Material Properties Of Trabecular Bone Research Articles

A graph model to describe the network connectivity of trabecular plates and rods.

Introduction: The trabecular network is perceived as a collection of interconnected plate- (P) and rod-like (R) elements. Previous research has highlighted how these elements and their connectivity influence the mechanical properties of bone, yet further work is required to elucidate better the deeply interconnected nature of the trabecular network with distinct element formations conducting forces per their mechanical boundary conditions. Within this network, forces act through elements: a rod or plate with force applied to one end will transmit this force to a component connected to the other end, defining the boundary conditions for the loading of each element. To that end, this study has two aims: First, to investigate the connectivity of individually segmented elements of trabecular bone with respect to their local boundary conditions as defined by the surrounding trabecular network and linking them directly to the bone's overall mechanical response during loading using a mathematical graph model of the plate and rod (PR) Network. Second, we use this model to quantify side artifacts, a known artifact when testing an excised specimen of trabecular bone, where vertical trabeculae lose their load-bearing capacity due to a loss of connectivity, ultimately resulting in a change of the trabecular network topology. Resuts: Connected elements derived from our model predicted apparent elastic modulus by fitting a linear regression (R 2 = 0.81). In comparison, prediction using conventional bone volume fraction results in a lower accuracy (R 2 = 0.72), demonstrating the ability of the PR Network to estimate compressive elastic modulus independent of specimen size or loading boundary condition. Discussion: PR Network models are a novel approach to describing connectivity within the trabecular network and incorporating mechanical boundary conditions within the morphological analysis, thus enabling the study of intrinsic material properties of trabecular bone. Ultimately, PR Network models may be an early predictor or provide further insights into osteo-degenerative diseases.

Regional variation of the cortical and trabecular bone material properties in the rabbit skull.

The material properties of some bones are known to vary with anatomical location, orientation and position within the bone (e.g., cortical and trabecular bone). Details of the heterogeneity and anisotropy of bone is an important consideration for biomechanical studies that apply techniques such as finite element analysis, as the outcomes will be influenced by the choice of material properties used. Datasets detailing the regional variation of material properties in the bones of the skull are sparse, leaving many finite element analyses of skulls no choice but to employ homogeneous, isotropic material properties, often using data from a different species to the one under investigation. Due to the growing significance of investigating the cranial biomechanics of the rabbit in basic science and clinical research, this study used nanoindentation to measure the elastic modulus of cortical and trabecular bone throughout the skull. The elastic moduli of cortical bone measured in the mediolateral and ventrodorsal direction were found to decrease posteriorly through the skull, while it was evenly distributed when measured in the anteroposterior direction. Furthermore, statistical tests showed that the variation of elastic moduli between separate regions (anterior, middle and posterior) of the skull were significantly different in cortical bone, but was not in trabecular bone. Elastic moduli measured in different orthotropic planes were also significantly different, with the moduli measured in the mediolateral direction consistently lower than that measured in either the anteroposterior or ventrodorsal direction. These findings demonstrate the significance of regional and directional variation in cortical bone elastic modulus, and therefore material properties in finite element models of the skull, particularly those of the rabbit, should consider the heterogeneous and orthotropic properties of skull bone when possible.

Effects of loading rate, age, and morphology on the material properties of human rib trabecular bone

The material and morphometric properties of trabecular bone have been studied extensively in bones bearing significant weight, such as the appendicular long bones and spine. Less attention has been devoted to the ribs, where quantification of material properties is vital to understanding thoracic injury. The objective of this study was to quantify the compressive material properties of human rib trabecular bone and assess the effects of loading rate, age, and morphology on the material properties. Material properties were quantified via uniaxial compression tests performed on trabecular bone samples at two loading rates: 0.005 s−1 and 0.5 s−1. Morphometric parameters of each sample were quantified before testing using micro-computed tomography. Rib trabecular bone material properties were lower on average compared to trabecular bone from other anatomical locations. Morphometric parameters indicated an anisotropic structure with low connectivity and a sparser density of trabeculae in the rib compared to other locations. No significant differences in material properties were observed between the tested loading rates. Material properties were only significantly correlated with age at the 0.005 s−1 loading rate, and no morphometric parameter was significantly correlated with age. Trabecular separation and thickness were most strongly correlated with the material properties, indicating the sparser trabecular matrix likely contributed to the lower material property values compared to other sites. The novel trabecular bone material properties reported in this study can be used to improve the thoracic response and injury prediction of computational models.

