The cancellous bone multiscale morphology-elasticity relationship

The cancellous bone effective properties relations are analysed on multiscale across two aspects; properties of representative volume element on micro scale and statistical measure of trabecular trajectory orientation on mesoscale. Anisotropy of the microstructure is described across fabric tensor measure with trajectory orientation tensor as bridging scale connection. The scatter measured data (elastic modulus, trajectory orientation, apparent density) from compression test are fitted by stochastic interpolation procedure. The engineering constants of the elasticity tensor are estimated by last square fitt procedure in multidimensional space by Nelder-Mead simplex. The multiaxial failure surface in strain space is constructed and interpolated by modified super-ellipsoid.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

The contribution of cancellous bone to long bone strength and rigidity

A recent article (Burr and Piotrowski, 1982) suggested that structural analyses of long bone cross-sectional geometry will be inaccurate and should be considered inappropriate when cancellous bone accounts for 10-15% or more of the cross-sectional area. Consideration of material property differences between compact and cancellous bone, however, indicates that even significant proportions of cancellous bone (10-40% of total cross-sectional area) will very likely have negligible effects on bone strength and rigidity, and can be effectively ignored in geometrical analyses of diaphyseal sections. In metaphyseal and epiphyseal regions, however, geometric analyses of section properties such as area moments of inertia are inappropriate, both because of significant trabecular bone effects, and because of the inherent constraints of mechanical beam models.     

Anisotropy of the fatigue behaviour of cancellous bone

The fatigue behaviour of materials is of particular interest for the failure prediction of materials and structures exposed to cyclic loading. For trabecular bone structures only a few sets of lifetime data have been reported in the literature and structural measures are commonly not considered. The influence of load contributions which are not aligned with the main physiological axis remains unclear. Furthermore site and species dependent relationships are not well described. In this study five different groups of trabecular bone, defined in terms of orientation, species and site were exposed to cyclic compression. In total, 108 fatigue tests were analysed. The lifetimes were found to decrease drastically when off-axis loads were applied. Additionally, species and site strongly affect fatigue lifetimes. Strains at failure were also found to be a function of orientation.     

Limitations of the continuum assumption in cancellous bone

Most existing stress analyses of the skeleton which consider cancellous bone assume that it can be modelled as a continuum. In this paper we develop a criterion for the validity of this assumption. The limitations of the continuum assumption appear in two areas: near biologic interfaces, and in areas of large stress gradients. These limitations are explored using a probabilistic line scanning model for density measurement, resulting in an estimate of density accuracy as a function of line length which is experimentally verified. Within three to five trabeculae of an interface, a continuum model is suspect. When results as predicted using continuum analyses vary by more than 20-30% over a distance spanning three to five trabeculae, the results are suspect.     

The mechanical behaviour of cancellous bone

Cancellous bone has a cellular structure: it is made up of a connected network of rods and plates. Because of this, its mechanical behaviour is similar to that of other cellular materials such as polymeric foams. A recent study on the mechanisms of deformation in such materials has led to an understanding of how their mechanical properties depend on their relative density, cell wall properties and cell geometry. In this paper, the results of this previous study are applied to cancellous bone in an attempt to further understand its mechanical behaviour. The results of the analysis agree reasonably well with experimental data available in the literature.     

Yield behavior of bovine cancellous bone

The compressive yield strain was measured for 61 specimens of bovine cancellous bone from three distal femora. There was no significant relationship (p = 0.08, R2 = 0.051) between yield strain and the degree of trabecular orientation. There was a significant positive correlation (p less than 0.00001, R2 = 0.319) between yield strain and structural (apparent) density and significant negative correlation (p less than 0.0025, R2 = 0.145) between yield strain and bone density. Yield strain correlated best with bone solid volume fraction Vv (epsilon y = 0.592 +2- 1.446vv, R2 = 0.337). The quantity, yield strain, is highly dependent on specific definitions of the yield point and the point of zero strain. For this study the yield point was defined by a 0.0003 offset criterion, and the point of zero strain was defined as the point where the tangent at 15 percent of yield crosses zero. The results using these definitions were compared with results using yield strain values determined by other definitions of the yield point and zero strain. The correlations between yield strain and trabecular orientation, structural density and bone density changed very little for differing definitions of yield. The results suggest that yield strain in cancellous bone is isotropic or independent of textural anisotropy, so the yield behaviour may be characterized by a maximum strain yield criterion. The results also suggest that the primary mode of yield in cancellous bone is buckling of the trabeculae.     

