Ebook: Bone Research in Biomechanics

This book is a collection of papers, based on the communications held at the 10th Conference of the European Society of Biomechanics, which took place at Leuven, Belgium, 28-31 August, 1996. The presentations were held at three symposia: “Validation of Computer Simulations of Bone Adaptation”, “Bone Architecture and the Competence of Bone” and “Ultrasound Research in Bone”.

All presentations in this book focus on the structure of bone, and the consequences for its mechanical behaviour. This field of research has a long history, dating back to the work of Wolff, and can be described by the question: “Why does bone possess the shape and structure it actually has?”. Such a question is far from purely academic, but can have important consequences in the fields of orthopedics and metabolic bone disease research.

The papers of the first symposium can be considered as the computer-age translation of issues raised by Wolff himself. They focus on the development of models predicting the adaptation of bone due to changes in the mechanical loading situation (such as those provoked by an implant). But, far more important than the computer power presently available, the incorporation of knowledge of biological processes has led to a new kind of models. Next to the development of models itself, the issue of model validation through comparison with clinical data is a main issue addressed in the papers of this symposium.

The papers of the second symposium, dealing with the relationship between bone architecture and competence of bone, focus on the morphology of trabecular bone structure. This work is mainly carried out in the context of research on osteoporosis, and looks for the relationship between bone structure and fracture risk. The progress made during the past years in high resolution imaging techniques opens new and fascinating perspectives for the assessment of bone structure. These three-dimensional representations of bone structure also call for new assessment methodologies. Whereas nowadays conventional morphometric techniques are adopted in most cases, it is likely that these new imaging techniques will intensify the search for new and better descriptors of bone structure.

The papers of the third symposium are devoted to ultrasound research in bone biomechanics. Ultrasound measurements are gaining clinical interest, since it is expected that they reflect to a certain extent the structural bone properties. Several methods have been described for the in vitro and in vivo measurement of ultrasound velocity and attenuation, both on cortical and on trabecular bone. As such, they could offer an alternative to the high resolution radiographic techniques, which are not yet fully applicable in vivo. However, next to their in vivo use, ultrasonic techniques are available at the microscopic level too, revealing information on the elastic properties at the bone tissue level.

When reading this book, the reader will not only discover the state-of-the-art of research of bone structure, but it is also our belief that in some respects a new direction has been taken. Firstly, there is an intensified research into the biological processes involved in the bone adaptation mechanism, and its results are now being implemented in a new generation of adaptation models. Secondly, with regard to structural assessment, it can be expected that the three-dimensional investigation of bone structure will lead to new insights in the mechanical integrity of bone. Therefore, we hope that this book will also give a taste of the fascinating perspectives which the research in bone biomechanics still has to offer, even after more than 100 years.

G. Lowet, P. Rüegsegger, H. Weinans and A. Meunier

Editors

Periprosthetic bone adaptation around orthopaedic implants can be studied with Finite Element models. It requires a comparison between the mechanical status of the bone in the operated (unnatural) situation and the natural situation. The difference between these two situations is the alteration in mechanical condition of the bone, which is assumed to be the driving force of the adaptation process. The time dependent bone adaptation process can be simulated with a computer algorithm by an iterative (time stepping) procedure. This study reviews some clinical and experimental issues, it addresses the value of computer models of periprosthetic bone adaptation and discusses a new development of voxel based models directly converted from CT scans.

The cross-sectional growth and development of the long bone diaphysis is strongly influenced by in vivo mechanical loading. An analytical approach was developed to model these mechanobiologic influences. First, human growth under normal loading conditions was modeled. Our model predictions were validated by comparison to human data obtained during adolescence. Next, skeletal adaptation during growth under altered loading conditions was examined using an animal model. Rat hindlimb suspension experiments were performed and femoral adaptation to reduced loading during growth was measured and compared to normal controls. Then our model predictions of adaptation during growth were compared directly to our experimental data.

Bone fractures are major problems for osteoporosis patients. To avoid such fractures, more information is needed about the factors that determine the bone fracture risk. In this chapter, it is discussed how recently developed finite element computer models that can represent the trabecular architecture in full detail can provide such information. It is concluded that a computer modeling approach to this problem is feasible, required and promising. It is expected that, eventually, such models can be used as a basis for an accurate diagnosis of the bone fracture risk.

