A theoretical model to predict distribution of the fabric tensor and apparent density in cancellous bone

 The adaptation of cancellous bone to mechanical forces is well recognized. Theoretical models for predicting cancellous bone architecture have been developed and have mainly focused on the distribution of trabecular mass or the apparent density. The purpose of this study was to develop a theoretical model which can simultaneously predict the distribution of trabecular orthotropy/orientation, as represented by the fabric tensor, along with apparent density. Two sets of equations were derived under the assumption that cancellous bone is a biological self-optimizing material which tends to minimize strain energy. The first set of equations provide the relationship between the fabric tensor and stress tensor, and have been verified to be consistent with Wolff’s law of trabecular architecture, that is, the principal directions of the fabric tensor coincide with the principal stress trajectories. The second set of equations yield the apparent density from the stress tensor, which was shown to be identical to those obtained based on local optimization with strain energy density of true bone tissue as the objective function. These two sets of equations, together with elasticity field equations, provide a complete mathematical formulation for the adaptation of cancellous bone. Received: 25 February 1997/Revised version: 23 September 1997     

Femoral head trabecular bone structure in two omomyid primates

The study of the three-dimensional structure of trabecular bone and its relationship to locomotor behavioral differences across different primate taxa provides a potentially useful analytic tool for reconstructing the behavior of extinct taxa. The purpose of the current study is to quantify the three-dimensional architecture of trabecular bone in the femoral head of Omomys carteri and Shoshonius cooperi and to compare this structure to that of several extant strepsirrhine taxa. Bone volume fraction (BV/TV) and fabric anisotropy were quantified in three dimensions using serial high-resolution X-ray computed tomography scan data collected from one femoral head from each fossil taxon. Three cubic volumes of interest (VOI) were identified within the femoral head. The BV/TV was quantified by assessing the percentage of bone voxels within each VOI and the structural anisotropy was quantified using the star volume distribution method. The Omomys femur used here has a high BV/TV with the galagine-like pattern of decreasing BV/TV from the superior to the inferior half of the femoral head. The fabric structure, however, is more lorisine-like in being relatively isotropic throughout the femoral head. The trabecular structure in Omomys is unique in its mix of features and appears to be most similar overall to the lorisines, suggesting that Omomys engaged in a quadrupedal mode of locomotion. By contrast the Shoshonius specimen possesses a relatively uniform BV/TV across the head but displays the distinctly galagine-like pattern of increasing anisotropy moving inferiorly in the femoral head. Taken as a whole, the trabecular structure in Shoshonius appears to be most like that of the galagines and is consistent with that of either an occasional leaper-quadruped or a specialized leaper. Despite the overall similarities in the external postcranial anatomy of Omomys and Shoshonius, the results of this study indicate potentially important differences in the magnitude and orientation of the external loads at the hip joint, suggesting that these animals engaged in divergent locomotor behaviors.     

Tensile properties of rat femoral bone as functions of bone volume fraction, apparent density and volumetric bone mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure-function properties of the skeleton. Tensile properties of cancellous and cortical bone have been reported previously; however, no relationships describing these properties for rat bone as a function of volumetric bone mineral density (ρ(MIN)), apparent density or bone volume fraction (BV/TV) have been reported in the literature. We have shown that at macro level, compression and torsion properties of rat cortical and cancellous bone can be well described as a function of BV/TV, apparent density or ρ(MIN) using non-destructive micro-computed tomographic imaging and mechanical testing to failure. Therefore, the aim of this study is to derive a relationship expressing the tensile properties of rat cortical bone as a function of BV/TV, apparent density or ρ(MIN) over a range of normal and pathologic bones. We used bones from normal, ovariectomized and osteomalacic animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial tension to failure. We obtained univariate relationships describing 74-77% of the tensile properties of rat cortical bone as a function of BV/TV, apparent density or ρ(MIN) over a range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity to provide a non-invasive method to assess the tensile behavior of bones affected by pathology and/or treatment options.     

