Anisotropy of the elastic modulus of trabecular bone specimens from different anatomical locations

The contribution of trabecular bone to the stiffness and strength of rat lumbar vertebrae

STUDY DESIGN

In vitro compressive load-displacement experiments on intact rat lumbar vertebrae and on the same vertebrae after part of their trabecular bone was removed.

OBJECTIVE

To determine the contribution of the trabecular bone component to the stiffness and strength of rat lumbar vertebrae.

SUMMARY OF BACKGROUND DATA

Vertebral fractures are common in the aging population, possibly resulting from the deterioration of the mechanical properties of vertebral bone. Studies of the contribution of trabecular bone to the mechanical behavior of whole vertebra were published, but yielded mixed results. Here, we propose a novel optical metrology approach to address this important question.

METHODS

The bodies of intact rat lumbar vertebrae and the bodies of the same vertebrae after part of their trabecular bone was removed were loaded within their elastic region in a wet environment. The amount of trabecular bone removed was determined by micro-computer tomography scanning. Deformation maps of the dorsal vertebral surface of the intact and manipulated vertebrae were obtained using an optical metrology method, and compared. Intact and manipulated vertebrae were also loaded to failure in compression and their strengths and stiffness were compared.

RESULTS

The preferred trabecular orientation was found to be along the anterior-posterior axis, which is similar to humans. Removal of up to 42% of the trabecular tissue in the intact vertebrae did not significantly affect lumbar vertebral stiffness. However, removal of even smaller amounts of the intact trabecular tissue significantly reduced vertebral strength.

CONCLUSION

Trabeculae in rat lumbar vertebrae fulfill an important role in failure resistance (strength), but have little or no effect on the deformational behavior (stiffness) of the bone. These results differ from previous results we reported for rat femora, where removal of trabecular bone surprisingly increased the stiffness of the whole bone, and suggest that trabecular tissue may have different functions depending on anatomic location, bone function and morphology, and mode of loading.

Mechanical properties of glenoid cancellous bone

BACKGROUND

Loosening of the glenoid component in total shoulder arthroplasty is the main late complication of this procedure; it may be assumed that it is highly dependent on the quality of the glenoid cancellous bone. Very little is known about the mechanical properties of this cancellous bone. The aim of this study was to determine these properties (Young's modulus and strength) as well as bone density in different parts of the glenoid cancellous bone to assess their variations.

METHODS

Eleven scapulas were obtained from six fresh-frozen, unembalmed human cadavers. Eighty-two cubic cancellous bone specimens were extracted and tested using a uniaxial compression test; then the specimens were defatted and correlations with bone density were determined.

FINDINGS

The study showed significant differences in the mechanical properties with anatomic location and directions of loading. Young's modulus and strength were found to be significantly higher at the posterior part of the glenoid with the weakest properties at the antero-inferior part. Cancellous bone was found to be anisotropic with higher mechanical properties in the latero-medial direction perpendicular to the articular surface of the glenoid. The apparent density was on average equal to 0.29 g/cm(3) with the higher values at the posterior and superior part of the glenoid. Good correlation between apparent density and elastic modulus was found only in the sagittal planes but not in the coronal and axial plane.

INTERPRETATION

The mechanical properties determined in this study showed the anisotropy of the glenoid cancellous bone; values of these properties could provide input data for finite element method analyses in shoulder prosthesis designs.

A quantitative analysis of the structure of human sternum

An extensive study of the human sternum has been carried out to obtain estimates of the omnidirectional path-length distributions and structural parameters for trabeculation and marrow spaces. Data for sternum samples have been collected, using an object plane scanning microscope. These data have been used to produce the omnidirectional path-length distributions and values of structural parameters for the whole sternum. For a typical adult man the mean trabecular and marrow space path lengths are 224 and 1364 μm, respectively. The percentage bone volume is 13.8 and the surface to volume ratio is 190 cm. Data on the structural variations within the whole sternum are presented. They show a percentage difference in bone volume between the manubrium and the body of sternum of about 36%.

