The mechanical behaviour of intracondylar cancellous bone of the femur at different loading rates

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.

Method for accurate removal of trabecular bone samples from a curved articulating surface of the distal femur

BACKGROUND

Knowing the mechanical properties of trabecular bone is critical for many branches of orthopaedic research. Trabecular bone is anisotropic and the principal trabecular direction is usually aligned with the load it transmits. It is therefore critical that the mechanical properties are measured as close as possible to this direction, which is often perpendicular to a curved articulating surface.

METHODS

This study presents a method to extract trabecular bone cores perpendicular to a curved articulating surface of the distal femur. Cutting guides were generated from computed tomography scans of 12 human distal femora and a series of cutting tools were used to release cylindrical bone cores from the femora. The bone cores were then measured to identify the angle between the bone core axis and the principal trabecular axis.

FINDINGS

The method yielded an 83% success rate in core extraction over 10 core locations per distal femur specimen. In the condyles, 97% of extracted cores were aligned with the principal trabecular direction.

INTERPRETATION

This method is a reliable way of extracting trabecular bone specimens perpendicular to a curved articular surface and could be useful across the field of orthopaedic research.

Computational models and their applications in biomechanical analysis of mandibular reconstruction surgery

Advanced head and neck cancers involving the mandible often require surgical removal of the diseased parts and replacement with donor bone or prosthesis to recreate the form and function of the premorbid mandible. The degree to which this reconstruction successfully replicates key geometric features of the original bone critically affects the cosmetic and functional outcomes of speaking, chewing, and breathing. With advancements in computational power, biomechanical modeling has emerged as a prevalent tool for predicting the functional outcomes of the masticatory system and evaluating the effectiveness of reconstruction procedures in patients undergoing mandibular reconstruction surgery. These models offer cost-effective and patient-specific treatment tailored to the needs of individuals. To underscore the significance of biomechanical modeling, we conducted a review of 66 studies that utilized computational models in the biomechanical analysis of mandibular reconstruction surgery. The majority of these studies employed finite element method (FEM) in their approach; therefore, a detailed investigation of FEM has also been provided. Additionally, we categorized these studies based on the main components analyzed, including bone flaps, plates/screws, and prostheses, as well as their design and material composition.

Anisotropy, Anatomical Region, and Additional Variables Influence Young's Modulus of Bone: A Systematic Review and Meta-Analysis

The importance of finite element analysis (FEA) is growing in orthopedic research, especially in implant design. However, Young's modulus (E) values, one of the most fundamental parameters, can range across a wide scale. Therefore, our study aimed to identify factors influencing E values in human bone specimens. We report our systematic review and meta-analysis based on the recommendation of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guideline. We conducted the analysis on November 21, 2021. We included studies investigating healthy human bone specimens and reported on E values regarding demographic data, specimen characteristics, and measurement specifics. In addition, we included study types reporting individual specimen measurements. From the acquired data, we created a cohort in which we performed an exploratory data analysis that included the explanatory variables selected by random forest and regression trees methods, and the comparison of groups using independent samples Welch's t test. A total of 756 entries were included from 48 articles. Eleven different bones of the human body were included in these articles. The range of E values is between 0.008 and 33.7 GPa. The E values were most heavily influenced by the cortical or cancellous type of bone tested. Measuring method (compression, tension, bending, and nanoindentation), the anatomical region within a bone, the position of the bone within the skeleton, and the bone specimen size had a decreasing impact on the E values. Bone anisotropy, specimen condition, patient age, and sex were selected as important variables considering the value of E. On the basis of our results, E values of a bone change with bone characteristics, measurement techniques, and demographic variables. Therefore, the evaluation of FEA should be performed after the standardization of in vitro measurement protocol. © 2023 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

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.

Standardizing compression testing for measuring the stiffness of human bone

Objectives

The ability to determine human bone stiffness is of clinical relevance in many fields, including bone quality assessment and orthopaedic prosthesis design. Stiffness can be measured using compression testing, an experimental technique commonly used to test bone specimens in vitro. This systematic review aims to determine how best to perform compression testing of human bone.

Methods

A keyword search of all English language articles up until December 2017 of compression testing of bone was undertaken in Medline, Embase, PubMed, and Scopus databases. Studies using bulk tissue, animal tissue, whole bone, or testing techniques other than compression testing were excluded.

Results

A total of 4712 abstracts were retrieved, with 177 papers included in the analysis; 20 studies directly analyzed the compression testing technique to improve the accuracy of testing. Several influencing factors should be considered when testing bone samples in compression. These include the method of data analysis, specimen storage, specimen preparation, testing configuration, and loading protocol.

Conclusion

Compression testing is a widely used technique for measuring the stiffness of bone but there is a great deal of inter-study variation in experimental techniques across the literature. Based on best evidence from the literature, suggestions for bone compression testing are made in this review, although further studies are needed to establish standardized bone testing techniques in order to increase the comparability and reliability of bone stiffness studies.

Cite this article: S. Zhao, M. Arnold, S. Ma, R. L. Abel, J. P. Cobb, U. Hansen, O. Boughton. Standardizing compression testing for measuring the stiffness of human bone. Bone Joint Res 2018;7:524–538. DOI: 10.1302/2046-3758.78.BJR-2018-0025.R1.