Transversely isotropic elasticity imaging of cancellous bone

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ??? is necessary to reconstruct C????), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.     

Bioinformatics, multiscale modeling and the IUPS Physiome Project

Multiscale modeling is required for linking physiological processes operating at the organ and tissue levels to signal transduction networks and other subcellular processes. Several XML markup languages, including CellML, have been developed to encode models and to facilitate the building of model repositories and general purpose software tools. Progress in this area is described and illustrated with reference to the heart Physiome Project which aims to understand cardiac arrhythmias in terms of structure-function relations from proteins up to cells, tissues and organs.     

Use of the cylinder osteotome for cancellous bone grafting

An instrument is described for removing iliac crest cancellous bone grafts under local anesthesia. The device has widespread applications for plastic and orthopedic surgery. The convenience of obtaining bone grafts with this device broadens the use of bone-grafting techniques in patients in whom the need for bone graft is unexpected.     

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.     

Post-yield relaxation behavior of bovine cancellous bone

Relaxation studies were conducted on specimens of bovine cancellous bone at post-yield strains. Stress and strain were measured for 1000 s and the relaxation modulus was determined. Fifteen cylindrical, cancellous bone specimens were removed from one bovine femur in the anterior–posterior direction. The relaxation modulus was found to be a function of strain. Therefore cancellous bone is non-linearly viscoelastic/viscoplastic in the plastic region. A power law regression was fit to the relaxation modulus data. The multiplicative constant was found to be statistically related through a power law relationship to both strain (p<0.0005) and apparent density (p<0.0005) while the power coefficient was found to be related through a power law relationship, E(t, ε)=A(ε)t^?n(ε), to strain (p<0.0005), but not apparent density.     

Alfacalcidol restores cancellous bone in ovariectomized rats

Active vitamin D metabolites have been demonstrated to reduce vertebral and hip fractures in elderly patients. A number of in vitro and in vivo pre-clinical studies have suggested that vitamin D may effectively stimulate osteoblastic activity and exert an anabolic effect on bone. The current study was designed to further explore the ability of an active vitamin D analog to restore bone in a skeletal site with established osteopenia in ovariectomized (OVX) rats. Female Sprague Dawley rats at five months of age and 8 weeks after sham ovariectomy or ovariectomy were randomly divided into 7 groups with 10 per group. At the beginning of the treatments, one group of sham-operated rats and one group of OVX rats were sacrificed to serve as baseline controls. Another group of sham-operated rats and one group of OVX rats were treated with vehicle for 4 weeks. The OVX rats in the remaining groups were treated with alfacalcidol at 0.05, 0.1 or 0.2 microg/kg/d by daily oral gavage, 5 days/week for 4 weeks. As expected, estrogen depletion caused high bone turnover and cancellous bone loss in lumbar vertebra of OVX rats. Alfacalcidol treatment at 0.1 or 0.2 but not 0.05 microg/kg/d increased serum calcium and phosphorus in OVX rats as compared with vehicle treatment. In addition, serum parathyroid hormone was suppressed, whereas serum osteocalcin was increased by alfacalcidol at all dose levels. Furthermore, histomorphometric data of 2nd lumbar vertebral body revealed that cancellous bone volume in OVX rats treated with alfacalcidol at 0.1 or 0.2 microg/kg/d was increased to the level of sham-operated rats treated with vehicle. This increment in cancellous bone mass was accompanied by increases in trabecular number and thickness and a decrease in trabecular separation. Moreover, osteoclast surface and number were significantly decreased, whereas bone formation variables such as mineralizing surface and bone formation rate were significantly increased in alfacalcidol- treated OVX rats compared with those of vehicle-treated OVX rats. Finally, a linear regression analysis showed that alfacalcidol treatment dose-dependently altered most of the variables measured in the current study. In conclusion, alfacalcidol completely restores cancellous bone by stimulating bone formation and suppressing bone resorption in lumbar vertebra of OVX rats when the treatment is started at an early phase of osteopenia. The evidence of increased bone formation by alfacalcidol treatments further supports the notion that active vitamin D metabolites or their analogs may exert anabolic effects on bone.     

Coarse-grained peptide modeling using a systematic multiscale approach

A systematic new approach to derive multiscale coarse-grained (MS-CG) models has been recently developed. The approach employs information from atomistically detailed simulations to derive CG forces and associated effective potentials. In this work, the MS-CG methodology is extended to study two peptides representing distinct structural motifs, alpha-helical polyalanine and the beta-hairpin V(5)PGV(5). These studies represent the first known application of this approach to peptide systems. Good agreement between the MS-CG and atomistic models is achieved for several structural properties including radial distribution functions, root mean-square deviation, and radius of gyration. The new MS-CG models are able to preserve the native states of these peptides within approximately 1 A backbone root mean-square deviation during CG simulations. The MS-CG approach, as with most coarse-grained models, has the potential to increase the length and timescales accessible to molecular simulations. However, it is also able to maintain a clear connection to the underlying atomistic-scale interactions.     