Characterization of bone-implant fixation using modal analysis: application to a press-fit implant model

Orthopaedic implant fixation is strongly dependant upon the effective mechanical properties of newly formed tissue. In this study, we evaluated the potential of modal analysis to derive viscoelastic properties of periprosthetic tissue. We hypothesized that Young's modulus and loss factor could be obtained by a combined theoretical, computational and experimental modal analysis approach. This procedure was applied to ex vivo specimens from a cylindrical experimental implant placed in cancellous bone in an unloaded press-fit configuration, obtained after a four week observation period. Four sections each from seven textured titanium implants were investigated. The first resonant frequency and loss factor were measured. Average experimentally determined loss factor was 2% (SD 0.4%) and average first resonant frequency was 2.1 KHz (SD: 50). A 2D axisymmetric finite element (FE) model identified effective Young's modulus of tissue using experimental resonant frequencies as input. Average value was 42 MPa (SD: 2.4) and no significant difference between specimens was observed. In this pilot study, the non-destructive method allowed accurate measure of dynamic loss factor and resonant frequency and derivation of effective Young's modulus. Prior to implementing this dynamic protocol for broader mechanical evaluation of experimental implant fixation, further work is needed to determine if this affects results from subsequent destructive shear push-out tests.

Age- and sex-related regional compressive strength characteristics of human lumbar vertebrae in osteoporosis

OBJECTIVE

To obtain the compressive load bearing and energy absorption capacity of lumbar vertebrae of osteoporotic elderly for the everyday medical praxis in terms of the simple diagnostic data, like computed tomography (CT), densitometry, age, and sex.

METHODS

Compressive test of 54 osteoporotic cadaver vertebrae L1 and L2, 16 males and 38 females (age range 43-93, mean age 71.6 ± 13.3 years, mean bone mineral density (BMD) 0.377 ± 0.089 g/cm(2), mean T-score -5.57 ± 0.79, Z-score -4.05 ± 0.77) was investigated. Based on the load-displacement diagrams and the measured geometrical parameters of vertebral bodies, proportional, ultimate and yield stresses and strains, Young's modulus, ductility and energy absorption capacity were determined. Three vertebral regions were distinguished: superior, central and inferior regions, but certain parameters were calculated for the upper/ lower intermediate layers, as well. Cross-sectional areas, and certain bone tissue parameters were determined by image analysis of CT pictures of vertebrae. Sex- and age-related decline functions and trends of strength characteristics were determined.

RESULTS

Size-corrected failure load was 15%-25% smaller in women, proportional and ultimate stresses were about 30%-35% smaller for women in any region, and 20%-25% higher in central regions for both sexes. Young's moduli were about 30% smaller in women in any region, and 20%-25% smaller in the central region for both sexes. Small strains were higher in males, large strains were higher in females, namely, proportional strains were about 25% larger in men, yield and ultimate strains were quasi equal for sexes, break strains were 10% higher in women. Ultimate energy absorption capacity was 10%-20% higher in men; the final ductile energy absorption capacity was quasi equal for sexes in all levels. Age-dependence was stronger for men, mainly in central regions (ultimate load, male: r = -0.66, p < 0.01, female: r = -0.52, p < 0.005; ultimate stress, male: r = -0.69, p < 0.01, female: r = -0.50, p < 0.005; Young's modulus, male: r = -0.55, p < 0.05, female: r = -0.52, p < 0.005, ultimate stiffness, male: r = -0.58, p < 0.05, female: r = -0.35, p < 0.03, central ultimate absorbed energy density, male: r = -0.59, p < 0.015, female: r = -0.29, p < 0.08).

CONCLUSIONS

For the strongly osteoporotic population (BMD < 0.4 g/cm(2), T-score < -4) the statical variables (loads, stresses) showed significant correlation; mixed variables (stiffness, Young's modulus, energy) showed moderate correlation; kinematical variables (displacements, strains) showed no correlation with age. The strong correlation of men between BMD and aging (r = -0.82, p < 0.001) and betwen BMD and strength parameters (r = 0.8-0.9, p < 0.001) indicated linear trends in age-related strength loss for men; however, the moderate correlation of women between BMD and aging (r = -0.47, p < 0.005) and between BMD and strength parameters (r = 0.4-0.5, p < 0.005) suggested the need of nonlinear (quadratic) approximation that provided the better fit in age-related strength functions of females modelling postmenopausal disproportionalities.