The effect of ageing and osteoarthritis on the mechanical properties of cartilage and bone in the human knee joint

Osteoarthritis is traditionally associated with cartilage degeneration although is now widely accepted as a whole-joint disease affecting the entire osteochondral unit; however site-specific cartilage and bone material properties during healthy ageing and disease are absent limiting our understanding. Cadaveric specimens (n = 12; 31–88 years) with grades 0–4 osteoarthritis, were dissected and spatially correlated cartilage, subchondral and trabecular bone samples (n = 8 per cadaver) were harvested from femoral and tibial localities. Nanoindentation was utilised to obtain cartilage shear modulus (G′) and bone elastic modulus (E). Cartilage G′ is strongly correlated to age (p = 0.003) and osteoarthritis grade (p = 0.007). Subchondral bone E is moderately correlated to age (p = 0.072) and strongly correlated to osteoarthritis grade (p = 0.013). Trabecular bone E showed no correlation to age (p = 0.372) or osteoarthritis grade (p = 0.778). Changes to cartilage G′ was significantly correlated to changes in subchondral bone E (p = 0.007). Results showed preferential medial osteoarthritis development and moderate correlations between cartilage G′ and sample location (p = 0.083). Also demonstrated for the first time was significant correlations between site-matched cartilage and subchondral bone material property changes during progressive ageing and osteoarthritis, supporting the role of bone in disease initiation and progression. This clinically relevant data indicates a causative link with osteoarthritis and medial habitual loading.

Tissue material properties and computational modelling of the human tibiofemoral joint: a critical review

Understanding how structural and functional alterations of individual tissues impact on whole-joint function is challenging, particularly in humans where direct invasive experimentation is difficult. Finite element (FE) computational models produce quantitative predictions of the mechanical and physiological behaviour of multiple tissues simultaneously, thereby providing a means to study changes that occur through healthy ageing and disease such as osteoarthritis (OA). As a result, significant research investment has been placed in developing such models of the human knee. Previous work has highlighted that model predictions are highly sensitive to the various inputs used to build them, particularly the mathematical definition of material properties of biological tissues. The goal of this systematic review is two-fold. First, we provide a comprehensive summation and evaluation of existing linear elastic material property data for human tibiofemoral joint tissues, tabulating numerical values as a reference resource for future studies. Second, we review efforts to model tibiofemoral joint mechanical behaviour through FE modelling with particular focus on how studies have sourced tissue material properties. The last decade has seen a renaissance in material testing fuelled by development of a variety of new engineering techniques that allow the mechanical behaviour of both soft and hard tissues to be characterised at a spectrum of scales from nano- to bulk tissue level. As a result, there now exists an extremely broad range of published values for human tibiofemoral joint tissues. However, our systematic review highlights gaps and ambiguities that mean quantitative understanding of how tissue material properties alter with age and OA is limited. It is therefore currently challenging to construct FE models of the knee that are truly representative of a specific age or disease-state. Consequently, recent tibiofemoral joint FE models have been highly generic in terms of material properties even relying on non-human data from multiple species. We highlight this by critically evaluating current ability to quantitatively compare and model (1) young and old and (2) healthy and OA human tibiofemoral joints. We suggest that future research into both healthy and diseased knee function will benefit greatly from a subject- or cohort-specific approach in which FE models are constructed using material properties, medical imagery and loading data from cohorts with consistent demographics and/or disease states.

A Finite Element Study of the Human Hip Joint

A finite element study of human hip joint is described. The results show that the articular cartilage is well able to distribute the applied load. Values for the compressive radial stress were calculated and compare favourably with published results. Values for compressive hoop stress and shear stress are also given.

Evaluating changes in structure and cytotoxicity during in vitro degradation of three-dimensional printed scaffolds

This study evaluated the structural, mechanical, and cytocompatibility changes of three-dimensional (3D) printed porous polymer scaffolds during degradation. Three porous scaffold designs were fabricated from a poly(propylene fumarate) (PPF) resin. PPF is a hydrolytically degradable polymer that has been well characterized for applications in bone tissue engineering. Over a 224 day period, scaffolds were hydrolytically degraded and changes in scaffold parameters, such as porosity and pore size, were measured nondestructively using micro-computed tomography. In addition, changes in scaffold mechanical properties were also measured during degradation. Scaffold degradation was verified through decreasing pH and increasing mass loss as well as the formation of micropores and surface channels. Current methods to evaluate polymer cytotoxicity have been well established; however, the ability to evaluate toxicity of an absorbable polymer as it degrades has not been well explored. This study, therefore, also proposes a novel method to evaluate the cytotoxicity of the absorbable scaffolds using a combination of degradation extract, phosphate-buffered saline, and cell culture media. Fibroblasts were incubated with this combination media, and cytotoxicity was evaluated using XTT assay and fluorescence imaging. Cell culture testing demonstrated that the 3D-printed scaffold extracts did not induce significant cell death. In addition, results showed that over a 224 day time period, porous PPF scaffolds provided mechanical stability while degrading. Overall, these results show that degradable, 3D-printed PPF scaffolds are suitable for bone tissue engineering through the use of a novel toxicity during degradation assay.

Material Properties of the Mandibular Trabecular Bone

The present paper introduces a numerical simulation aided, experimental method for the measurement of Young's modulus of the trabecular substance in the human mandible. Compression tests were performed on fresh cadaveric samples containing trabecular bone covered with cortical layer, thus avoiding the destruction caused by the sterilization, preservation, and storage and the underestimation of the stiffness resulting from the individual failure of the trabeculae cut on the surfaces. The elastic modulus of the spongiosa was determined by the numerical simulation of each compression test using a specimen specific finite element model of each sample. The received mandibular trabecular bone Young's modulus values ranged from 6.9 to 199.5 MPa.