Accuracy of osseointegrated screw-bone construct stiffness and peri-implant loading predicted by homogenized FE models relative to micro-FE models

Computational predictions of stiffness and peri-implant loading of screw-bone constructs are highly relevant to investigate and improve bone fracture fixations. Homogenized finite element (hFE) models have been used for this purpose in the past, but their accuracy has been questioned given the numerous simplifications, such as neglecting screw threads and modelling the trabecular bone structure as a continuum. This study aimed to investigate the accuracy of hFE models of an osseointegrated screw-bone construct when compared to micro-FE models considering the simplified screw geometry and different trabecular bone material models.Micro-FE and hFE models were created from 15 cylindrical bone samples with a virtually inserted, osseointegrated screw (fully bonded interface). Micro-FE models were created including the screw with threads (=reference models) and without threads to quantify the error due to screw geometry simplification. In the hFE models, the screws were modelled without threads and four different trabecular bone material models were used, including orthotropic and isotropic material derived from homogenization with kinematic uniform boundary conditions (KUBC), as well as from periodicity-compatible mixed uniform boundary conditions (PMUBC). Three load cases were simulated (pullout, shear in two directions) and errors in the construct stiffness and the volume average strain energy density (SED) in the peri-implant region were evaluated relative to the micro-FE model with a threaded screw.The pooled error caused by only omitting screw threads was low (max: 8.0%) compared to the pooled error additionally including homogenized trabecular bone material (max: 92.2%). Stiffness was predicted most accurately using PMUBC-derived orthotropic material (error: -0.7 ± 8.0%) and least accurately using KUBC-derived isotropic material (error: +23.1 ± 24.4%). Peri-implant SED averages were generally well correlated (R2 ≥ 0.76), but slightly over- or underestimated by the hFE models and SED distributions were qualitatively different between hFE and micro-FE models.This study suggests that osseointegrated screw-bone construct stiffness can be predicted accurately using hFE models when compared to micro-FE models and that volume average peri-implant SEDs are well correlated. However, the hFE models are highly sensitive to the choice of trabecular bone material properties. PMUBC-derived isotropic material properties represented the best trade-off between model accuracy and complexity in this study.

An open-access plug-in program for 3D modelling distinct material properties of cortical and trabecular bone

BackgroundFinite element modelling the material behavior of bone in-silico is a powerful tool to predict the best suited surgical treatment for individual patients.ResultsWe demonstrate the development and use of a pre-processing plug-in program with a 3D modelling image processing software suite (Synopsys Simpleware, ScanIP) to assist with identifying, isolating, and defining cortical and trabecular bone material properties from patient specific computed tomography scans. The workflow starts by calibrating grayscale values of each constituent element with a phantom – a standardized object with defined densities. Using an established power law equation, we convert the apparent density value per voxel to a Young’s Modulus. The resulting “calibrated” scan can be used for modeling and in-silico experimentation with Finite Element Analysis.ConclusionsThis process allows for the creation of realistic and personalized simulations to inform a surgeon’s decision-making. We have made this plug-in program open and accessible as a supplemental file.

Assigning trabecular bone material properties in finite element models simulating the pelvis before and after the development of peri-prosthetic osteolytic lesions

Estimating strain distribution in the acetabulum before and after the development of peri-prosthetic osteolytic lesions secondary to total hip arthroplasty may assist with understanding the pathogenesis of this condition. This could be achieved by performing patient-specific finite element analysis of (1) total hip arthroplasty recipients with developed acetabular osteolytic lesions, and (2) models simulating the patient's pelvis and implant immediately after primary surgery. State of the art patient-specific total hip arthroplasty finite element analysis simulations obtain trabecular bone material properties from Hounsfield units within computed tomography (CT) scans of patients. However, this is not feasible when an implant is already in situ due to metal artefact disruption and, in turn, incorrectly reproduced Hounsfield units. Therefore, alternative methods of assigning trabecular bone material properties within such models were tested and strain results compared. It was found that assigning set material properties throughout the trabecular bone geometry was sufficient for the desired application. Simulating the primary implant and pelvis requires geometric and material based assumptions. Therefore, comparisons were made between strain values obtained from simulated primary models, from state of the art methods using material properties obtained from intact bone within a CT scan, and from models with osteolytic lesions. Strain values found using the finite element models simulating the pelvis before osteolytic lesion developed were considerably closer to those found using state of the art methods than those found for the bone loss models. These models could be used to determine relationships between strain distribution and factors such as bone loss.