The effects of the spatial influence function on orthotropic femur remodelling

The morphology and internal structure of bone are modulated by the mechanical stimulus. The osteocytes can sense the stimulus signals from the adjacent regions and respond to them through bone growth or bone absorption. This mechanism can be modelled as the spatial influence function (SIF) in bone adaptation algorithm. In this paper, the remodelling process was simulated in human femurs using an adaptation algorithm with and without SIF, and the trabecular bone was assumed to be orthotropic. A different influence radius and weighting factor were adopted to study the effects of the SIF on the bone density distribution and trabecular alignment. The results have shown that the mean density and L—T ratio (the ratio of longitudinal modulus to transverse modulus) had an excellent linear relationship with the weighting factor when the influence radius was small. The characteristics of density distribution and L—T ratio accorded with the actual observation or measurement when a small weighting factor was used. The large influence radius and weighting factor led to unrealistic results. In contrast, the SIF hardly affected the trabecular alignment, as the mean variation angles of principal axes were less than 1.0 degree for any influence radius and weighting factor

Prediction of mechanical properties of cortical bone by quantitative computed tomography

The relevance of Finite-Element models for hip fracture prediction should be increased by the recent subject-specific methods based on computed tomography (CT-scan), regarding the geometry as well as the material properties. The present study focused on the prediction of subject-specific mechanical parameters of cortical bone (Young's modulus and ultimate strength) from the bone density measured by CT. A total of 46 compression and 46 tension samples from 13 donors (mean age+/-S.D.: 81.8+/-12.7 years) were harvested in the femoral mid-diaphysis and tested until failure. The Young's modulus and ultimate strength were linearly correlated with the bone density measured by CT, for tension as well as compression (0.43<r(2)<0.72, p<0.001). To take into account the remaining uncertainties on the mechanical properties prediction, the standard error of the estimate (S.E.E.) was evaluated in each case (2694-2788MPa for Young's modulus, 13-16MPa for ultimate strength). The significant correlations obtained in the present study and the quantification of the errors will be helpful for the assessment of the cortical mechanical properties from the CT-scan data in order to create subject-specific FE-models.

On shear properties of trabecular bone under torsional loading: effects of bone marrow and strain rate

To further improve our understanding of trabecular bone mechanical behavior in torsion, our objective was to determine the effects of strain rate, apparent density, and presence of bone marrow on trabecular bone shear material properties. Torsion tests of cylindrical trabecular bone specimens from sheep lumbar vertebrae with and without bone marrow were conducted. The bones with marrow were divided into two groups and tested at shear strain rates of 0.002 and 0.05s(-1) measured at the specimen perimeter. The bones without marrow were divided into three groups and tested at shear strain rates of 0.002, 0.015, and 0.05s(-1). Comparing the results of bones with and without marrow tested at low (0.002s(-1)) and high (0.05s(-1)) strain rates, presence of bone marrow did not have any significant effect on trabecular bone shear modulus and strength. In specimens without marrow, power relationships were used to define shear strength and modulus as dependent variables in terms of strain rate and apparent density as independent variables. The shear strength was proportional to the apparent density raised to the 1.02 power and to the strain rate raised to the 0.13 power. The shear modulus was proportional to the apparent density raised to the 1.08 power and to the strain rate raised to the 0.07 power. This study provides further insight into the mechanism of bone failure in trauma as well as failure at the interface between bone and implants as it relates to prediction of trabecular bone shear properties.

The initial stability and contact mechanics of a press-fit resurfacing arthroplasty of the hip

Finite element analysis was used to examine the initial stability after hip resurfacing and the effect of the procedure on the contact mechanics at the articulating surfaces. Models were created with the components positioned anatomically and loaded physiologically through major muscle forces. Total micromovement of less than 10 μm was predicted for the press-fit acetabular components models, much below the 50 μm limit required to encourage osseointegration. Relatively high compressive acetabular and contact stresses were observed in these models. The press-fit procedure showed a moderate influence on the contact mechanics at the bearing surfaces, but produced marked deformation of the acetabular components. No edge contact was predicted for the acetabular components studied.