Do regional modifications in tissue mineral content and microscopic mineralization heterogeneity adapt trabecular bone tracts for habitual bending? Analysis in the context of trabecular architecture of deer calcanei

Calcanei of mature mule deer have the largest mineral content (percent ash) difference between their dorsal 'compression' and plantar 'tension' cortices of any bone that has been studied. The opposing trabecular tracts, which are contiguous with the cortices, might also show important mineral content differences and microscopic mineralization heterogeneity (reflecting increased hemi-osteonal renewal) that optimize mechanical behaviors in tension vs. compression. Support for these hypotheses could reveal a largely unrecognized capacity for phenotypic plasticity - the adaptability of trabecular bone material as a means for differentially enhancing mechanical properties for local strain environments produced by habitual bending. Fifteen skeletally mature and 15 immature deer calcanei were cut transversely into two segments (40% and 50% shaft length), and cores were removed to determine mineral (ash) content from 'tension' and 'compression' trabecular tracts and their adjacent cortices. Seven bones/group were analyzed for differences between tracts in: first, microscopic trabecular bone packets and mineralization heterogeneity (backscattered electron imaging, BSE); and second, trabecular architecture (micro-computed tomography). Among the eight architectural characteristics evaluated [including bone volume fraction (BVF) and structural model index (SMI)]: first, only the 'tension' tract of immature bones showed significantly greater BVF and more negative SMI (i.e. increased honeycomb morphology) than the 'compression' tract of immature bones; and second, the 'compression' tracts of both groups showed significantly greater structural order/alignment than the corresponding 'tension' tracts. Although mineralization heterogeneity differed between the tracts in only the immature group, in both groups the mineral content derived from BSE images was significantly greater (P < 0.01), and bulk mineral (ash) content tended to be greater in the 'compression' tracts (immature 3.6%, P = 0.03; mature 3.1%, P = 0.09). These differences are much less than the approximately 8% greater mineral content of their 'compression' cortices (P < 0.001). Published data, suggesting that these small mineralization differences are not mechanically important in the context of conventional tests, support the probability that architectural modifications primarily adapt the tracts for local demands. However, greater hemi-osteonal packets in the tension trabecular tract of only the mature bones (P = 0.006) might have an important role, and possible synergism with mineralization and/or microarchitecture, in differential toughening at the trabeculum level for tension vs. compression strains.

Propriétés mécaniques de greffons humains provenant de têtes fémorales et traitées par un procédé d’épuration physico-chimique (Ostéopure™)

PURPOSE OF THE STUDY

Bone grafts and bone substitutes must be biocompatible osteoconductors with satisfactory mechanical properties similar to native bone. When the bone treatment is conducted under specific conditions, the elasticity module under infra-maximal loading can be optimized to achieve reproducible values. The purpose of this work was to determine the effect of the cleaning and sterilization process using Osteopure on the biomechanical properties of trabecular bone harvested from human femoral heads.

MATERIAL AND METHOD

Seventy trabecular bone samples were tested: group 1F (fresh samples); group 1N (after application of Osteopure cleaning); group 1S (after Osteopure cleaning and sterilization). Non-destructive and destructive tests (group 1D) were performed. Two fresh femoral heads were used as controls for the destructive test (group 2). The first non-destructive test was applied directly after section (group 1F). Other samples were then purified with Osteopure treatment and a second non-destructive test was conducted (group 1N). A third non-destructive test was conducted after sterilization with 25 kgray radiation (group 1S). Treatments 1 and 2 were performed by OST Developpement SA (Clermont-Ferrand). Finally a destruction test was applied along the directional axis (group 1D). For the 31 samples in group 2 (control) the destructive test was applied along the directional axis immediately after section. Compression tests were performed at a deformation speed of 3 mm/min for 0.3% deformation.

RESULTS

The Young module did not exhibit any significant difference between the three steps of the testing in the three orthogonal directions. The Young module was not significantly different between group 1F and group 2 (controls). Maximal force of compression was significantly different (P<0.01). There was a linear relationship between maximal force at rupture and the Young module obtained during destructive tests, for groups 1D and 2 respectively. The compression curves obtained from sterilized samples (group 1D) were not significantly different from those observed for fresh trabecular bone in group 2 (controls).

DISCUSSION

The Young module values measured from 70-673 MPa. For non-destructive tests, the module values were to the order of 64% of those obtained for destructive tests. Decreased maximal force of rupture observed for treated samples in comparison with fresh samples can be explained by the extraction of most of the lipids.

CONCLUSION

The Osteopure method does not alter stiffness of bone allografts. The elasticity module observed in treated bones is close to that observed in fresh bones. Mechanical resistance to compression is however only half the force of compression observed in the hip joint for daily activities. The linear relationship between the elasticity mode and loading required for rupture is not affected by treatment with Osteopure. The advantages related to elimination of prions or viral contamination appear by far to be more important than the minor changes observed in the mechanical characteristics of allografts.

Effects of end boundary conditions and specimen geometry on the viscoelastic properties of cancellous bone measured by dynamic mechanical analysis

The viscoelastic properties of cancellous bone can be measured nondestructively in compression testing using a dynamic mechanical analyzer. In this study, we examined the effects of end boundary conditions and specimen geometry on the viscoelastic properties of cancellous bone measured by dynamic mechanical analysis. During dynamic compression testing, the cancellous bone specimens may be mechanically fixed (e.g., glued) to the loading platens or they may be free to expand across the platen surface. When specimens of cancellous bone were tested between platens with gluing, the dependence of loss tangent on frequency was not consistent with previously observed strain-rate-dependent mechanical behavior of cancellous bone. When long specimens of cancellous bone (length = 10 mm, diameter = 8 mm) were tested without gluing, the relationship between loss tangent and frequency depended on the level of load applied. For short specimens (length = 5 mm, diameter = 8 mm) tested without gluing, however, the frequency dependence of loss tangent agreed with existing data reported for the strain-rate-dependent behavior of cancellous bone and also with the frequency dependence of cortical bone viscoelasticity. Therefore, we recommend that short cancellous bone cylinders with a length of 5 mm and a diameter of 8 mm should be used without gluing in the dynamic mechanical analysis of cancellous bone. This is consistent with the American Society for Testing and Materials testing recommendations for plastics, but different from current practice for unimodal mechanical testing of cancellous bone.

