The behavior of adaptive bone-remodeling simulation models

The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely.\ud \ud It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur.\ud \ud It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing; denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process.\ud \ud It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization

Reduced Diaphyseal Strength Associated with High Intracortical Vascular Porosity within Long Bones of Children with Osteogenesis Imperfecta

Osteogenesis imperfecta is a genetic disorder resulting in bone fragility. The mechanisms behind this fragility are not well understood. In addition to characteristic bone mass deficiencies, research suggests that bone material properties are compromised in individuals with this disorder. However, little data exists regarding bone properties beyond the microstructural scale in individuals with this disorder. Specimens were obtained from long bone diaphyses of nine children with osteogenesis imperfecta during routine osteotomy procedures. Small rectangular beams, oriented longitudinally and transversely to the diaphyseal axis, were machined from these specimens and elastic modulus, yield strength, and maximum strength were measured in three-point bending. Intracortical vascular porosity, bone volume fraction, osteocyte lacuna density, and volumetric tissue mineral density were determined by synchrotron micro-computed tomography, and relationships among these mechanical properties and structural parameters were explored. Modulus and strength were on average 64–68% lower in the transverse vs. longitudinal beams (P \u3c 0.001, linear mixed model). Vascular porosity ranged between 3 and 42% of total bone volume. Longitudinal properties were associated negatively with porosity (P ≤ 0.006, linear regressions). Mechanical properties, however, were not associated with osteocyte lacuna density or volumetric tissue mineral density (P ≥ 0.167). Bone properties and structural parameters were not associated significantly with donor age (P ≥ 0.225, linear mixed models). This study presents novel data regarding bone material strength in children with osteogenesis imperfecta. Results confirm that these properties are anisotropic. Elevated vascular porosity was observed in most specimens, and this parameter was associated with reduced bone material strength. These results offer insight toward understanding bone fragility and the role of intracortical porosity on the strength of bone tissue in children with osteogenesis imperfecta

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 [mu]m). While the modulus values for relatively large specimens (h > 500 [mu]m) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28937/1/0000774.pd

Age, gender, and bone lamellae elastic moduli

To enhance preventative and therapeutic strategies for metabolic bone diseases and bone fragility disorders, we began to explore the physical properties of bone tissue at the cellular level. Proximal femurs were harvested from 27 cadavera (16 male and 11 female) for in vitro measurement of the mechanical properties. We measured the variations in lamellar-level elastic modulus and hardness in human bone as a function of age and gender to identify microstructural properties responsible for age and gender-related reductions in the mechanical integrity. The lateral femoral necks were examined, and age, gender, height, body mass, and body mass index were not found to correlate with lamellar-level elastic modulus or hardness. This result was consistent for osteonal, interstitial, and trabecular tissue. These data suggest that increased bone mass maintenance, known to occur in heavier individuals, is not accompanied by increases in the lamellar-level elastic modulus or hardness. The independence of elastic modulus and hardness from age and gender suggests that age and gender-related decreases in mechanical integrity do not involve alterations in elastic modulus or hard ness of the extracellular matrix. Lamellar-level ultimate, fatigue, and fracture toughness properties should also be investigated. Other factors, such as tissue mass and organization, may also contribute to age and gender-related decreases in the mechanical integrity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34918/1/1100180315_ftp.pd

Finite Element Analysis of Bone and Experimental Validation

This chapter describes the application of the finite element (FE) method to bone tissues. The aspects that differ the most between bone and other materials’ FE analysis are the type of elements used, constitutive models, and experimental validation. These aspects are looked at from a historical evolution stand point. Several types of elements can be used to simulate similar bone structures and within the same analysis many types of elements may be needed to realistically simulate an anatomical part. Special attention is made to constitutive models, including the use of density-elasticity relationships made possible through CT-scanned images. Other more complex models are also described that include viscoelasticity and anisotropy. The importance of experimental validation is discussed, describing several methods used by different authors in this challenging field. The use of cadaveric human bones is not always possible or desirable and other options are described, as the use of animal or artificial bones. Strain and strain rate measuring methods are also discussed, such as rosette strain gauges and optical devices.publishe

A review of trabecular bone functional adaptation: what have we learned from trabecular analyses in extant hominoids and what can we apply to fossils?

Many of the unresolved debates in palaeoanthropology regarding evolution of particular locomotor or manipulative behaviours are founded in differing opinions about the functional significance of the preserved external fossil morphology. However, the plasticity of internal bone morphology, and particularly trabecular bone, allowing it to respond to mechanical loading during life means that it can reveal greater insight into how a bone or joint was used during an individual's lifetime. Analyses of trabecular bone have been commonplace for several decades in a human clinical context. In contrast, the study of trabecular bone as a method for reconstructing joint position, joint loading and ultimately behaviour in extant and fossil non-human primates is comparatively new. Since the initial 2D studies in the late 1970s and 3D analyses in the 1990s, the utility of trabecular bone to reconstruct behaviour in primates has grown to incorporate experimental studies, expanded taxonomic samples and skeletal elements, and improved methodologies. However, this work, in conjunction with research on humans and non-primate mammals, has also revealed the substantial complexity inherent in making functional inferences from variation in trabecular architecture. This review addresses the current understanding of trabecular bone functional adaptation, how it has been applied to hominoids, as well as other primates and, ultimately, how this can be used to better interpret fossil hominoid and hominin morphology. Because the fossil record constrains us to interpreting function largely from bony morphology alone, and typically from isolated bones, analyses of trabecular structure, ideally in conjunction with that of cortical structure and external morphology, can offer the best resource for reconstructing behaviour in the past