It is concluded that the frictional compressive stresses generated by the 1 mm to 2 mm interference-fit acetabular components, together with the minimal micromovement, would provide adequate stability for the implant, at least in the immediate post-operative situation.

A method for patient-specific evaluation of vertebral cancellous bone strength: in vitro validation

BACKGROUND

In the context of osteoporosis, important determinants of the fracture risk are the apparent strength and stiffness of cancellous bone, as well as its brittleness and energy absorption capacity. Standard medical imaging, however, cannot measure these mechanical properties directly. Consequently, an estimation of the risk for fracture is made by correlating relative density or mineral density at a skeletal site with statistics of fracture occurrence, which provides limited and partial indications on fracture risks. A better method for evaluating the patient-specific mechanical properties of cancellous bone is therefore required.

METHODS

In order to asses the mechanical properties of vertebral cancellous bone, we developed a finite element parametric model of lattice trabecular architecture that, in the future, will be suitable for use with bone imaging modalities. The model inputs are apparent morphological parameters (trabecular thickness and trabecular separation) and the bone mineral density. We conducted uniaxial compression tests on 36 canine vertebral cancellous bone specimens (C7 and L1) to validate model predictions of strength and stiffness in vitro.

FINDINGS

Predictions of strength and stiffness matched the experimental results within relative absolute errors of 17.7% and 12.8%, respectively (average of differences between model-predicted and measured values, divided by the average of measured values). We also employed the model for evaluation of strength and stiffness of human L1 and L5 vertebrae and found mean strength of 1.67 MPa (confidence interval 0.42 MPa) and mean elastic modulus of 190 MPa (confidence interval 50 MPa), which are well within the range of previously reported apparent strength and stiffness properties.

INTERPRETATION

The present model can be used to improve medical imaging-based evaluation of the spine in osteoporotic individuals by providing more specific information on the individual bone's susceptibility to fracture once clinical bone scans will be able to provide more reliable measures of trabecular thickness and separation.

Mechanical testing of cancellous bone from the femoral head: experimental errors due to off-axis measurements

The aim of this study was to verify whether a misalignment between the testing direction and the trabecular main direction has a significant effect on the compressive behaviour of cancellous bone. Ten cylindrical specimens were extracted from femoral heads with a misalignment to the trabecular main direction of approximately 20 degrees. Each specimen was paired with a specimen extracted aligned with the main direction of the trabeculae on the basis of the closest bone volume fraction, obtaining two groups, one 'aligned' and one 'misaligned'. The average off-axis angle was 6.1 degrees and 21.6 degrees for the 'aligned' and 'misaligned' group, respectively. The specimens underwent micro-tomographic analysis, compressive testing, micro-indentation testing and ashing. No significant differences were found in histomorphometric parameters, hardness and ash density between the two groups, whereas significant differences were found in Young's modulus and ultimate stress: both parameters, measured for the 'misaligned' group, were about 40% lower than those measured for the 'aligned' group. These results demonstrate a great effect of the angle between the testing direction and the main direction of the trabecular structure on the compressive behaviour of cancellous bone. This angle should be reduced as much as possible (in the present work the average value was 6.6+/-3.3 degrees), in any case measured, and always reported together with the mechanical parameters of cancellous bone.

Trabecular bone density of male human cervical and lumbar vertebrae

The objective of this study was to determine the bone mineral density (BMD) of cervical vertebrae and correlate with the lumbar spine. Fifty-seven young adult healthy male volunteers, ranging from 18 to 41 years of age, underwent quantitative computed tomography (QCT) scanning of C2-T1 and L2-L4 vertebrae. To account for correlations, repeated measures techniques were used to compare data as a function of spinal level and region. Linear regression methods were used (+/-95% CI) to compare data as a function of spinal level and region. The mean age and body height were 25.0 +/- 5.8 years and 181.0 +/- 7.6 cm. BMD decreased from the rostral to caudal direction along the spinal column. Grouped data indicated that the neck is the densest followed by the first thoracic vertebra and low back with mean BMD of 256.0 +/- 48.1, 194.3 +/- 44.2, and 172.2 +/- 28.4 mg/cm(3), respectively; differences were statistically significant. While BMD did not vary significantly between the three lumbar bodies, neck vertebrae demonstrated significant trends. The matrix of correlation coefficients between BMD and spinal level indicated that the relationship is strong in the lumbar (r = 0.92-0.96) and cervical (r = 0.73-0.92) spines. Data from the present study show that the trabecular bony architecture of the neck is significantly different from the low back. These quantitative BMD data from a controlled young adult healthy human male volunteer population may be valuable in establishing normative data specifically for the neck. From a trabecular bone density perspective, these results indicate that lumbar vertebrae cannot act as the best surrogates for neck vertebrae. Significant variations in densities among neck vertebrae, unlike the low back counterpart, may underscore the need to treat these bones as different structures.