Modeling modulus reduction in bovine trabecular bone damaged in compression

Loading bone beyond its yield point creates microdamage, leading to reduction in stiffness. Previously, we related microdamage accumulation to changes in mechanical properties. Here, we develop a model that predicts stiffness loss based on the presence of microdamage. Modeling is done at three levels: (1) a single trabecula, (2) a cellular solid consisting of intact, damaged, and fractured trabeculae, and (3) a specimen with a localized damage band. Predictions of a reduced modulus agree well with experimental measured modulus reductions of post-yield compression of bovine trabecular bone. The predicted reduced modulus is relatively insensitive to changes in the input parameters.

Poroelastic properties of bovine vertebral trabecular bone

The theory of poroelasticity has been used to study bone mechanics without directly measuring poroelastic properties. In this study, we developed an experimental protocol and measured the poroelastic properties of bovine vertebral trabecular bone. Mean (+/-SD) values for drained shear modulus, drained Poisson's ratio, undrained Poisson's ratio, Skempton's coefficient, and permeability coefficient were, respectively, 90.85 (+/-59.59) MPa and 0.242 (+/-0.099), 0.399 (+/-0.083), 0.851 (+/-0.144), and 16.31 (+/-8.02) x 10(-8) m2/Pa/sec, respectively. The experimental protocol can be used generally for the measurement of poroelastic properties of bone when cylindrical specimens are available. Measured poroelastic properties can be used directly or converted to Biot's coefficient and modulus, without assuming the incompressibility of solid and fluid constituents, for the poroelastic modeling of bone.

Predictive value of bone mineral density and Singh index for the in vitro mechanical properties of cancellous bone in the femoral head

OBJECTIVE

The purpose of this study was to assess the validity of two methodically different radiological parameters, bone mineral density and Singh Index, for the prediction of mechanical properties in femoral cancellous bone.

DESIGN

Coherence between in vitro evaluation of mechanical properties and bone mineral density on a femoral bone slice, combined with clinical determination of Singh Index on ordinary X-rays.

BACKGROUND

It is accepted that bone densitometry yields excellent prediction of mechanical bone quality, but is considered to be an expensive and not widely available method for routine diagnostics in clinical practice. In contrast, determination of Singh Index is an inexpensive and simple technique, but its predictive value for bone mechanics is still controversially discussed.

METHODS

We used cortically confined bone slices from 33 femoral heads. Bone mineral density was measured using quantitative computed tomography. Strength and elastic modulus were assessed by mechanical testing in up to 39 circular positions on each slice. Singh Index was evaluated on ordinary X-rays of the hip by two independent readers.

RESULTS

Bone mineral density showed strong correlations with strength (r=0.86) and good correlations with elastic modulus (r=0.68). Singh Index correlated well with strength (r=0.70), but only moderately with elastic modulus (r=0.52).

CONCLUSIONS

The strong validity of bone mineral density in predicting mechanical bone quality was confirmed. Singh Index assessment permits a rough estimation of mechanical strength in particular and can therefore be used for first estimations of mechanical bone quality, provided that readings were performed by experienced clinicians.

RELEVANCE

Reduced mechanical bone quality induces an increase in fracture risk. Whenever performed, bone mineral density measurement allows an excellent evaluation of the mechanical properties of cancellous bone in the hip and can be recommended for screening evaluations. The assessment of Singh Index on ordinary X-rays of the hip is an inexpensive and simple method, and allows a rough estimation of the mechanical quality of the femur. However, due to its subjective character, its predictive value for the mechanical quality of bone in individual patients remains uncertain.

Material properties assignment to finite element models of bone structures: a new method

Finite element analysis (FEA) is widely adopted to investigate the mechanical behaviour of bone structures. Computed tomography (CT) data are frequently used to generate FE models of bone. If properly calibrated, CT images are capable of providing accurate information about the bone morphology and tissue density. The aim of this work was to develop a special program able to read a CT data set as well as the FEA mesh generated from it, and to assign to each element of the mesh the material properties derived from the bone tissue density at the element location. The program was tested on phantom data sets and was adopted to evaluate the effects of the discrete description of the bone material properties. A three-dimensional FE model was generated automatically from a 16 bit CT data set of a distal femur acquired in vivo. The strain energy density (SED) was evaluated for each model element for increasing model complexity (number of different material cards assigned to the model). The computed SED were strongly dependent on the material mapping strategy.

Ultrasonic determination of the elastic modulus of human cortical bone

The elastic modulus (Cii) of the cortical bones of 19 individuals (14 femurs and 16 tibias, fixed in formalin) was determined ultrasonically. Elastic moduli were measured at four anatomical positions (anterior, posterior, medial and lateral) and in all three planes of orientation (transverse, longitudinal and radial). The mean tibial Cii (34.11 GPa) was greater than that obtained for femurs (32.52 GPa). The tibial longitudinal plane Cii (34.1 GPa) was significantly greater than the femoral longitudinal plane Cii (32.5 GPa). Cii was significantly higher in the tibia than the femur in both the medial and posterior anatomical positions. The anterior tibia had a significantly lower C11 compared to other positions. Cii was significantly higher in the longitudinal plane than the transverse or radial planes in both the femur and the tibia. There was no consistent difference in modulus between left and right sides. No age effects were observed. There were no significant differences between males and females, or between African Americans and European Americans.