Compressive axial mechanical properties of rat bone as functions of bone volume fraction,apparent density and micro-ct based mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure–function properties of the skeleton. With recent advances in computing power of personal computers, virtual alternatives to mechanical testing are gaining acceptance and use. We have previously introduced such a technique called structural rigidity analysis to assess mechanical strength of skeletal tissue with defects. The application of this technique is predicated upon the use of relationships defining the strength of bone as a function of its density for a given loading mode. We are to apply this technique in rat models to assess their compressive skeletal response subjected to a host of biological and pharmaceutical stimulations. Therefore, the aim of this study is to derive a relationship expressing axial compressive mechanical properties of rat cortical and cancellous bone as a function of equivalent bone mineral density, bone volume fraction or apparent density over a range of normal and pathologic bones.We used bones from normal, ovariectomized and partially nephrectomized animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial compression to failure.We obtained univariate relationships describing 71–78% of the mechanical properties of rat cortical and cancellous bone based on equivalent mineral density, bone volume fraction or apparent density over a wide range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity analysis introduced by the authors to provide a non-invasive method to assess the compressive strength of bones affected by pathology and/or treatment options.     

On the dependence of the elasticity and strength of cancellous bone on apparent density

This paper presents a statistical analysis of the pooled data from a number of previous experiments concerning the dependence of the Young's moduli and strength of cancellous bone tissue upon apparent density. The results show that both the Young's moduli and the strength are proportional to the square of apparent density of the tissue and are therefore proportional to one another. It is shown that the coefficient of proportionality is different for human and bovine tissue. It is concluded that the suggestion of Wolff (Das Gesetz der Transformation der Knochen, Hirschwald, Berlin, 1892) that compact bone tissue is simply more dense cancellous bone tissue is not an accurate statement when only the mechanical properties of these two tissues are considered. It is noted that estimates for the elastic modulus of the individual trabecula of human cancellous bone vary from 1 to 20 GPa and it is suggested that this question needs further study.     

Estimation of bone matrix apparent stiffness variation caused by osteocyte lacunar size and density

The role of osteocyte lacunar size and density on the apparent stiffness of bone matrix was predicted using a mechanical model from the literature. Lacunar size and lacunar density for different bones from different gender and age groups were used to predict the range of matrix apparent stiffness values for human cortical and cancellous tissue. The results suggest that bone matrix apparent stiffness depends on tissue type (cortical versus cancellous), age, and gender, the magnitudes of the effects being significant but small in all cases. Males had a higher predicted matrix apparent stiffness than females for vertebral cancellous bone (p< I0(-7)) and the difference increased with age (p =0.0007). In contrast, matrix apparent stiffness was not different between males and females forfemoral cortical bone and increased with age in both males (p < 0.0001) and females (p < 0.0364). Osteocyte lacunar density and size may cause significant gender and age-related variations in bone matrix apparent stiffness. The magnitude of variations in matrix apparent stiffness was small within the physiological range of lacunar size and density for healthy bone, whereas the variations can be profound in certain pathological cases. It was proposed that the mechanical effects of osteocyte density be uncoupled from their biological effects by controlling lacunar size in normal bone.     

Evaluation of optimization workflow using custom-made planning through predicted dose distribution for head and neck tumor treatment

PurposeLack of a reference dose distribution is one of the challenges in the treatment planning used in volumetric modulated arc therapy because numerous manual processes result from variations in the location and size of a tumor in different cases. In this study, a predicted dose distribution was generated using two independent methods. Treatment planning using the predicted distribution was compared with the clinical value, and its efficacy was evaluated.MethodsComputed tomography scans of 81 patients with oropharynx or hypopharynx tumors were acquired retrospectively. The predicted dose distributions were determined using a modified filtered back projection (mFBP) and a hierarchically densely connected U-net (HD-Unet). Optimization parameters were extracted from the predicted distribution, and the optimized dose distribution was obtained using a commercial treatment planning system.ResultsIn the test data from ten patients, significant differences between the mFBP and clinical plan were observed for the maximum dose of the brain stem, spinal cord, and mean dose of the larynx. A significant difference between the dose distributions from the HD-Unet dose and the clinical plan was observed for the mean dose of the left parotid gland. In both cases, the equivalent coverage and flatness of the clinical plan were observed for the tumor target.ConclusionsThe predicted dose distribution was generated using two approaches. In the case of the mFBP approach, no prior learning, such as deep learning, is required; therefore, the accuracy and efficiency of treatment planning will be improved even for sites where sufficient training data are unavailable.     

