Fabric-mechanical property relationships of trabecular bone allografts are altered by supercritical CO2 treatment and gamma sterilization

Tissue grafts are implanted in orthopedic surgery every day. In order to minimize infection risk, bone allografts are often delipidated with supercritical CO2 and sterilized prior to implantation. This treatment may, however, impair the mechanical behavior of the bone graft tissue. The goal of this study was to determine clinically relevant mechanical properties of treated/sterilized human trabecular bone grafts, e.g. the apparent modulus, strength, and the ability to absorb energy during compaction. They were compared with results of identical experiments performed previously on untreated/fresh frozen human trabecular bone from the same anatomical site (Charlebois, 2008). We tested the hypothesis that the morphology–mechanical property relationships of treated cancellous allografts are similar to those of fresh untreated bone. The morphology of the allografts was determined by μCT. Subsequently, cylindrical samples were tested in unconfined and confined compression. To account for various morphologies, the experimental data was fitted to phenomenological mechanical models for elasticity, strength, and dissipated energy density based on bone volume fraction (BV/TV) and the fabric tensor determined by MIL. The treatment/sterilization process does not appear to influence bone graft stiffness. However, strength and energy dissipation of the bone grafts were found to be significantly reduced by 36% to 47% and 66% to 81%, respectively, for a broad range of volume fraction (0.14 < BV/TV < 0.39) and degree of anisotropy (1.24 < DA < 2.18). Since the latter properties are strongly dominated by BV/TV, the clinical consequences of this reduction can be compensated by using grafts with lower porosity. The data of this study suggests that an increase of 5–10% in BV/TV is sufficient to compensate for the reduced post-yield mechanical properties of treated/sterilized bone in monotonic compression. In applications where graft stiffness needs to be matched and strength is not a concern, treated allograft with the same BV/TV as an appropriate fresh bone graft may be used.

Hydrogels for nucleus replacement—Facing the biomechanical challenge

Hydrogels are considered promising for disc regeneration strategies. However, it is currently unknown whether the destruction of the natural interface between nucleus and surrounding structures caused by nucleotomy and an inadequate annulus closure diminishes the mechanical competence of the disc. This in vitro study aimed to clarify these mechanisms and to evaluate whether hydrogels are able to restore the biomechanical behaviour of the disc. Nucleus pressure in an ovine intervertebral disc was measured in vivo during day and night and adapted to an in vitro axial compressive diurnal (15min) and night (30min) load. Effects of different defects on disc height and nucleus pressure were subsequently measured in vitro using 30 ovine motion segments. Following cases were considered: intact; annulus incision repaired by suture and glue; annulus incision with removal and re-implantation of nucleus tissue; and two different hydrogels repaired by suture and glue. The intradiscal pressure in vivo was 0.75MPa during day and 0.5MPa during night corresponding to an in vitro axial compressive force of 130 and 58N, respectively. The compression test showed that neither the implantation of hydrogels nor the re-implantation of the natural nucleus, assumed as being the ideal implant, was able to restore the mechanical functionality of an intact disc. Results indicate the importance of the natural anchorage of the nucleus with its surrounding structures and the relevance of an appropriate annulus closure. Therefore, hydrogels that are able to mimic the mechanical behaviour of the native nucleus may fail in restoring the mechanical behaviour of the disc.

Impact of measurement errors on the determination of the linear modulus of human meniscal attachments

For the development of meniscal substitutes and related finite element models it is necessary to know the mechanical properties of the meniscus and its attachments. Measurement errors can falsify the determination of material properties. Therefore the impact of metrological and geometrical measurement errors on the determination of the linear modulus of human meniscal attachments was investigated. After total differentiation the error of the force (+0.10%), attachment deformation (−0.16%), and fibre length (+0.11%) measurements almost annulled each other. The error of the cross-sectional area determination ranged from 0.00%, gathered from histological slides, up to 14.22%, obtained from digital calliper measurements. Hence, total measurement error ranged from +0.05% to −14.17%, predominantly affected by the cross-sectional area determination error. Further investigations revealed that the entire cross-section was significantly larger compared to the load-carrying collagen fibre area. This overestimation of the cross-section area led to an underestimation of the linear modulus of up to −36.7%. Additionally, the cross-sections of the collagen-fibre area of the attachments significantly varied up to +90% along their longitudinal axis. The resultant ratio between the collagen fibre area and the histologically determined cross-sectional area ranged between 0.61 for the posterolateral and 0.69 for the posteromedial ligament. The linear modulus of human meniscal attachments can be significantly underestimated due to the use of different methods and locations of cross-sectional area determination. Hence, it is suggested to assess the load carrying collagen fibre area histologically, or, alternatively, to use the correction factors proposed in this study.