Using computer models based on Finite Element Analysis (FEA), Wolff's paradigm of mechanically-controlled adaptive bone remodeling can be simulated. These simulation models use empirical mathematical rules that describe the assumed relationships between local bone loads and bone mass. These models are particularly valuable for preclinical testing of orthopaedic implants, relative to their bone-maintaining capacities. In this Chapter the question of validity of these models for these purposes is considered. Furthermore, an overview is presented of validation studies that were performed by the research group of the author.

The structural properties of trabecular bone have been shown to vary significantly with age, anatomic location, and metabolic condition. Micro-computed tomography (μCT) is an emerging technique for the nondestructive assessment and analysis of the three-dimensional trabecular bone architecture. Within the framework of the European Union BIOMED I project “Assessment of Bone Quality in Osteoporosis”, a total of 350 bone biopsies from five different anatomical locations were harvested post mortem from 70 donors (aged 23 to 92 years). These biopsies were measured using a newly devised compact micro-tomographic system, also referred to as desk-top μCT. Samples with a diameter from a few millimeters to a maximum of 18 mm and a length of up to 55 mm can be measured. For this study fresh, untreated bone biopsies with a diameter of 8 mm were measured micro-tomographically with a nominal isotropic resolution of 14 μpm. For all samples, the volumes of interest (4 × 4 × 4 mm³) were binarized using a uniform threshold. Subsequently, standard structural indices such as bone volume density (BV/TV), bone surface density (BS/BV), trabecular plate number (Tb.N), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp) and the degree of anisotropy (DA) were computed for all specimens incorporating mean intercept length (MIL) measurements. Regression analysis was used to estimate the correlations of single structural parameters with age or with a second parameter and also among different measurement sites. The nondestructive μCT measurements allowed not only to perform quantitative bone morphometry but also to assess other important microstructural features in the determination of the mechanical integrity of trabecular bone such as the incidence and prevalence of microcallus formations. The findings from the BIOMED I study are expected to improve our understanding of the relative importance of bone architecture, damage accumulation, and bone mineralization in the characterization of bone quality in the progress of age- and disease-related bone loss.

Although bone mineral density is one of the most important contributing factors to bone strength and risk of fracture, studies have shown that changes in bone quality and structure independent of bone mineral density, influence both bone strength and individual risk of fracture. The influence of these other factors is thought to explain at least partially the observed overlap in bone mineral measurements between patients with and without osteoporotic fractures, irrespective of measurement site or technique. Thus, several new emerging techniques have been aimed at quantifying trabecular bone structure in addition to bone density. With recent hardware and software advances magnetic resonance (MR) images with spatial resolutions of 80 - 150 μm and slice thickness of 300 - 700 μm which resolve the trabecular structure have been obtained both in vitro and in vivo. Both modified spin-echo and gradient echo based imaging sequences have been used to obtain these images, and although the technical parameters and the sequence specific mechanisms affect the depiction of trabecular bone. In conjunction with three dimensional image processing and an understanding of the mechanisms of image formation, these high resolution images may be used to quantify trabecular bone architecture. In addition to obtaining standard stereological measures such as trabecular bone volume, mean trabecular width, mean trabecular spacing, mean intercept length as a function of angle, parameters such as three dimensional connectivity as measured by the Euler number, fabric tensor in three dimensions and texture related parameters such as fractal dimension may be derived from such images. Quantitative measures of trabecular architecture derived from such images have been compared with those obtained from higher resolution 18 μm images, and with biomechanical properties. In vivo studies in the radius and calcaneus have been performed and differences between osteoporotic and normal subjects are distinguishable. Thus, MR imaging techniques coupled with computerized image analysis may potentially be very useful for studying osteoporosis and quantifying trabecular bone architecture and may provide information in addition to bone density.

Most standard methods to predict bone quality are merely based on apparent density measurements. However, apparent density alone does neither explain all variation of the mechanical properties nor does it account for the structural anisotropy of trabecular bone. Thus, apparent density alone might not be sufficient to accurately predict the quality of bone. This study investigates if a new approach based on microstructural computer models can provide additional and relevant information on bone quality.