Dramatic shifts in Hawaiian monk seal distribution predicted from divergent regional trends

Total estimated abundance of Hawaiian monk seals was just 1,161 individuals in 2008 and this number is decreasing. Most monk seals reside in the remote Northwestern Hawaiian Islands (NWHI) where the decline is approximately 4%/yr, whereas relatively fewer seals currently occupy the main Hawaiian Islands (MHI). It is widely accepted that the MHI population is increasing, although there are no formal estimates of total abundance, population growth rate or vital rates. This lack of information has hampered efforts to anticipate future scenarios and plan conservation measures. We present the first estimates of MHI monk seal survival and age‐specific reproductive rates. Using these rates, a conservative estimate of current MHI abundance and a previously published stochastic simulation model, we estimate the MHI population growth rate and projected abundance trend. Analogous estimates for the NWHI are derived from a much richer data set. Estimated survival from weaning to age 1 yr is 77% in the MHI, much higher than recent NWHI estimates ranging from 42% to 57%. Moreover, MHI females begin reproducing at a younger age and attain higher birth rates than observed in the NWHI. The estimated MHI intrinsic rate of population growth is 1.07 compared to a 0.89–0.96 range in the NWHI. Assuming an initial abundance of 152 animals in the MHI, projections indicate that if current demographic trends continue, abundance in the NWHI and MHI will equalize in approximately 15 yr. These results underscore the imperative to mitigate the NWHI decline while devoting conservation efforts to foster population growth in the MHI, where documented threats including fishery interactions, direct killing, and disease could rapidly undo the current fragile positive trend.     

On the fibre composite material models of disc annulus--comparison of predicted stresses

An axisymmetric finite element model of a body-disc-body unit has been developed and used to study the relative effects of two distinct direction-dependent material representations of the disc annulus on the predicted state of stresses in the disc. The annulus fibrosus is modelled either as nonhomogeneous fibre reinforced composite or alternatively as homogeneous orthotropic with transverse isotropy. In order to have identical states of displacements and hence strains, the unknown properties of the latter model are chosen to be equivalent with those of the former. The fibre slopes of 20 degrees, 30 degrees, and 40 degrees are considered in this study. The stresses in the annulus matrix in the circumferential planes parallel to the fibre layers are predicted to be significantly different depending on the annulus model used. In the nonhomogeneous model, the fibre membranes while under tensile forces, in turn, apply compression to the annulus matrix and, hence, decrease the annulus normal stresses in the above planes. Had the membranes carried compressive forces, a reverse trend would have resulted. The foregoing relative differences are dependent on the fibre orientation, and the magnitude of the tensile forces carried by the fibre layers. The latter also depends, amongst others, on the orientation of the fibres, decreasing as the fibre slope increases from 20 degrees to 30 degrees and 40 degrees. On the basis of the annulus micro-structure and the relative mechanical functions of its components, namely the annulus bulk and the collagenous fibre layers, it appears that nonhomogeneous fibre reinforced composite model of the disc annulus is more realistic resulting in a more accurate computation of stresses in the annulus fibrosus.     

Vernier acuity predicted from changes in the light distribution of the retinal image

If two thin bars of different luminance are placed side by side, their joint spatial position in a Vernier alignment task is determined simply by their relative luminances. The threshold luminance contrast difference required to produce a just detectable change in spatial position corresponds to a spatial shift of 5-20 arcsec in the centroid of the retinal light distribution, depending upon contrast relative to the background. This technique may be used to measure acuity with a display that has a spatial resolution considerably worse than the Vernier offset threshold. We have also extended the centroid technique to components that differ both in wavelength and luminance. Colour was found to make no essential difference to the task. Taking into account the spread of light in the retinal image, the manifest contrast thresholds are equivalent to threshold intensity increments between adjacent foveal receptors of less than 1% comparable to the values reported by Hecht and Mintz for dark line detection.     

Numerical estimation of bone density and elastic constants distribution in a human mandible

In this paper, we try to predict the distribution of bone density and elastic constants in a human mandible, based on the stress level produced by mastication loads using a mathematical model of bone remodelling. These magnitudes are needed to build finite element models for the simulation of the mandible mechanical behavior. Such a model is intended for use in future studies of the stability of implant-supported dental prostheses. Various models of internal bone remodelling, both phenomenological and more recently mechanobiological, have been developed to determine the relation between bone density and the stress level that bone supports. Among the phenomenological models, there are only a few that are also able to reproduce the level of anisotropy. These latter have been successfully applied to long bones, primarily the femur. One of these models is here applied to the human mandible, whose corpus behaves as a long bone. The results of bone density distribution and level of anisotropy in different parts of the mandible have been compared with various clinical studies, with a reasonable level of agreement.     