Regional structural characteristics of bovine periodontal ligament samples and their suitability for biomechanical tests

Mechanical testing of the periodontal ligament requires a practical experimental model. Bovine teeth are advantageous in terms of size and availability, but information is lacking as to the anatomy and histology of their periodontium. The aim of this study, therefore, was to characterize the anatomy and histology of the attachment apparatus in fully erupted bovine mandibular first molars. A total of 13 teeth were processed for the production of undecalcified ground sections and decalcified semi-thin sections, for NaOH maceration, and for polarized light microscopy. Histomorphometric measurements relevant to the mechanical behavior of the periodontal ligament included width, number, size and area fraction of blood vessels and fractal analysis of the two hard-soft tissue interfaces. The histological and histomorphometric analyses were performed at four different root depths and at six circumferential locations around the distal and mesial roots. The variety of techniques applied provided a comprehensive view of the tissue architecture of the bovine periodontal ligament. Marked regional variations were observed in width, surface geometry of the two bordering hard tissues (cementum and alveolar bone), structural organization of the principal periodontal ligament connective tissue fibers, size, number and numerical density of blood vessels in the periodontal ligament. No predictable pattern was observed, except for a statistically significant increase in the area fraction of blood vessels from apical to coronal. The periodontal ligament width was up to three times wider in bovine teeth than in human teeth. The fractal analyses were in agreement with the histological observations showing frequent signs of remodeling activity in the alveolar bone - a finding which may be related to the magnitude and direction of occlusal forces in ruminants. Although samples from the apical root portion are not suitable for biomechanical testing, all other levels in the buccal and lingual aspects of the mesial and distal roots may be considered. The bucco-mesial aspect of the distal root appears to be the most suitable location.

Hierarchical Markov Random Fields Applied to Model Soft Tissue Deformations on Graphics Hardware

Many methodologies dealing with prediction or simulation of soft tissue deformations on medical image data require preprocessing of the data in order to produce a different shape representation that complies with standard methodologies, such as mass–spring networks, finite element method s (FEM). On the other hand, methodologies working directly on the image space normally do not take into account mechanical behavior of tissues and tend to lack physics foundations driving soft tissue deformations. This chapter presents a method to simulate soft tissue deformations based on coupled concepts from image analysis and mechanics theory. The proposed methodology is based on a robust stochastic approach that takes into account material properties retrieved directly from the image, concepts from continuum mechanics and FEM. The optimization framework is solved within a hierarchical Markov random field (HMRF) which is implemented on the graphics processor unit (GPU See Graphics processing unit ).