Cyclic cryopreservation affects the nanoscale material properties of trabecular bone

Tissues such as bone are often stored via freezing, or cryopreservation. During an experimental protocol, bone may be frozen and thawed a number of times. For whole bone, the mechanical properties (strength and modulus) do not significantly change throughout five freeze-thaw cycles. Material properties at the trabecular and lamellar scales are distinct from whole bone properties, thus the impact of freeze-thaw cycling at this scale is unknown. To address this, the effect of repeated freezing on viscoelastic material properties of trabecular bone was quantified via dynamic nanoindentation. Vertebrae from five cervine spines (1.5-year-old, male) were semi-randomly assigned, three-to-a-cycle, to 0–10 freeze-thaw cycles. After freeze-thaw cycling, the vertebrae were dissected, prepared and tested. ANOVA (factors cycle, frequency, and donor) on storage modulus, loss modulus, and loss tangent, were conducted. Results revealed significant changes between cycles for all material properties for most cycles, no significant difference across most of the dynamic range, and significant differences between some donors. Regression analysis showed a moderate positive correlation between cycles and material property for loss modulus and loss tangent, and weak negative correlation for storage modulus, all correlations were significant. These results indicate that not only is elasticity unpredictably altered, but also that damping and viscoelasticity tend to increase with additional freeze-thaw cycling.

Mechanical Properties of Trabecular Bone through Compression and Combined Compression-Torsion Test: A Comparative Study

In realistic service of life, trabecular bone is subjected to multiaxial stress histories during physiological routine activities thus investigation on the mechanical environment is important to evaluate the mechanistic aspects of bone failure in trauma. This study attempts to compare the material properties of trabecular bone with regard to mechanical properties in axial compression and combined compression-torsion. How superimposed axial compression and torsion loads would alter the axial mechanical properties is explained. Shear loading demonstrates tenfold reduction in modulus and 27% reduction in yield strength of bone in comparison to the properties of bone in pure compression. This condition shows that superimposed torsional loading is possible to accelerate bone yielding.

Anterior and posterior variations in mechanical properties of human vertebrae measured by nanoindentation

Osteoporotic spinal fractures are a significant global public health issue affecting more than 200 million people. Local degradation of the mechanical properties of bone and changes in global spine curvature increase fracture risk. However, a gap in knowledge exists relating material properties of trabecular bone in different regions of the spine. The purpose of our project was to measure the intrinsic mechanical properties of the anterior and posterior regions of human vertebral bodies in the thoracic and lumbar spine. Nanoindentation was used to evaluate Young's modulus (E) and hardness (H) of anterior and posterior trabecular bone regions from each vertebra (T7, T8 and L4). One-way ANOVA and the Turkey–Kramer test were used to analyze significance between vertebrae and t-test was used to test for significance within vertebrae. There was no difference in (E) and (H) within vertebrae. Young's modulus in the anterior regions of T7 (19.8±1.3) and T8 (19.6±1.4) were statistically greater than that in L4 (17.6±0.5). There was no difference between the posterior regions of all the vertebrae. There was a statistical significant difference in hardness between the anterior regions of T7 and T8 compared to L4, while the posterior regions demonstrated no difference. The results presented in this study, for the first time, reveal the differences in bone properties between the kyphotic thoracic spine and lordotic lumbar spine regions. This information will be helpful in understanding vertebral body remodeling and adaption in different regions of the spine which may be associated with spinal curvature and loading conditions.

