Bone modeling involves the addition of bone material through osteoblast-mediated deposition or the removal of bone material via osteoclast-mediated resorption in response to perceived changes in loads by osteocytes. This process is characterized by the independent occurrence of deposition and resorption, which can take place simultaneously at different locations within the bone due to variations in stress levels across its different regions. The principle of bone functional adaptation states that cortical and trabecular bone tissues will respond to mechanical stimuli by adjusting (i.e., bone modeling) their morphology and architecture to mechanically improve their mechanical function in line with the habitual in vivo loading direction. This principle is relevant to various research areas, such as the development of improved orthopedic implants, preventative medicine for osteopenic elderly patients, and the investigation of locomotion behavior in extinct species. In the present review, the mammalian tibia is used as an example to explore cortical and trabecular bone modeling and to examine its implications for the functional adaptation of bones. Following a short introduction and an exposition on characteristics of mechanical stimuli that influence bone modeling, a detailed critical appraisal of the literature on cortical and trabecular bone modeling and bone functional adaptation is given. By synthesizing key findings from studies involving small mammals (rodents), large mammals, and humans, it is shown that examining both cortical and trabecular bone structures is essential for understanding bone functional adaptation. A combined approach can provide a more comprehensive understanding of this significant physiological phenomenon, as each structure contributes uniquely to the phenomenon.

UNASSIGNED: Captivity alters the locomotor behavior of wild artiodactyls and affects the mechanical loading of the calcaneus; however, the resulting adaptive changes in calcaneus morphology have not been sufficiently studied to date. This study aimed to investigate the morphological and mechanical adaptive variations in the calcaneus of Saiga tatarica to understand further the functional adaptation of the calcaneus in wild artiodactyl to captivity.
UNASSIGNED: Paired calcanei from autopsy samples of six captive wild artiodactyls (S. tatarica) and six domesticated artiodactyls (Ovis aries) were divided into skeletally immature and mature groups using X-ray evaluation of growth plate closure. High-resolution microcomputed tomography revealed a calcaneal diaphyseal cross-section. The mechanical and nanomorphological characteristics of the trabecular bone were determined by atomic force microscopy.
UNASSIGNED: The percent cortical bone area (%CA), cortical thickness ratio (CTR), and Young\'s modulus (E) differed between species in the immature groups but not in the mature groups. S. tatarica had significantly higher growth rates for %CA, CTR, and E in the mid-shaft than O. aries (p < 0.05).
UNASSIGNED: The calcaneus morphology of S. tatarica converges with that of domesticated O. aries during ontogeny. These results indicate that the calcaneus of wild artiodactyls can undergo potentially transitional changes during the short-term adaptation to captivity. The above parameters can be preliminarily identified as morphological signs of functional bone adaptation in artiodactyls.

We propose a variational approach that employs a generalized principle of virtual work to estimate both the mechanical response and the changes in living bone tissue during the remodeling process. This approach provides an explanation for the adaptive regulation of the bone substructure in the context of orthotropic material symmetry. We specifically focus upon the crucial gradual adjustment of bone tissue as a structural material that adapts its mechanical features, such as materials stiffnesses and microstructure, in response to the evolving loading conditions. We postulate that the evolution process relies on a feedback mechanism involving multiple stimulus signals. The mechanical and remodeling behavior of bone tissue is clearly a complex process that is difficult to describe within the framework of classical continuum theories. For this reason, a generalized continuum elastic theory is employed as a proper mathematical context for an adequate description of the examined phenomenon. To simplify the investigation, we considered a two-dimensional problem. Numerical simulations have been performed to illustrate bone evolution in a few significant cases: the bending of a rectangular cantilever plate and a three-point flexure test. The results are encouraging because they can replicate the optimization process observed in bone remodeling. The proposed model provides a likely distribution of stiffnesses and accurately represents the arrangement of trabeculae macroscopically described by the orthotropic symmetry directions, as supported by experimental evidence from the trajectorial theory.

Trabecular bone-the spongy bone inside marrow cavities-adapts to its mechanical environment during growth and development. Trabecular structure can therefore be interpreted as a functional record of locomotor behavior in extinct vertebrates. In this paper, we expand upon traditional links between form and function by situating ontogenetic trajectories of trabecular bone in four primate species into the broader developmental context of neural development, locomotor control, and ultimately life history. Our aim is to show that trabecular bone structure provides insights into ontogenetic variation in locomotor loading conditions as the product of interactions between increases in body mass and neuromuscular maturation. Our results demonstrate that age-related changes in trabecular bone volume fraction (BV/TV) are strongly and linearly associated with ontogenetic changes in locomotor kinetics. Age-related variation in locomotor kinetics and BV/TV is in turn strongly associated with brain and body size growth in all species. These results imply that age-related variation in BV/TV is a strong proxy for both locomotor kinetics and neuromuscular maturation. Finally, we show that distinct changes in the slope of age-related variation in bone volume fraction correspond to the age of the onset of locomotion and the age of locomotor maturity. Our findings compliment previous studies linking bone development to locomotor mechanics by providing a fundamental link to brain development and life history. This implies that trabecular structure of fossil subadults can be a proxy for the rate of neuromuscular maturation and major life history events like locomotor onset and the achievement of adult-like locomotor repertoires.