Finite element analysis for prediction of bone strength

Article preview View full access options BoneKEy Reports | Review Print Email Share/bookmark Finite element analysis for prediction of bone strength Philippe K Zysset, Enrico Dall'Ara, Peter Varga & Dieter H Pahr Affiliations Corresponding author BoneKEy Reports (2013) 2, Article number: 386 (2013) doi:10.1038/bonekey.2013.120 Received 03 January 2013 Accepted 25 June 2013 Published online 07 August 2013 Article tools Citation Reprints Rights & permissions Abstract Abstract• References• Author information Finite element (FE) analysis has been applied for the past 40 years to simulate the mechanical behavior of bone. Although several validation studies have been performed on specific anatomical sites and load cases, this study aims to review the predictability of human bone strength at the three major osteoporotic fracture sites quantified in recently completed in vitro studies at our former institute. Specifically, the performance of FE analysis based on clinical computer tomography (QCT) is compared with the ones of the current densitometric standards, bone mineral content, bone mineral density (BMD) and areal BMD (aBMD). Clinical fractures were produced in monotonic axial compression of the distal radii, vertebral sections and in side loading of the proximal femora. QCT-based FE models of the three bones were developed to simulate as closely as possible the boundary conditions of each experiment. For all sites, the FE methodology exhibited the lowest errors and the highest correlations in predicting the experimental bone strength. Likely due to the improved CT image resolution, the quality of the FE prediction in the peripheral skeleton using high-resolution peripheral CT was superior to that in the axial skeleton with whole-body QCT. Because of its projective and scalar nature, the performance of aBMD in predicting bone strength depended on loading mode and was significantly inferior to FE in axial compression of radial or vertebral sections but not significantly inferior to FE in side loading of the femur. Considering the cumulated evidence from the published validation studies, it is concluded that FE models provide the most reliable surrogates of bone strength at any of the three fracture sites.

An experimentally validated finite element method for augmented vertebral bodies

Background Finite element models of augmented vertebral bodies require a realistic modelling of the cement infiltrated region. Most methods published so far used idealized cement shapes or oversimplified material models for the augmented region. In this study, an improved, anatomy-specific, homogenized finite element method was developed and validated to predict the apparent as well as the local mechanical behavior of augmented vertebral bodies. Methods Forty-nine human vertebral body sections were prepared by removing the cortical endplates and scanned with high-resolution peripheral quantitative CT before and after injection of a standard and a low-modulus bone cement. Forty-one specimens were tested in compression to measure stiffness, strength and contact pressure distributions between specimens and loading-plates. From the remaining eight, fourteen cylindrical specimens were extracted from the augmented region and tested in compression to obtain material properties. Anatomy-specific finite element models were generated from the CT data. The models featured element-specific, density-fabric-based material properties, damage accumulation, real cement distributions and experimentally determined material properties for the augmented region. Apparent stiffness and strength as well as contact pressure distributions at the loading plates were compared between simulations and experiments. Findings The finite element models were able to predict apparent stiffness (R2 > 0.86) and apparent strength (R2 > 0.92) very well. Also, the numerically obtained pressure distributions were in reasonable quantitative (R2 > 0.48) and qualitative agreement with the experiments. Interpretation The proposed finite element models have proven to be an accurate tool for studying the apparent as well as the local mechanical behavior of augmented vertebral bodies.

Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation

Purpose The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. Methods Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5 µm were performed and the indentation modulus was computed for each measurement. Results The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8 GPa, compared to the circumferential one, 12.3±3.5 GPa, and radial one, 8.3±3.1 GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9 GPa, and along the lateral, 12.0±3.0 GPa, directions) and the trabecular bone (Ei= 13.7±3.4 GPa along the axial direction versus Ei=10.9±3.7 GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3 GPa). Conclusions The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis.

Clinical versus pre-clinical FE models for vertebral body strength predictions

The finite element analysis is an accepted method to predict vertebral body compressive strength. This study compares measurements obtained from in vitro tests with the ones from two different simulation models: clinical quantitative computer tomography (QCT) based homogenized finite element (hFE) models and pre-clinical high-resolution peripheral QCT-based (HR-pQCT) hFE models. About 37 vertebral body sections were prepared by removing end-plates and posterior elements, scanned with QCT (390/450μm voxel size) as well as HR-pQCT (82μm voxel size), and tested in compression up to failure. Non-linear viscous damage hFE models were created from QCT/HT-pQCT images and compared to experimental results based on stiffness and ultimate load. As expected, the predictability of QCT/HR-pQCT-based hFE models for both apparent stiffness (r2=0.685/0.801r2=0.685/0.801) and strength (r2=0.774/0.924r2=0.774/0.924) increased if a better image resolution was used. An analysis of the damage distribution showed similar damage locations for all cases. In conclusion, HR-pQCT-based hFE models increased the predictability considerably and do not need any tuning of input parameters. In contrast, QCT-based hFE models usually need some tuning but are clinically the only possible choice at the moment.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.