Intrinsic Material Properties of Trabecular Bone by Nanoindentation Testing of Biopsies Taken from Healthy Women Before and After Menopause

Postmenopausal osteoporosis in women is characterized by an increase in bone fragility and risk of fracture. In addition to transmenopausal decline in three-dimensional trabecular bone architecture, changes in intrinsic material properties (local stiffness, damping, and hardness) may contribute to increased bone fragility. In this study, nanoindentation was used to quantify transmenopausal changes in the intrinsic properties of trabecular bone. Paired transilial biopsy specimens were used from a previously reported study in which bone biopsies were obtained from women prior to menopause (premenopausal, age 49.0±1.9) and at 12months past the last menstrual period (postmenopausal, age 54.6±2.2). Elastic and viscoelastic material properties of the trabecular bone were measured using quasi-static and dynamic nanoindentation techniques, respectively. Paired Student's t tests (n=15) were performed to assess the significance of the measured intrinsic properties. Trabecular bone microarchitecture is compromised in postmenopausal women, and although this loss is associated with a trend toward reduction in some intrinsic properties (storage modulus), we found no statistically significant changes in bone intrinsic properties between healthy pre- and postmenopausal biopsies in the quasi-static results and frequency-averaged dynamic results.

Effects of one year daily teriparatide treatment on trabecular bone material properties in postmenopausal osteoporotic women previously treated with alendronate or risedronate

In the present work we examined the effect of teriparatide administration following bisphosphonate treatment on bone compositional properties by Raman and Fourier Transform Infrared Imaging (FTIR) microspectroscopic analysis. Thirty two paired iliac crest biopsies (before and after 1year teriparatide) from sixteen osteoporotic women previously treated with either Alendronate (ALN) or Risedronate (RIS) and subsequently treated 12months with teriparatide (TPTD) were analyzed at anatomical areas of similar tissue age in bone forming areas (within the fluorescent double labels). The outcomes that were monitored and reported were mineral to matrix ratio (corresponding to ash weight), mineral maturity (indicative of the mineral crystallite chemistry and stoichiometry, and having a direct bearing on crystallite shape and size), relative proteoglycan content (regulating mineralization commencement), and the ratio of two of the major enzymatic collagen cross-links (pyridinoline/divalent). Significant differences in mineral/matrix, mineral maturity/crystallinity, and collagen cross-link ratio bone quality indices after TPTD treatment were observed, indicating a specific response of these patients to TPTD treatment. Moreover differences between ALN and RIS treated patients at baseline in the collagen cross-link ratio were observed. Since tissue areas of similar tissue age were analyzed, these differences may not be attributed to differences in bone turnover.

The evaluation of maxillary advancement technique using internal distraction osteogenesis in unilateral cleft lip and palate patient with finite element analysis

The aim of this study is to evaluate the parameters that commonly used in mechanical analysis of materials like displacement, strain and von Misses stress distributions after maxillary advancement in unilateral cleft lip and palate (UCLP) patients using distraction osteogenesis. The 3D skull model of a 20-year-old UCLP patient with normal mandibular development (SNB: 79.5 o ) and maxillary hypoplasia (SNA: 70.7°) with negative overjet was reconstructed by using the computed tomography (CT) data. The surface mesh of the model was prepared by using the MIMICS software, and then the model was transferred into ANSYS (FE package). 854023 nodes and 623177 elements (Solid92) were used during the analysis. To obtain more realistic model, the maxillary cortical bone was defined as anisotropic. On the other hand the material properties of trabecular bone and callus were selected as linear, isotropic and homogenous. After a LeFort I osteotomy was performed on the model, the maxillary advancement was simulated in 6 steps with 1 mm translation in each step with a total of 6 mm displacement. Non-linear finite element analysis was used due to large deformations. Compared to the similar studies, more elements and nodes were defined especially in maxilla and zygoma. Selection of material properties of maxillary cortical bone has an important role on the calculation of bone strain and deformations during the finite element analysis (FEA). Therefore, the maxillary cortical bone was defined as anisotropic. Asymmetrical displacements and von Misses stresses were found in both right and left half-jaw. The maximum stresses were obtained at foramen infraorbitale and infraorbital margin regions at non-cleft side (mean 350 and 410 MPa, respectively). Relatively high von Misses stresses were found on sutura naso-maksillaris, fronto-nasalis, and zygomaticomaksillaris. Sagittal displacements of anterior nasal spina and point A were found to be 6.24 and 6.65 mm, respectively. The difference in the displacements was due to the asymmetrical anatomical structure in CLP patients. In this study the finite element method has been used to simulate the sagittal maxillary advancement. The simulation results obtained from numerical method show that asymmetrical stresses and displacements in the sagittal plane in UCLP patients reveal the difference in routine patients. Non-invasive methods such as the FEA help us to determine the mechanical response of the skull before any treatment is applied to the patients.