Biomechanical analysis of tension band fixation for olecranon fracture treatment

This study assessed the strength of various tension band fixation methods with wire and cable applied to simulated olecranon fractures to compare stability and potential failure or complications between the two. Transverse olecranon fractures were simulated by osteotomy. The fracture was anatomically reduced, and various tension band fixation techniques were applied with monofilament wire or multifilament cable. With a material testing machine load displacement curves were obtained and statistical relevance determined by analysis of variance. Two loading modes were tested: loading on the posterior surface of olecranon to simulate triceps pull and loading on the anterior olecranon tip to recreate a potential compressive loading on the fragment during the resistive flexion. All fixation methods were more resistant to posterior loading than to an anterior load. Individual comparative analysis for various loading conditions concluded that tension band fixation is more resilient to tensile forces exerted by the triceps than compressive forces on the anterior olecranon tip. Neither wire passage anterior to the K-wires nor the multifilament cable provided statistically significant increased stability.

Anatomic and directional variation in the mechanical properties of the mandibular condyle in pigs

Stereologic studies of trabecular architecture suggest that the pig mandibular condyle is strongest when loaded supero-inferiorly, and that stress is concentrated in the antero-inferior region (Teng and Herring, 1995). To test these hypotheses, we investigated the uni-axial mechanical properties of 22 pig mandibular condyles in three loading directions at a mean strain rate of 0.14 (+/- 0.12)% s-1. A total of 91 rectangular beam specimens (averaging 9.0 mm x 6.0 mm x 5.0 mm) was tested. For each specimen, 5 or 6 non-destructive tests were performed before compressive failure. Strain in both longitudinal and transverse directions was measured by foil strain gauges on the central part of the specimen. Data were normalized at a strain rate of 0.1% s-1, specimen length of 9 mm, and cross-sectional area of 30.25 mm2. Generally, modulus of elasticity (E) and ultimate stress (sigma u) in the anterior regions of the condyle were greater than those in the posterior. E, sigma u, and Poisson's ratio (upsilon) were significantly different among the test directions, but ultimate strain (epsilon u) was not. The highest values of E (4.04 GPa), sigma u (14.97 MPa), and rho (0.81 g/cm3) were seen in the anterior inferior/middle region under supero-inferior loading. The lowest values (0.94 GPa for E, 2.38 MPa for sigma u, and 0.52 g/cm3 for rho) were found in the inferior/posterior region in medio-lateral loading. Although the mechanical properties of the condyle vary depending upon location, these results verify that the condyle is strongest and stiffest under compressive loads in the supero-inferior direction, and that the anterior-inferior region is particularly strong and stiff.

Postfailure compressive behavior of tibial trabecular bone in three anatomic directions

To obtain information describing the postfailure behavior of human proximal tibial trabecular bone, cube specimens of bone were mechanically tested in compression beyond the point of failure. Tests were performed in the three anatomic directions, plots of stress versus strain were obtained, and measures to describe the stress-strain relations before, during, and after failure were defined. These measures included elastic modulus, strength, postfailure slope, strain during maximum stress, and first postfailure minimum stress. For each anatomic direction, analyses were performed to correlate these parameters with ash density. Each of these measures was significantly correlated with ash density at the p < 0.05 level for all test directions, except for postfailure slope, which was correlated in the mediolateral and superior-inferior directions, and strain during maximum stress, which was correlated only in the superior-inferior direction. The data from this study enable trilinear stress-strain relations to be estimated for proximal tibial trabecular bone of various densities, and can serve as a first step toward modeling the behavior of trabecular bone before, during, and after failure.

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 percent 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 percent of the variance in modulus and 50-60 percent 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.

Relations of mechanical properties to density and CT numbers in human bone

Mechanical properties of cortical and cancellous bone from eight human subjects were determined using an ultrasonic transmission technique. Raw computerized tomography (CT) values obtained from scans of the bones in water were corrected to Hounsfield units. The correlations between CT numbers and mechanical property estimated from cortical bone were found to be low (r2 < 0.2), while these relationships for cancellous bone were found to be higher (r2 > 0.6). These results suggest that CT values may be useful in predicting mechanical properties only for cancellous bone. Poor correlations were found between modulus in the radial or circumferential direction and modulus in the superior-inferior direction for cortical bone, whereas good correlations were found between modulus in the anterior-posterior direction or medial-lateral direction and modulus in the S-I direction for cancellous bone. These results indicate that modulus in the radial or circumferential direction could not be predicted from modulus in the S-I direction for cortical bone, but could be predicted for cancellous bone. The predictive capabilities of linear and power models evaluated for cancellous bone alone were approximately equal. However, the power function gives a better fit of data at the low and high density values. The specific relationships, depending on the types of bone, that predict elastic modulus from density and CT numbers were suggested for human cortical and cancellous bone. These specific correlations may help a number of researchers develop more accurate models; however, these hypotheses should be proven by further study.

