientific literature regarding appropriate predictive models for local material properties of cancellous bone. We sought to confirm that density-mechanical property relationships were consistent from subject to subject, and that three-dimensional QCT measurements were stronger predictors of mechanical properties than two-dimensional DXA results. Linear and power fit relationships between these densitometric measures and material properties were also examined to determine which were more appropriate. Bone cubes from specific regions of highly oriented trabeculae were analyzed separately to determine if cube orientation had an effect on mechanical properties independent of bone density. Ten pairs of ex vivo femurs (five male, five female; age 30–93, mean age 62) were prepared such that specific anatomic planes were visible radiographically. Both QCT and DXA measurements were made on all 20 femurs. Cancellous bone cubes were obtained proceeding along two distinct directions from the proximal end of each femur pair. Unexpectedly, the density-modulus relationships among these ten donors were found to be significantly different at p < 0.01 (83% of the tests were different at p < 0.0001). Density-strength regressions were also significantly different at p < 0.01, but this effect was not as consistent nor as statistically significant. In general, the QCT method did not produce predictions of local cancellous bone material properties superior to the DXA method. The linear and power fit models appeared to produce consistent results, with neither being obviously more advantageous. These density measurements explained at best 30–40% of the variance in modulus and 50–60% of the variance in ultimate stress. The orientation of cancellous cubes in the principal compressive trabeculae region was a significant contributor to mechanical properties ( p = 0.0001) independent of bone density. This finding was not as dramatic in the femoral neck cancellous bone region.

Three-dimensional finite element modelling of non-invasively assessed trabecular bone structures

The three-dimensional microstructure of cancellous bone seems to be one of the key factors in the prediction of mechanical bone properties like bone strength or bone stiffness. In this paper trabecular bone structure was assessed nondestructively by means of high-resolution computed tomography (CT) with a spatial resolution of 250 μm. Mineralized bone was separated from bone marrow and muscle tissue with the help of a three-dimensional segmentation algorithm based on the analysis of directional derivatives. From the three-dimensional stack of CT slices a subvolume comparable in size (3.6 × 3.4 × 3.4 mm 3) to standard histologic bone sections was selected. We refer to this subvolume as non-invasive bone biopsy. A new automated mesh generator was developed to create a three-dimensional finite element model of the non-invasive bone biopsy. Four-noded tetrahedron solid elements were used to guarantee a smooth surface representation. The aim of the presented work was to demonstrate the potential of high-resolution CT imaging in the prediction of the anisotropic material properties of cancellous bone. Preliminary results of the 3D finite element stress analysis are very promising. The predicted value of the apparent Young's modulus (564 MPa) is within the range reported for uniaxial compression testings of cancellous bone specimens.

Cancellous bone material properties in osteoarthritic and rheumatoid total knee patients.

One hundred and thirty-four cancellous bone biopsy specimens were taken from the proximal tibias and distal femurs of 55 patients undergoing total knee replacement for analysis of their area fraction and mechanical testing to determine their strength and stiffness. The purpose of the study was to measure the material properties of cancellous bone taken from arthritic patients and compare these with bone from normal subjects. The results showed a wide variation of strength (0.5-18.1 MPa, mean 5.6 MPa) and stiffness (11-504 MPa, mean 152 MPa). These values are in the same range or less than those reported for bone from normal tibias.

Material properties of cancellous bone in repetitive axial loading.

Machined cancellous bone specimens from human cadaver knees were tested under repetitive nondestructive axial compression. Loads were applied up to 50 per cent of the ultimate strength of the specimens predicted from their mineral content measured by photon absorption technique. The stiffness increased greatly between the first two compressions, and thereafter asymptotically approached a constant level. There was a 44 per cent median increase in the modulus of elasticity from compression No. 1 to compression No. 10. Steady state was apparently reached after the fifth compression with intervals between compression cycles of not more than 2 minutes. The results were reproducible, and the precision of the modulus of elasticity determined by double measurement at compression No. 10 was Ē ± 9.8 per cent (95 per cent confidence limits). The modulus of elasticity at steady state determined as the mean of compressions 6–10 was found to be Ē ± 5.6 per cent (95 per cent confidence limits). With both methods there was a strong linear correlation between the ultimate strength and the modulus of elasticity. The correlation coefficient was r = 0.95 ( p &lt; 0.005) and r = 0.99 ( p &lt; 0.001), respectively. Due to the calculation error the figures for ultimate stress (US) in Table 2 and Fig. 4, and ultimate stress derived from the regression equations in Table 3 are reduced by a factor of two. The present technique allows studies of viscous properties without engaging in otherwise time-demanding creep studies; yet in order to approach the issue quantitatively, the technical arrangement must be more meticulously prepared. Studies of viscous properties may, however, be of importance to evaluate the damping effect of cancellous bone and its role in the musculo-skeletal damping system.

Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis.

An investigation has been made of the source and magnitude of anisotropic material properties of cancellous bone in the proximal epiphysis of the human tibia. Results are reported for stiffness measurements made in three orthogonal directions on 21 cubes of cancellous bone before testing to failure along one of the three principal axes. The structure is approximately transversely isotropic. Strength and stiffness are linear with area fraction for loading along the isotropic axis. Strength is proportional to stiffness for all directions. A finite element model is proposed, based on experimental observations, which enables one to predict the elastic constants of cylindrically structured cancellous bone in the tibia from morphological measurements in the transverse plane.