Single-trabecula building block for large-scale finite element models of cancellous bone

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) 'building-block' of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of approximately 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of approximately 30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.

Simulated influence of osteoporosis and disc degeneration on the load transfer in a lumbar functional spinal unit

As life expectancy increases, age-related disorders and the search for related medical care will expand. Osteoporosis is the most frequent skeletal disease in this context with the highest fracture risk existing for vertebrae. The aging process is accompanied by systemic changes, with the earliest degeneration occurring in the intervertebral discs. The influence of various degrees of disc degeneration on the load transfer was examined using the finite element method. The effect of different possible alterations of the bone quality due to osteoporosis was simulated by adjusting the corresponding material properties and their distribution and several loadings were applied. An alteration of the load transfer, characterised by changed compression stiffness and strain distributions as well as magnitudes, due to osteoporotic bone and degenerated discs was found. When osteoporosis was simulated, the stiffness was substantially decreased, larger areas of the cancellous bone were subjected to higher strains and strain maxima were increased. Increasing ratios of transverse isotropy in the osteoporotic bone yielded smaller effects than reduced bone properties. Including a degenerated disc mainly altered the strain distribution. Combining osteoporosis and degenerated discs reduced the areas of cancellous bone subjected to substantial strain. Based on these results, it can be concluded that the definition of a healthy disc in osteoporotic spines might be considered as a worst-case scenario. One attempt to evaluate the progress of osteoporosis can be made by introducing increasing degrees of anisotropy. If several parameters in a model are changed to simulate degeneration, it should be pointed out how each individual definition influences the overall result.

Distribution of bone mineral density with age and gender in the proximal tibia

OBJECTIVE

To investigate both the age and gender related distributions of bone mineral density in the proximal tibia, specifically in aged patients.

BACKGROUND

For surgeons to achieve stable long-term fixation of implants in the proximal tibia, the distribution of bone mineral density must first be known. The changes that occur due to age or gender can alter these distributions.

METHODS

Quantitative computed tomography and indentation testing were used to investigate 40 human tibiae (27 female, 13 male, average age 63.3 years).

RESULTS

A significant reduction in bone mineral density was found in female tibiae between the age groups of < 60 and > or =60. This difference was not found in the male groups and no other significant difference was found between consecutive age groups. A three-dimensional map of the bone mineral density of the proximal tibia is therefore presented for the groups female < 60, female > or =60 and male. Reduced bone mineral density was consistently found in the central regions, whilst the regions of highest bone quality varied from postero-lateral to postero-medial.

CONCLUSIONS

Implant fixation for fracture treatment as well as joint replacement of the proximal tibia are now able to take the regions of both high and low bone mineral density into consideration in older patients and those suffering from osteoporosis.

RELEVANCE

Knowledge regarding the regional distribution of bone mineral density in the proximal tibia is necessary in order to achieve stable primary and long-term fixation of implants. This manuscript documents the bone mineral density changes that occur with age and gender.

Glucocorticoid treatment of ovariectomized sheep affects mineral density, structure, and mechanical properties of cancellous bone

Thus far, orthopedic research lacks a suitable animal model of osteoporosis. In OVX sheep, 6 months of steroid exposure reduced bone density and mechanical competence. Bone properties and bone formation did not recover for another 6 months. Therefore, steroid-treated OVX sheep may serve as a large animal model for osteopenic bone.