Femoral component migration in total knee arthroplasty: randomized study comparing cemented and uncemented fixation of the Miller-Galante I design

The Miller-Galante I knee replacement was inserted in 25 women and three men (33 knees) with osteoarthrosis. All patients received a TiAlV femoral component with a commercially pure titanium fiber-mesh undersurface. Cemented or cementless fixation was used based on a randomization protocol. Micromotions of the femoral components were recorded with roentgen stereophotogrammetric analysis during the first 2 postoperative years. The magnitude of migration did not differ between cemented and uncemented fixation. The number of nonmigrating prostheses decreased from 21 (12 cemented and nine uncemented) at 3 months to six (three cemented and three uncemented) at 24 months. In both groups, the magnitude of prosthetic tilting about the longitudinal axis (internal-external rotation) was as large as that about the transverse axis (flexion-extension). Rotation into extension was as common as rotation into flexion. The largest translations were recorded at either of the posterior condyles. In 10 uncemented components, radiolucent lines were seen at the distal interface postoperatively. Proximal migration of the femoral component was recorded in these knees, and the width of the lines decreased or the lines disappeared totally at 24 months. After 2 years, lines were noted around four cemented and four uncemented replacements, mainly anteriorly or distally. All of these prostheses migrated. One prosthesis, revised because of malalignment, displayed pronounced migration after an initial period of stability. Bone ingrowth was observed anteriorly and anterodistally despite the presence of motions of 1 mm or more.

Stress relaxation behaviour of trabecular bone specimens

The present study defines several conditions under which stress relaxation tests can be performed and investigates the viscoelastic behaviour of trabecular bone in compression through a series of stress relaxation tests at three strain levels and in three loading directions of each cubic specimen. A viscoelastic model is proposed to characterize the behaviour of trabecular bone and a spectrum of relaxation times is determined. Trabecular bone from the femoral head is non-linearly viscoelastic and displays anisotropic behaviour, which cannot be more symmetric elastically than orthotropic.

Predicting the compressive mechanical behavior of bone

The principal objectives of this study were to determine the mathematical dependency of the compressive mechanical properties of human bone on several commonly used measures of bone composition, and to assess variations in this dependency based upon the composition range spanned by the data. Destructive mechanical tests were conducted along the superior-inferior axis of 496 cubic specimens of human trabecular and cortical bone from five male donors (ages 46-84 yr), including specimens from lumbar vertebrae and femoral metaphyses and diaphyses. There was over a 3000-fold variation in strength (S, ultimate stress) and over a 20,000-fold variation in stiffness (E, elastic modulus) over the range of apparent dry density (rho a = 0.05-1.89 g cm-3), apparent ash density (rho alpha = 0.03-1.22 g cm-3) and mineral content (alpha = 17.4-66.2%) examined. Both linear and power models produced very high correlations (R2 > 0.81) between mechanical properties and bone composition, but the linear models resulted in a much greater percent deviation (PD) of the predicted dependent variable with respect to the measured value, in comparison to power models. The best correlations were obtained using rho alpha as the only independent variable: S (MPa) = 117 rho alpha 1.93 +/- 0.04 (R2 = 0.969, PD = 29.9, E (GPa) = 10.5 rho alpha 2.57 +/-0.04 (R2 = 0.965, PD = 46.7). Power models of bone stiffness and strength, incorporating only low density data (rho alpha < 0.2 g cm-3, rho a < 0.3), were characterized by approximately squared exponents and these models underestimated the stiffness (five-fold) and overestimated the strength (two-fold) for higher density data, which were characterized by exponents greater than two. Using a subset of the data based upon an apparent dry density range of 0.22 < rho a < 1.89 g cm-3, it was possible to obtain a mathematical relationship in which bone stiffness and strength were precisely proportional to the cube and square, respectively, of the apparent dry density. These results indicate that the mathematical dependency of bone compressive mechanical properties on composition is closely dependent upon the density and mineral content range examined and, in terms of a single compositional measure, is best predicted by apparent ash density expressed as a power function.

Bone strength and histomorphometry of the distal femur

The ultimate bone strength of the distal femur was measured radially, by indentation testing, around the transepicondylar line in 3 mm depth steps up to 12 mm below the subchondral bone plate. Specimens from 10 cadavers were used. This orientation of specimens was chosen as a way to provide measurement in a more physiologic orientation for load bearing and to standardize the assessment. Bone hardness declined sharply over the first 6 mm below the surface, tending to plateau at deeper levels. Within the top 6 mm layer the lateral condyle was softer than both the medial condyle and the central patellofemoral area (P < .05), but at deeper levels it maintained greater hardness. Of the histomorphometric parameters, those showing the greatest consistent correlation with hardness were bone volume fraction and trabecular separation. When the tibiofemoral and patellofemoral compartments were compared it was found that for a given value of bone volume fraction, condylar bone is marginally harder than patellofemoral bone. The data are relevant to the design of implants that match their geometric and material properties to the shape and strength of the underlying bone.

Comparison of mechanical properties of human, bovine bone and a new processed bone xenograft

The study compared the mechanical properties of human bone, fresh bovine bone and a new highly purified bone xenograft: T650 (Lubboc-Laddec). Destructive, compressive tests were performed to determine Young's modulus and ultimate strength, with a constant deformation rate of 0.025 mm min-1. The stress-strain curves obtained from all the non-human specimens especially the T650, did not differ significantly from those observed with human bone. Human and fresh bovine samples presented a significantly different Young's modulus. The T650 samples, depending upon their trabecular texture (dense or medium) also differed significantly from each other (132.9 +/- 52.3 versus 80.0 +/- 37.3 MPa, P < 0.05). Their moduli were similar to those of bovine and human cancellous bone, respectively (117.49 +/- 61.53 versus 77.36 +/- 54.96. P < 0.05). The ultimate strength of T650 dense (9.6 +/- 3.7 MPa) was similar to bovine (8.5 +/- 4.2 MPa) and human bone (8.78 +/- 5.2 MPa): the T650 medium (5.9 +/- 2.8 MPa) was significantly different from the other specimens.