58 human trabecular bone samples from the femoral head were measured with a 3-D micro-Computed Tomography (micro-CT) system providing a voxel representation of the bone microarchitecture with a resolution of 28 μm. Based on such representations, the orthotropic stiffness matrices and the principal directions were computed for 5 mm cubes with microstructural Finite Element Analysis (FEA). For a subset of six samples the moduli were then validated with tri-axial mechanical compression tests. The results show that on average 15% of the variation of the elastic properties are not explained by bone volume fraction. Differences of elastic properties between samples with the same bone volume fraction range up to 53%. The variation of the degree of anisotropy is unrelated to that of the bone volume fraction. Finally, the direction-dependent stiffness of the trabecular bone differs by a factor of four, indicating that one single (isotropic) modulus as predicted from apparent density measurements might not be adequat. It is concluded that micro-CT-based FEA provides new and additional information about anisotropy and mechanical properties in a direct and non-destructive way, and thus will be important in the future for advanced failure risk prediction. An extension to patient examinations using high-resolution CT or MRI techniques is envisaged.

An Olympus UH3 Scanning Acoustic Microscope (Tokyo, Japan) has been used in the burst mode at 400 and 600 MHz to study the elastic properties of osteons and osteonic lamellae in both canine and human compact cortical bone. The nominal resolution at each frequency is within the width of an individual lamella. Three important new observations have been made regarding the acoustic properties of individual lamellae. Firstly, the acoustic impedance, as measured by shade of gray levels, of the outer most lamellae of adjacent osteons interdigitate (blend) although the structures, as determined by backscatter scanning electron microscopy, are seen to be quite separate. Secondly, in almost every osteon observed in this study, the shade of gray level for individual lamellae appear to alternate-dark, light etc. - translating to alternating compliant, stiff lamellar units respectively. Thirdly, the outermost lamella of each osteon appears to be the most compliant (darkest gray level). A preliminary SAM study of sheep femoral trabecular bone has shown the some alternation of lamellar gray levels as observed in osteonic lamellae.

Results on the ultrasonic wave propagation in porous materials are presented with emphasis on the measurement of acoustic parameters and on the discrepancy between experimental results and theoretical predictions for the attenuation at high frequencies. This discrepancy can be observed in Biomedical Engineering where the propagation in different sorts of bones is studied as well as in the fields of Geophysics and Material Science. In the present study, the slow wave propagation in polyurethane foams saturated by different gases is investigated in a frequency range of [70-800 kHz]. Methods are presented to determine the tortuosity and the viscous and thermal characteristic lengths. The experimental results, obtained using standard ultrasonic and vacuum equipments, show that an excess attenuation occurs when the wavelength is not sufficiently large compared to the lateral dimensions of the fibers. This effect constitutes a limit of the classical models of equivalent phases. It is evaluated with the help of a model of ultrasonic scattering. A numerical simulation of osteoporosis using Biot's model is also presented.

The aim of the study was to assess mechanical properties of human cancellous bone in vitro. Six hundred cubic specimens of cancellous bone were obtained from the tibia, femur, patella, lumbar spine and humerus of eight subjects. The elastic properties were assessed using an ultrasonic transmission technique developed and validated by Ashman (1). The results showed that differences exist between subjects significantly (p<0.05) and that the mechanical properties vary along the length and the periphery (about a factor 3 to 5). Cancellous bone should be considered heterogeneous and as orthotropic materials exhibiting degrees of anisotropy varying from 2 to 4. Linear and power fit elationships for cancellous bone were found approximately equal. Powers vary from 1.3 to 1.7 for axial modulus versus density and 1.3 and 2.3 for strength versus density.

Finally, these results suggest the use of appropriate mechanical properties upon the type of bone for finite element analysis.

This paper describes our recent findings on the relationships between ultrasonic measurements (velocity and broadband ultrasonic attenuation) and some physical properties of human and bovine cancellous bone (density, trabecular orientation and Young's modulus of elasticity). We have found velocity to be an extremely effective measure of Young's modulus (R² ≈ 95%). When velocity is combined with a measure of apparent density R² improves to approximately 97%. We demonstrate that this is due to the ability of ultrasound velocity to measure structural anisotropy in the tissue.

The findings for broadband ultrasonic attenuation (BUA) are more complex. In the same specimens BUA is not as good as velocity at predicting Young's modulus (R² ≈ 62%). We demonstrate that this is due to a non-linear relationship between BUA and tissue density (porosity). However there is a strong indication that BUA is also affected by variation in cancellous structure.

The measurement of ultrasound velocity is gaining increasing interest in clinical and biomedical research. Its applications are mostly in the quantitative assessment of fracture healing, and in the study of the effect of osteoporosis on the bone mechanical properties. We will give an overview of the studies that have been made in the past, aiming at the development of a reliable measurement technique. Further the concept and importance of the wavepath analysis will be discussed and finally we will report on the results obtained so far in clinical trials.