A subject-specific pelvic bone model and its application to cemented acetabular replacements

A subject-specific three-dimensional finite element (FE) pelvic bone model has been developed and applied to the study of bone–cement interfacial response in cemented acetabular replacements. The pelvic bone model was developed from CT scan images of a cadaveric pelvis and validated against the experiment data obtained from the same specimen at a simulated single-legged stance. The model was then implanted with a cemented acetabular cup at selected positions to simulate some typical implant conditions due to the misplacement of the cup as well as a standard cup condition. For comparison purposes, a simplified FE model with homogeneous trabecular bone material properties was also generated and similar implant conditions were examined.The results from the homogeneous model are found to underestimate significantly both the peak von Mises stress and the area of the highly stressed region in the cement near the bone–cement interface, compared with those from the subject-specific model. Non-uniform cement thickness and non-standard cup orientation seem to elevate the highly stressed region as well as the peak stress near the bone–cement interface.

The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the Human Vertebral Body

Classical finite element (FE) models can estimate vertebral stiffness and strength with much lower computational costs than muFE analyses, but the accuracy of these models rely on calibrated material properties that are not necessarily consistent with experimental results. In general, trabecular bone material properties are scaled with computer tomography (CT) density alone, without accounting for local variations in anisotropy or micro-architecture. Moreover, the cortex is often omitted or assigned with a constant thickness. In this work, voxel FE models, as well as surface-based homogenized FE models with topologically-conformed geometry and assigned with experimentally validated properties for bone, were developed from a series of 12 specimens tested up to failure. The effects of changing from a digital mesh to a smooth mesh, including a cortex of variable thickness and/or including heterogeneous trabecular fabric, were investigated. In each case, FE predictions of vertebral stiffness and strength were compared with the experimental gold-standard, and changes in elastic strain energy density and damage distributions were reported. The results showed that a smooth mesh effectively removed zones of artificial damage locations occurring in the ragged edges of the digital mesh. Adding an explicit cortex stiffened and strengthened the models, unloading the trabecular centrum while increasing the correlations to experimental stiffness and strength. Further addition of heterogeneous fabric improved the correlations to stiffness (R(2)=0.72) and strength (R(2)=0.89) and moved the damage locations closer to the vertebral endplates, following the local trabecular orientations. It was furthermore demonstrated that predictions of vertebral stiffness and strength of homogenized FE models with topologically-conformed cortical shell and heterogeneous trabecular fabric correlated well with experimental measurements, after assigning purely experimental data for bone without further calibration of material laws at the macroscale of bone. This study successfully demonstrated the limitations of current classical FE methods and provided valuable insights into the damage mechanisms of vertebral bodies.

ANATOMY- AND MORPHOLOGY-BASED SMOOTH FINITE ELEMENT MODELS OF THE VERTEBRAL BODY

Classical finite element (FE) models can estimate vertebral stiffness and strength with much lower computational effort than μFE analyses, but the accuracy of these models rely on calibrated material properties that are not necessarily consistent with experimental results. In general, trabecular bone material properties are scaled with CT density without accounting for local variations in architecture. Moreover, the cortex is often omitted or assigned with a constant thickness [Imai et al, 2006]. In this work, anatomyand morphologybased FE models were developed with experimentally validated fabric-based elastic properties for trabecular bone and a cortical shell with variable thickness.

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.