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens was studied by non-destructive uniaxial compression to 0.4% strain using cylindrical specimens with different sizes and length-to-diameter ratios, and by comparing cubic and cylindrical specimens with the same cross-sectional area. Both the length and the cross-sectional area of the specimen had a highly significant influence on the mechanical behaviour (p less than 0.0001). Within the actual range of length (2.75-11.0 mm) the normalized stiffness (Young's modulus) was related nearly linearly to the specimen length. This dependency on specimen length is suggested to be caused mainly by structural disintegrity of the trabecular specimens near the surface. The normalized stiffness (Young's modulus) was also positively correlated to the cross-sectional area. This dependency on cross-sectional area is probably due to friction-induced stress inhomogeneity at the platen-specimen interface. A cube with side length 6.5 mm or a cylindrical specimen with 7.5 mm diameter and 6.5 mm length are suggested as standard specimens for comparative studies on trabecular bone mechanics.

Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography

We evaluated the orthogonal mechanical properties of human trabecular bone from the major metaphyseal regions with materials testing and quantitative computed tomography (CT). The proximal tibia, distal femur, proximal femur, distal radius, and proximal humerus from fresh cadaver specimens between the ages of 55 and 70 years were excised and prepared for experimentation. The bones were embedded and scanned at 1 or 1.5 mm intervals on a Technicare HPS 1440 and GE 9800 CT scanner. After scanning, the bones were sectioned, producing 8-mm cubes of trabecular bone which were mechanically tested in uniaxial compression at a strain rate of 1%. The testing sequence consisted of preyield tests in two of the three orthogonal directions and failure in the third. After testing, the cubes were evaluated for apparent density and ash weight. The results of the study show that the strength and stiffness of trabecular bone varies significantly within metaphyseal regions and from metaphysis to metaphysis. The power and significance of relationships between density and modulus varied as a function of metaphyseal location. Both linear and nonlinear models were significant, suggesting that trabecular deformation occurs in response to both axial and bending loads. Finally, the need for architectural measures of trabecular bone to predict mechanical properties is emphasized.

Mechanical properties of trabecular bone. Dependency on strain rate

The effect of strain rate (epsilon) and apparent density (rho) on stiffness (E), strength (sigma u), and ultimate strain (epsilon u) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s-1. Apparent density ranged between 0.23 and 0.59 g cm-3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables (Y) and strain rate and apparent density as independent variables were performed using the following models: Y = a rho b epsilon c, Y = rho b(a + c epsilon; Y = (a + b rho)epsilon c, Y = a rho 2 epsilon c, E = a rho 3 epsilon c. The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent = 0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.

Tensile and compressive properties of cancellous bone

The relationship between the mechanical properties of trabecular bone in tension and compression was investigated by non-destructive testing of the same specimens in tension and compression, followed by random allocation to a destructive test in either tension or compression. There was no difference between Young's modulus in tension and compression, and there was a strong positive correlation between the values (R = 0.97). Strength, ultimate strain and work to failure was significantly higher in tensile testing than in compressive testing.

Non-linear three-dimensional finite element analysis of a cementless hip endoprosthesis

In this finite element study the stresses between a stem component of a cementless hip endoprosthesis (Young modulus of Co-Cr-Mo) and the human femur were calculated for two different loading types. Linear and non-linear models were used to simulate the interface implant bone. Two models, a stem with a porous coated surface over the entire length and a stem with a porous coated surface in the proximal region were compared regarding the load transmission to the femur. An additional calculation of an 'isoelastic' stem (Young modulus of cortical bone) was done to show the influence of the stem stiffness. A porous coated surface over the entire length causes principal shear stresses up to 2.75 MPa in the distal-medial region during level walking. The highest compressive stresses were calculated in the proximal-lateral region as 1.5 MPa in cancellous bone. A more physiological load transmission is obtained by limiting the coated area to the proximal region. All stresses in the two models are lower than experimentally evaluated strengths in the interface between implant and bone. A strong influence of the Young modulus of the stem material on the interface stresses was found. An 'isoelastic' stem causes compressive stresses in the proximal-lateral region whose values exceed the experimental strength of cancellous bone.

X-ray quantitative computed tomography: the relations to physical properties of proximal tibial trabecular bone specimens

Cylindrical bone specimens from the proximal epiphysis of ten normal human proximal tibiae were randomly assigned to a destructive axial compression test-series (N = 94) or to a protocol of standardized mechanical conditioning followed by non-destructive repeated testing to 0.6% strain and a final destructive test (N = 121). Specimen X-ray quantitative computed tomography (QCT) obtained at different scanning energies (100, 120 and 140 kVp) yielded closely related results (r = 1.00). Accordingly, predictions of physically measured densities or mechanical properties were not improved by using more than one scanning energy. QCT and physically measured densities were intimately related (QCT at 140 kVp to apparent density using linear regression: r = 0.94, and to apparent ash density: r = 0.95) and did not differ significantly in their ability to predict the mechanical properties, thus favouring the more easily implemented QCT for routine work. Evaluation of the relation of apparent density to Young's modulus and ultimate strength suggested that a power law regression model is preferable to a linear model, although linear model prediction of mechanical properties does not have significantly worse accuracy within the narrow density range investigated. The effect of conditioning on the behaviour of bone specimens subjected to destructive compression tests was to increase the stiffness and strength by approximately 50 and 20% respectively.