INTRODUCTION

The purpose of this study was to explore the effects of glucocorticoid treatment on cancellous bone density, microarchitecture, biomechanics, and formation of new bone.

MATERIALS AND METHODS

Sixteen ovariectomized merino sheep received either a 6-month glucocorticoid treatment (GLU; 0.45 mg/kg methylprednisolone) or were left untreated (control). Cancellous bone biopsy specimens from the tibia were harvested 6 months after ovariectomy. After 12 months, the animals were killed, and biopsy specimens were obtained from the contralateral tibia and the lumbar spine. All biopsy specimens were scanned for apparent bone mineral density by peripheral quantitative computed tomography (pQCT) and tested mechanically in uniaxial compression. Three-dimensional bone reconstructions were obtained by microcomputed tomography. Formation of new bone was analyzed using histologies of the femoral condyles.

RESULTS

After 6 months, mineral density (-19%) and mechanical competence (-45%) were reduced by glucocorticoid treatment (p < 0.1). BV/TV (-21%; p < 0.01) and trabecular thickness (-20%; p = 0.01) declined, whereas BS/BV increased (24%; p = 0.01). After 12 months, mineral density (-33%) and mechanical properties (-55%) were reduced even more profoundly (p < 0.05). Also, the structural parameters (BS/BV and Tb.Th.) still seemed to be affected by glucocorticoid treatment (p < 0.05). New bone formation, assessed by measurement of osteoid surface, was markedly reduced (-63%, p < 0.1) by glucocorticoid treatment. The differences between groups were generally more pronounced at the tibia and the femur than at the spine.

CONCLUSION

The effects of short-term high-dose steroid administration on bone mineral in this animal model were comparable with those observed in humans after long-term corticoid treatment. Reduction in bone quality and bone formation rate persisted after the cessation of steroid administration. Glucocorticoid treatment of ovariectomized sheep may therefore serve as a large animal model for steroid-induced osteopenia.

Influence of the stiffness of bone defect implants on the mechanical conditions at the interface--a finite element analysis with contact

The study focused on the influence of the implant material stiffness on stress distribution and micromotion at the interface of bone defect implants. We hypothesized that a low-stiffness implant with a modulus closer to that of the surrounding trabecular bone would yield a more homogeneous stress distribution and less micromotion at the interface with the bony bed. To prove this hypothesis we generated a three-dimensional, non-linear, anisotropic finite element (FE) model. The FE model corresponded to a previously developed animal model in sheep. A prismatic implant filled a standardized defect in the load-bearing area of the trabecular bone beneath the tibial plateau. The interface was described by face-to-face contact elements, which allow press fits, friction, sliding, and gapping. We assumed a physiological load condition and calculated contact pressures, shear stresses, and shear movements at the interface for two implants of different stiffness (titanium: E=110GPa; composite: E=2.2GPa). The FE model showed that the stress distribution was more homogeneous for the low-stiffness implant. The maximum pressure for the composite implant (2.1 MPa) was lower than for the titanium implant (5.6 MPa). Contrary to our hypothesis, we found more micromotion for the composite (up to 6 microm) than for the titanium implant (up to 4.5 microm). However, for both implants peak stresses and micromotion were in a range that predicts adequate conditions for the osseointegration. This was confirmed by the histological results from the animal studies.

Factors influencing stresses in the lumbar spine after the insertion of intervertebral cages: finite element analysis

Intervertebral cages in the lumbar spine have been an advancement in spinal fusion to relieve low back pain. Even though initial stability is accepted as a requirement for fusion, there are other factors. The load transfer and its effect on the tissues adjacent to the cage may also play an essential role, which is not easily detectable with experimental tests. In this study the effects of an intervertebral cage insertion on a lumbar functional spinal unit were investigated using finite element analyses. The influences of cage material, cancellous bone density and spinal loading for the stresses in a functional spinal unit were evaluated. Three-dimensional (3D) finite element models of L2-L3 were developed for this purpose. An anterior approach for a monobloc, box-shaped cage was modelled. Models with cage were compared to the corresponding intact ones. The results showed that inserting a cage increased the maximum von Mises stress and changed the load transfer in the adjacent structures. Varying the cage material or the loading conditions had a much smaller influence than varying the cancellous bone density. The denser the cancellous bone, the more the stress was concentrated underneath the cage, while the remaining regions were unloaded. This study showed that the density of the underlying cancellous bone is a more important factor for the biomechanical behaviour of a motion segment stabilized with a cage, and its eventual clinical success, than the cage material or the applied load. Inserting an intervertebral cage markedly changed the load transfer. The altered stress distribution may trigger bone remodelling and explain damage of the underlying vertebrae.