Variation in human trabecular bone morphology can be linked to habitual behavior, but it is difficult to investigate in vivo due to the radiation required at high resolution. Consequently, functional interpretations of trabecular morphology remain inferential. Here we introduce a method to link low- and high-resolution CT data from dry and fresh bone, enabling bone functional adaptation to be studied in vivo and results compared to the fossil and archaeological record.
We examine 51 human dry bone distal tibiae from Nile Valley and UK and two pig tibiae containing soft tissues. We compare low-resolution peripheral quantitative computed tomography (pQCT) parameters and high-resolution micro CT (μCT) in homologous single slices at 4% bone length and compare results to our novel Bone Ratio Predictor (BRP) method.
Regression slopes between linear attenuation coefficients of low-resolution pQCT images and bone area/total area (BA/TA) of high-resolution μCT scans differ substantially between geographical subsamples, presumably due to diagenesis. BRP accurately predicts BA/TA (R2 = .97) and eliminates the geographic clustering. BRP accurately estimates BA/TA in pigs containing soft tissues (R2 = 0.98) without requiring knowledge of true density or phantom calibration of the scans.
BRP allows automated comparison of image data from different image modalities (pQCT, μCT) using different energy settings, in archeological bone and wet specimens. The method enables low-resolution data generated in vivo to be compared with the fossil and archaeological record. Such experimental approaches would substantially improve behavioral inferences based on trabecular bone microstructure.

This study evaluated chronological changes in physiological stress and levels of habitual loading of Ibizan populations from the Late Roman-Early Byzantine (LREB) to the Islamic period (300-1,235 AD) using measures of body size and bone cross-sectional properties to compare Urban LREB, Urban Medieval Islamic, and Rural Medieval Islamic groups. It also explored the effect of diet, modeled using stable isotopes, on physiological stress levels and behavior.
The sample comprised individuals from three archeological populations: Urban Late Roman- Early Byzantine (LREB) (300-700 AD), Medieval Urban Islamic (902-1,235 AD), and Medieval Rural Islamic. Bone lengths, femoral head dimensions, and cross-sectional properties, diaphyseal products and circumferences, were compared to assess differences in body size and habitual loading in 222 adult individuals. Ordinary least squares regression evaluated the correlations between these measures and carbon (δ13 C) and nitrogen (δ15 N) stable isotope ratios in 115 individuals for whom both isotope values and osteological measures are available.
The Medieval Rural Islamic group had shorter stature and reduced lower limb cross-sectional properties compared to the two urban groups. Limb shape differs between Urban LREB and Urban Medieval Islamic groups. Measures of body size length were positively correlated with δ13 C values in all individuals and separately in the Urban LREB and Rural Medieval Islamic groups. δ15 N showed a positive correlation with left humerus shape in the Urban LREB sample.
The low stature and cross-sectional properties of the Medieval Rural Islamic group may be an indicator of greater physiological stress, potentially due to poorer diet. Positive correlations between measures of body size and δ13 C values further suggest that greater access to C4 resources improved diet quality. Alternatively, this relationship could indicate greater body size among migrants from areas where individuals consumed more C4 resources.

Trabecular structure is frequently used to differentiate between highly divergent mechanical environments. Less is known regarding the response of the structural properties to more subtle behavioral differences, as the range of intrapopulation variation in trabecular architecture is rarely studied. Examining the extent to which lower limb trabecular architecture varies when inferred mobility levels and environment are consistent between groups within a relatively homogenous population may aid in the contextualization of interpopulation differences, improve detectability of sexual dimorphism in trabecular structure, and improve our understanding of trabecular bone functional adaptation.
The study sample was composed of adult individuals from three high/late medieval cemeteries from Cambridge (10th-16th c.), a hospital (n = 57), a parish cemetery (n = 44) and a friary (n = 14). Trabecular architecture was quantified in the epiphyses of the femur and tibia, using high resolution computed tomography.
The parish individuals had the lowest bone volume fraction and trabecular thickness in most regions. Multiple sex differences were observed, but the patterns were not consistent across volumes of interest.
Differences between the three groups highlight the great variability of trabecular bone architecture, even within a single sedentary population. This indicates that trabecular bone may be used in interpreting subtle behavioral differences, and suggests that multiple archaeological sites need to be studied to characterize structural variation on a population level. Variation in sex and group differences across anatomical locations further demonstrates the site-specificity in trabecular bone functional adaptation, which might explain why little consistent sexual dimorphism has been reported previously.