The effect of constraint on the mechanical behaviour of trabecular bone specimens

The effect of the boundary conditions between trabecular bone specimens and the test columns of the testing machine was studied together with the effect of side-constraint on the mechanical behaviour of trabecular bone during axial compression. Cylindrical specimens taken from the upper tibial epiphysis of autopsy knees were tested non-destructively by cyclic compression to 0.8% strain under different conditions. Fixation of the specimens to the test columns by a thin layer of bone cement increased the stiffness by 40% and reduced the energy dissipation to 67% of those measured under unconstrained conditions (p less than 0.001). The thin cement layer alone increased the stiffness 19% and reduced energy dissipation to 86% (n.s.). When the machine was equipped with polished steel columns coated by a film of low-viscous oil, both the stiffness and the energy dissipation were reduced to 93% of those measured under standard conditions (p less than 0.005). Trabecular bone specimens tested side-constrained by the surrounding trabecular bone (in situ) showed a 19% larger stiffness than that measured during later testing of the corresponding machined specimens (p less than 0.005) whereas the energy dissipation was not altered significantly. The same specimens showed a 22% increase of stiffness and a 68% increase of energy dissipation when they were side-constrained by a closely fitting steel cylinder (p less than 0.005).

Compressive axial strain distributions in cancellous bone specimens

The compressive axial strain distribution in cylindrical trabecular bone specimens was studied using digitized images of the specimen surface. Specimens were tested with strain rate 0.00015 s-1. Images were taken at 0, 1, 2, 3, 4, 6, 8 and 10% strain. Using an optical illusion of movement by rapidly changing succeeding images, failures were classified as transverse (33%) or oblique collapses (67%). The location of failure was not determined by the specimen density gradient. Local axial strain in the distal, intermediate and proximal third was measured throughout the compression in the transversely failing specimens, whereas local strain in the obliquely failing specimens was measured in the pre-failure phase only. Axial strain inhomogeneity was observed in the pre-failure as well as in the post-failure phase. In the pre-failure phase the intermediate third was strained significantly less than the thirds near the ends. In the post-failure phase specimen strain occurred solely in the collapsed part. Ultimate strain of the transversely failing specimens was 2.5% and ultimate strain of the failing third was 3.7%. At failure less than 1% strain was observed in the intermediate third and at 10% specimen strain 1.5% local strain was found in the intermediate third. The results indicate unreliability of conventional stiffness and strain measurements in trabecular bone specimens probably due to lack of trabecular constraint at the end surfaces. Conventional measurements tend to underestimate stiffness and, by giving an average value of strain in spite of considerable strain inhomogeneity, to underestimate failure strain.

The limitations of canine trabecular bone as a model for human: a biomechanical study

Distal canine femurs were sectioned into 8 mm cubic specimens. Orthogonal compression tests were performed to preyield in two or three directions and to failure in a third. Apparent density and ash weight density were measured for a subset of specimens. The results were compared to the human distal femur results of Ciarelli et al. (Transactions of the 32nd Annual Meeting of the Orthopaedic Research Society, Vol. 11, p. 42, 1986). Quantitative similarities existed in the fraction of components comprising the trabecular tissue of the two species. Qualitative similarities were seen in the positional and anisotropic variation of the mechanical properties, and also in the form and strength of the relationships between the mean modulus and bone density, ultimate stress and density, and ultimate stress and modulus. However, significantly different regression equations resulted for the mean modulus-density, and ultimate stress modulus relationships, indicating that for the same density, canine trabecular bone displays a lower modulus than human, and may achieve greater compressive strains before failure.

Mechanical properties of trabecular bone by a non-destructive compression testing approach

In order to optimize non-destructive mechanical testing of trabecular bone specimens, different techniques were analysed, and correlations were established between properties derived from such non-destructive testings and those derived from destructive testing. Non-destructive testing to a fixed percentage of predicted ultimate stress was hampered by inaccuracy of this prediction. Simulation of non-destructive testing conducted to the linear' part of the compression curve using a drop of the increase of the stiffness (slope of the compression curve) below a certain value as stop criterion revealed strong correlations ( r: 0.97–0.99) between the stiffness at the stop point and modulus of elasticity derived from destructive testing. However, trabecular damage will probably occur during such testing because high strain values were obtained. Testing to a fixed strain (0.6 per cent) also revealed strong correlation between the stiffness at the 0.6 per cent strain level and modulus of elasticity ( r = 0.96) derived from destructive testing. By this technique trabecular damage was avoided and standardized elastic and viscoelastic energies could be obtained. Prediction of modulus of elasticity by indirect methods such as modulus of elasticity of specimens from the opposite symmetric location ( r = 0.73), bone mineral concentration ( r = 0.72) derived from photon absorptiometry and the CT number ( r = 0.78) derived from quantitative computed tomography showed less strong correlations.

Sex differences in age-related remodeling of the femur and tibia

Changes with age in cross-sectional geometry of the lower limb bones were investigated in a large sample of cadaveric skeletal material from U.S. white adults. Section properties (areas and second moments of area) were determined at 11 locations by sectioning and direct measurement of 103 femora and 99 tibiae. All properties were standardized for body size differences by dividing by powers of bone length, and age trends were determined through linear regression analysis. Results indicate that while both men and women undergo endosteal resorption of bone and medullary expansion with aging, only men exhibit concurrent subperiosteal bone apposition and expansion. As a consequence, men show little change in cortical area and some increase in second moments of area with age, while women show decreases in both cortical area and second moments of area. Thus, only men appear to remodel bone in a way that would tend to compensate for loss of bone material strength with aging. In a previous study of a preindustrial sample with high activity levels, both men and women exhibited bone subperiosteal expansion and increase in second moments of area with aging. Together with observed differences in fracture incidence among living populations, these findings suggest that relatively low activity levels may not stimulate optimal bone remodeling throughout life and thus may contribute to higher risk of fracture in old age.

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.

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 < 0.005) and r = 0.99 ( p < 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.