3-D numerical simulation of wave propagation in porous media: Influence of the microstructure and of the material properties of trabecular bone

Finite-difference time domain simulations coupled to 3-D microstructural models of 30 trabecular bones reconstructed from synchrotron radiation microtomography were employed herein to compare and quantify the effects of bone volume fraction, microstructure, and material properties of trabecular bone on QUS parameters. Scenarios of trabecular thinning and thickening using an iterative dedicated algorithm allowed the estimation of the sensitivity of QUS parameters to bone volume fraction. The sensitivity to bone material properties was assessed by considering independent variations of density and stiffness. The effect of microstructure was qualitatively assessed by producing virtual bone specimens of identical bone volume fraction (13%). Both BUA and SOS show a strong correlation with BV/TV (r2=0.94 p10−4) and vary quasi-linearly with BV/TV at an approximate rate of 2 dB/cm/MHz and 11 m/s per % increase of BV/TV, respectively. Bone alterations caused by variation in BV/TV (BUA: 40 dB/cm.MHz; SOS: 200 m/s) is much more detrimental to QUS variables than that caused by alterations of material properties or diversity in microarchitecture (BUA: 7.8 dB/cm.MHz; SOS: 36 m/s). QUS variables are changed more dramatically by BV/TV than by changes in material properties or microstructural diversity. However, material properties and structure also appear to play a role.

Glucocorticoid-Treated Mice Have Localized Changes in Trabecular Bone Material Properties and Osteocyte Lacunar Size That Are Not Observed in Placebo-Treated or Estrogen-Deficient Mice

This study compares changes in bone microstructure in 6-month-old male GC-treated and female ovariectomized mice to their respective controls. In addition to a reduction in trabecular bone volume, GC treatment reduced bone mineral and elastic modulus of bone adjacent to osteocytes that was not observed in control mice nor estrogen-deficient mice. These microstructural changes in combination with the macrostructural changes could amplify the bone fragility in this metabolic bone disease. Patients with glucocorticoid (GC)-induced secondary osteoporosis tend to fracture at higher bone mineral densities than patients with postmenopausal osteoporosis. This suggests that GCs may alter bone material properties in addition to BMD and bone macrostructure. Changes in trabecular bone structure, elastic modulus, and mineral to matrix ratio of the fifth lumbar vertebrae was assessed in prednisolone-treated mice and placebo-treated controls for comparison with estrogen-deficient mice and sham-operated controls. Compression testing of the third lumbar vertebrae was performed to assess whole bone strength. Significant reductions in trabecular bone volume and whole bone strength occurred in both prednisolone-treated and estrogen-deficient mice compared with controls after 21 days (p < 0.05). The average elastic modulus over the entire surface of each trabecula was similar in all the experimental groups. However, localized changes within the trabeculae in areas surrounding the osteocyte lacunae were observed only in the prednisolone-treated mice. The size of the osteocyte lacunae was increased, reduced elastic modulus around the lacunae was observed, and a "halo" of hypomineralized bone surrounding the lacunae was observed. This was associated with reduced (nearly 40%) mineral to matrix ratio determined by Raman microspectroscopy. These localized changes in elastic modulus and bone mineral to matrix ratio were not observed in the other three experimental groups. Based on these results, it seems that GCs may have direct effects on osteocytes, resulting in a modification of their microenvironment. These changes, including an enlargement of their lacunar space and the generation of a surrounding sphere of hypomineralized bone, seem to produce highly localized changes in bone material properties that may influence fracture risk.

The mechanical properties of trabecular bone: Dependence on anatomic location and function

In 1961, Evans and King documented the mechanical properties of trabecular bone from multiple locations in the proximal human femur. Since this time, many investigators have cataloged the distribution of trabecular bone material properties from multiple locations within the human skeleton to include femur, tibia, humerus, radius, vertebral bodies, and iliac crest. The results of these studies have revealed tremendous variations in material properties and anisotropy. These variations have been attributed to functional remodeling as dictated by Wolff's Law. Both linear and power functions have been found to explain the relationship between trabecular bone density and material properties. Recent studies have re-emphasized the need to accurately quantify trabecular bone architecture proposing several algorithms capable of determining the anisotropy, connectivity and morphology of the bone. These past studies, as well as continuing work, have significantly increased the accuracy of analytical and experimental models investigating bone, and bone implant interfaces as well as enhanced our perspective towards understanding the factors which may influence bone formation or resorption.

The orthogonal material properties of trabecular bone: Correlation with computed tomography density measurements

The orthogonal material properties of trabecular bone: Correlation with computed tomography density measurements