High bone density and bone health

The aim of this paper is to review the main aspects related to high bone density (HBD) as well as to discuss the physiologic mechanisms involved in bone health. There are still no well-defined criteria for identification of individuals with HBD and there are few studies on the topic. Most studies demonstrate that overweight, male gender, black ethnic background, physical activity, calcium and fluoride intake and use of medications such as statins and thiazide diuretics play a relevant and positive role on bone mineral density. Moreover, it is known that individuals with certain diseases such as obesity, diabetes, estrogen receptor-positive breast or endometrial cancer have greater bone density than healthy individuals, as well as athletes having higher bone density than non-athletes does not necessarily mean that they have healthy bones. A better understanding of risk and protective factors may help in the management of patients with bone frailty and have applicability in the treatment and in the prevention of osteoporosis, especially intervening on non-modifiable risk factors.     

Femoral strength is better predicted by finite element models than QCT and DXA.

Clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in-vivo were available. A group of 51 human femurs (age range 21-93; 23 females, 28 males) were evaluated for bone density and geometry using quantitative computed tomography (QCT) and dual energy X-ray absorptiometry (DXA). Regional bone density and dimensions obtained from QCT and DXA were used to develop statistical models to predict femoral strength ex vivo. The QCT data also formed the basis of a three-dimensional finite element (FE) models to predict structural stiffness. The femurs were separated into two groups; a model training set (n = 25) was used to develop statistical models to predict ultimate load, and a test set (n = 26) was used to validate these models. The main goal of this study was to test the ability of DXA, QCT and FE techniques to predict fracture load non-invasively, in a simple load configuration which produces predominantly femoral neck fractures. The load configuration simulated the single stance phase portion of normal gait; in 87% of the specimens, clinical appearing sub-capital fractures were produced. The training/test study design provided a tool to validate that the predictive models were reliable when used on specimens with "unknown" strength characteristics. The FE method explained at least 20% more of the variance in strength than the DXA models. Planned refinements of the FE technique are expected to further improve these results. Three-dimensional FE models are a promising method for predicting fracture load, and may be useful in monitoring strength changes in vivo.     

Osteoprotegerin and bone density

Aim of study was determine if a correlation exists between bone mass density and concentration of osteoprotegerin. We examined the group of 199 patients of mean age of 63 years. Of the group under study, 31 patients had normal bone density (T score > -1 and < 1) and 168 probands had osteopenia or osteoporosis (T < -1). Persons with normal BMD values had median values of OPG 60.8 ng/l, while patients with reduced bone density had median values of 73 ng/l OPG. Cut-off for reduction of bone density was 128 ng/l OPG. We demonstrated that OPG concentrations vary inversely with bone density values (correlation coefficient -0.31). These results suggest that determination of OPG could allow discrimination of individuals with normal bone density and those with reduced bone density.     

Local stream habitat variables predicted from catchment scale characteristics are useful for predicting fish distribution

South-east Queensland (Australia) streams were described by 21 local habitat variables that were chosen because of their potential association with fish distribution. An Assessment by a Nearest Neighbour Analysis (ANNA) model used large-scale variables that are robust to human influence to predict what the values of each of the 21 local habitat variables at each site would be without modification from human activity. The ANNA model used elevation, stream order, distance from source and longitude to predict the local habitat variables; other candidate predictor variables (mean rainfall, latitude and catchment area) were not found to be useful. The ANNA model was able to predict five of the 21 local habitat variables (average width, sand (%), cobble (%), rocks (%) and large woody debris) with an R ² of at least 0.2. The observed values of these five local habitat variables were used to model the distributions of individual fish species. The species distribution models were developed using logistic regression based on a subset of the data (some of the data were withheld for model validation) and a forward stepwise model selection procedure. There was no difference in predictive performance of fish distribution models for model predictions based on observed values and model predictions based on ANNA predicted values of local habitat variables in the withheld data (p-value = 0.85). Therefore, it is possible to predict the suitability of sites as habitat for given fish species using estimated (estimates based on large-scale variables) natural values of local habitat variables.     

On the discrimination between band-limited coherent and random apparent stresses in transitional pulsatile flow

A frequency domain approach that incorporates a matched filter was examined for discriminating between ordered velocity fluctuations with band-limited frequency content and random velocity variations in pulsatile disturbed flows. Fluctuations at pseudo-discrete frequencies may yield a significant contribution to the apparent stress tensor computed from the unsteady Navier Stokes equations, and an estimate of the stresses arising from these ordered structures can be obtained once the velocity variations have been decomposed. This type of decomposition permits the estimation of the apparent stresses in turbulent flows, consisting of coherent and random parts, in blood flow applications such as diseased constricted arteries or downstream of artificial heart valves.