Direct perfusion measurements of cancellous bone anisotropic permeability

More extensive characterization of trabecular connectivity and intertrabecular space will be instrumental in understanding disease states and designing engineered bone. This project presents an experimental protocol to define the directional dependence of transport properties as measured from healthy cancellous bone when considered as a biologic, porous medium. In the initial design phases, mature bovine bone was harvested from the femoral neck (n=6 cylinders) and distal condyle (n=4 cubes) regions and used for "proof of concept" experimentation. A power study on those results led to the presented work on 20 cubic samples (mean volume=4.09cm(3)) harvested from a single bovine distal femur. Anisotropic intrinsic permeabilities (k(i)) were quantified along the orthogonal anatomic axes (i=medial-lateral, anterior-posterior, and superior-inferior) from each individual cubic bone sample. Using direct perfusion measurements, permeability was calculated based upon Darcy's Law describing flow through porous media. The maximum mean value was associated with the superior-inferior orientation (4.65x10(-10)m(2)) in comparison with the mean anterior-posterior (4.52x10(-10)m(2)) and medial-lateral (2.33x10(-10)m(2)) direction values. The results demonstrate the anisotropic (p=0.0143) and heterogeneous (p=0.0002) nature of the tissue and encourage the ongoing quantification of parameters within the established poroelastic models.     

Postoperative irradiation of fresh autogenic cancellous bone grafts

Discontinuity defects were created in the mandibles of dogs and then reconstructed immediately with fresh autogenic cancellous bone grafts and Dacron-urethane prostheses. The grafts were irradiated to a total dose of 5000 rads after waiting intervals of between 3 and 12 weeks. Nonirradiated grafts served as controls. The grafts were evaluated clinically, radiographically, and histologically. There was complete incorporation of all grafts, regardless of the interval between surgery and radiotherapy. There were no soft-tissue complications. The controls were distinguishable from the irradiated grafts only by the presence of hematopoietic bone marrow. Fibrofatty marrow was observed in the irradiated grafts. Theoretical support for this technique is found in the biology of cancellous bone grafting and the pathology of radiation injury. In view of the difficulties associated with mandibular bone grafting in preoperatively irradiated patients, a new method of reconstructing selected cancer patients who require both mandibular resection and radiotherapy is suggested.     

Application of neural networks and finite element computation for multiscale simulation of bone remodeling

In this paper, a novel multiscale hierarchical model based on finite element analysis and neural network computation was developed to link mesoscopic and macroscopic scales to simulate the bone remodeling process. The finite element calculation is performed at the macroscopic level, and trained neural networks are employed as numerical devices for substituting the finite element computation needed for the mesoscale prediction. Based on a set of mesoscale simulations of representative volume elements of bones taken from different bone sites, a neural network is trained to approximate the responses at the meso level and transferred at the macro level.     

A new bone banking technique to maintain osteoblast viability in frozen human iliac cancellous bone

The aim of this study was to develop a new cryopreservation technique to maintain the osteoblast viability in frozen iliac bone and to prove cell viability using cell culture techniques.Human iliac cancellous bones were frozen with and without 10% Me(2)SO at -80 degrees C. The tubes were kept in a -80 degrees C freezer for at least 2 days. After the storage period, the frozen bone was thawed by placing the tube in a 37 degrees C water bath. A serial enzymatic digestion technique using 0.2% collagenase was employed to isolate osteoblast-like cells from the bone. The cells that were released were inoculated into tissue culture flasks containing DMEM supplemented with 10% FCS. They were incubated at 37 degrees C in a humidified atmosphere of 95% air and 5% CO(2). Cells of the second passage were plated at a density of 5 x 10(3)cells/cm(2) in a 24-well plate and used for characterization. For characterization, WST-1 assay, determination of alkaline phosphatase, Type I collagen assay, osteocalcin assay, and von Kossa staining were used. The assays were performed at 3, 6, 9, and 12 days after plating the cells. Based on the results of this study, we conclude that the osteoblast-like cells in the frozen bone can survive, only when the bone is frozen with cryoprotectants to prevent injury during freezing and thawing.