Local 3D scaling properties for the analysis of trabecular bone extracted from high-resolution magnetic resonance imaging of human trabecular bone: comparison with bone mineral density in the prediction of biomechanical strength in vitro

RATIONALE AND OBJECTIVES

A novel, nonlinear morphologic measure [DeltaP(alpha)] based on local 3D scaling properties was applied to high-resolution magnetic resonance images (HR-MRI) of human trabecular bone to predict biomechanical strength in vitro.

METHODS

We extracted DeltaP(alpha) and traditional morphologic parameters (apparent trabecular volume fraction, apparent trabecular separation) from HR-MR images of 32 femoral and 13 spinal bone specimens. Furthermore, bone mineral density (BMD) and maximum compressive strength (MCS) were determined. The morphologic measures were compared with BMD in predicting the biomechanical strength.

RESULTS

In the vertebral (femoral) specimens, R2 for MCS versus DeltaP(alpha) was 0.87 (0.61) (P < 0.001). Correlation between BMD and MCS was 0.53 (P = 0.05) (0.79 [P < 0.001]) for the vertebral (femoral) specimens. For the femoral specimens, prediction of MCS could be improved further by combining BMD and morphologic parameters by multiple regression (R2 = 0.88).

CONCLUSIONS

Morphologic measures extracted from HR-MRI considering local 3D-scaling properties can be used to predict biomechanical properties of bone in vitro. They are superior to 2-dimensional standard linear morphometric measures and, depending on the anatomic location, more reliably predict bone strength as measured by MCS than does BMD.

Speed of sound reflects Young's modulus as assessed by microstructural finite element analysis

We analyzed the ability of the quantitative ultrasound (QUS) parameter, speed of sound (SOS), and bone mineral density (BMD), as measured by dual-energy X-ray absorptiometry (DXA), to predict Young's modulus, as assessed by microstructural finite element analysis (muFEA) from microcomputed tomography (muCT) reconstructions. With muFEA simulation, all bone elements in the model can be assigned the same isotropic Young's modulus; therefore, in contrast to mechanical tests, only the trabecular structure plays a role in the determination of the elastic properties of the specimen. SOS, BMD, and microCT measurements were performed in 15 cubes of pure trabecular bovine bone in three orthogonal directions: anteroposterior (AP); mediolateral (ML); and craniocaudal (CC). The anisotropy of the architecture was determined using mean intercept length (MIL) measurements. SOS, MIL, and Young's modulus (E) values were significantly different in all three directions (p < 0.001), with the highest values in the CC direction. There was a strong linear relationship between E and SOS in each of the three orthogonal directions, with r(2) being 0.88, 0.92, and 0.84 (all p < 0.0001) for the CC, ML, and AP directions, respectively. The relationship between E and BMD was less strong, with r(2) being between 0.66 and 0.85 (all p < 0.0001) in the different directions. There was also a significant, positive correlation between SOS and BMD in each of the three axes (r(2) being 0.81, 0.42, and 0.92 in the CC, ML, and AP directions, respectively; p < 0.0001). After correction for BMD, the correlations between SOS and E in each of the three directions remained highly significant (r(2) = 0.77, p < 0. 0001 for the AP direction; r(2) = 0.48, p < 0.001 for the CC direction; r(2) = 0.52, p < 0.005 for the ML direction). After correction for SOS, BMD remained significantly correlated with Young's modulus in the AP and CC directions (r(2) = 0.52, p < 0.005; r(2) = 0.30, p < 0.05, respectively), but the correlation in the ML direction was no longer statistically significant. In a stepwise regression model, E was best predicted by SOS in each of the orthogonal directions. These observations illustrate the ability of the SOS technique to assess the architectural mechanical quality of trabecular bone.