Trabecular bone structure in adulthood is a product of a process of modelling during ontogeny and remodelling throughout life. Insight into ontogeny is essential to understand the functional significance of trabecular bone structural variation observed in adults. The complex shape and loading of the human calcaneus provides a natural experiment to test the relationship between trabecular morphology and locomotor development. We investigated the relationship between calcaneal trabecular bone structure and predicted changes in loading related to development of gait and body size in growing children. We sampled three main trabecular regions of the calcanei using micro-computed tomography scans of 35 individuals aged between neonate to adult from the Norris Farms #36 site (1300 AD, USA) and from Cambridge (1200-1500 AD, UK). Trabecular properties were calculated in volumes of interest placed beneath the calcaneocuboid joint, plantar ligaments, and posterior talar facet. At birth, thin trabecular struts are arranged in a dense and relatively isotropic structure. Bone volume fraction strongly decreases in the first year of life, whereas anisotropy and mean trabecular thickness increase. Dorsal compressive trabecular bands appear around the onset of bipedal walking, although plantar tensile bands develop prior to predicted propulsive toe-off. Bone volume fraction and anisotropy increase until the age of 8, when gait has largely matured. Connectivity density gradually reduces, whereas trabeculae gradually thicken from birth until adulthood. This study demonstrates that three different regions of the calcaneus develop into distinct adult morphologies through varying developmental trajectories. These results are similar to previous reports of ontogeny in human long bones and are suggestive of a relationship between the mechanical environment and trabecular bone architecture in the human calcaneus during growth. However, controlled experiments combined with more detailed biomechanical models of gait maturation are necessary to establish skeletal markers linking growth to loading. This has the potential to be a novel source of information for understanding loading levels, activity patterns, and perhaps life history in the fossil record.

The human foot is highly derived relative to that of other hominoids and therefore a topic of intense research in paleoanthropology. While trabecular bone is thought to be highly plastic in response to habitual behavior, knowledge of how trabecular structure scale with body size is essential for making functional inferences from trabecular bone morphology. Trabecular bone properties scale with negative allometry in interspecific studies that includes a wide range of body size; however, intraspecific scaling patterns often differ from interspecific trends. In this paper we examine patterns of trabecular bone scaling in the calcaneus, talus, and first metatarsal of four human populations with different subsistence strategies and associated levels of terrestrial mobility. We report Bayesian linear regressions between the natural logarithms of femoral head diameter and five standard trabecular variables calculated in five spherical volumes of interest. We additionally report regressions on population-specific z-scores of femoral head diameter and trabecular variables as a way of placing the four populations on a common scale. Results show that with increasing body size there is no change in bone volume fraction (BV/TV) and trabecular thickness (Tb.Th), a slight increase in trabecular spacing (Tb.Sp), and a sharp decrease in connectivity density (Conn.D). Degree of anisotropy was found to scale with positive allometry in the calcaneus, negative allometry in the talar trochlea, and shows no relationship with femoral head diameter in the talar and first metatarsal heads. These results show that scaling of the degree of anisotropy can vary substantially within and between bones. Degree of anisotropy is often used as a proxy for directionality in joint loading when interpreting variation in trabecular structures of fossils and extant primates. Body size should therefore be an important consideration when trabecular bone structure is used to interpret function from fossil morphology.

In the past years, many attempts have been made in order to model the process of bone remodeling. This process is complex, as it is governed by not yet completely understood biomechanical coupled phenomena. It is well known that bone tissue is able to self-adapt to different environmental demands of both mechanical and biological origin. The mechanical aspects are related to the functional purpose of the bone tissue, i.e., to provide support to the body and protection for the vitally important organs in response to the external loads. The many biological aspects include the process of oxygen and nutrients supply. To describe the biomechanical process of functional adaptation of bone tissue, the approach commonly adopted is to consider it as a \'feedback\' control regulated by the bone cells, namely osteoblasts and osteoclasts. They are responsible for bone synthesis and resorption, respectively, while osteocytes are in charge of \'sensing\' the mechanical status of the tissue. Within this framework, in  Lekszycki and dell\'Isola (ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 92(6):426-444, 2012), a model based on a system of integro-differential equations was introduced aiming to predict the evolution of the process of remodeling in surgically reconstructed bones. The main idea in the aforementioned model was to introduce a scalar field, describing the biological stimulus regulating the interaction among all kinds of bone cells at a macroscale. This biological field was assumed to depend locally on certain deformation measures of the (reconstructed) bone tissue. However, biological knowledge suggests that this stimulus, after having been produced, \'diffuses\' in bone tissue, so controlling in a complex way its remodeling. This means that the cells which are target of the stimulus may not be located in the same place occupied by the cells producing it. In this paper, we propose a model which intends to explain the diffusive nature of the biological stimulus to encompass the time-dependent and space-time displaced effects involved in bone reconstruction process. Preliminary numerical simulations performed in typical cases are presented. These numerical case studies suggest that the \'diffusive\' model of stimulus is promising: we plan to continue these kinds of studies in further investigations.