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.

Impact of bone graft harvesting techniques on bone formation and graft resorption: a histomorphometric study in the mandibles of minipigs.

BACKGROUND: Harvesting techniques can affect cellular parameters of autogenous bone grafts in vitro. Whether these differences translate to in vivo bone formation, however, remains unknown. OBJECTIVE: The purpose of this study was to assess the impact of different harvesting techniques on bone formation and graft resorption in vivo. MATERIAL AND METHODS: Four harvesting techniques were used: (i) corticocancellous blocks particulated by a bone mill; (ii) bone scraper; (iii) piezosurgery; and (iv) bone slurry collected from a filter device upon drilling. The grafts were placed into bone defects in the mandibles of 12 minipigs. The animals were sacrificed after 1, 2, 4 and 8 weeks of healing. Histology and histomorphometrical analyses were performed to assess bone formation and graft resorption. An explorative statistical analysis was performed. RESULTS: The amount of new bone increased, while the amount of residual bone decreased over time with all harvesting techniques. At all given time points, no significant advantage of any harvesting technique on bone formation was observed. The harvesting technique, however, affected bone formation and the amount of residual graft within the overall healing period. Friedman test revealed an impact of the harvesting technique on residual bone graft after 2 and 4 weeks. At the later time point, post hoc testing showed more newly formed bone in association with bone graft processed by bone mill than harvested by bone scraper and piezosurgery. CONCLUSIONS: Transplantation of autogenous bone particles harvested with four techniques in the present model resulted in moderate differences in terms of bone formation and graft resorption.

Bone-Conditioned Medium Inhibits Osteogenic and Adipogenic Differentiation of Mesenchymal Cells In Vitro

BACKGROUND AND PURPOSE Autografts are used for bone reconstruction in regenerative medicine including oral and maxillofacial surgery. Bone grafts release paracrine signals that can reach mesenchymal cells at defect sites. The impact of the paracrine signals on osteogenic, adipogenic, and chondrogenic differentiation of mesenchymal cells has remained unclear. MATERIAL AND METHODS Osteogenesis, adipogenesis, and chondrogenesis were studied with murine ST2 osteoblast progenitors, 3T3-L1 preadipocytes, and ATDC5 prechondrogenic cells, respectively. Primary periodontal fibroblasts from the gingiva, from the periodontal ligament, and from bone were also included in the analysis. Cells were exposed to bone-conditioned medium (BCM) that was prepared from porcine cortical bone chips. RESULTS BCM inhibited osteogenic and adipogenic differentiation of ST2 and 3T3-L1 cells, respectively, as shown by histological staining and gene expression. No substantial changes in the expression of chondrogenic genes were observed in ATDC5 cells. Primary periodontal fibroblasts also showed a robust decrease in alkaline phosphatase and peroxisome proliferator-activated receptor gamma (PPARγ) expression when exposed to BCM. BCM also increased collagen type 10 expression. Pharmacologic blocking of transforming growth factor (TGF)-β receptor type I kinase with SB431542 and the smad-3 inhibitor SIS3 at least partially reversed the effect of BCM on PPARγ and collagen type 10 expression. In support of BCM having TGF-β activity, the respective target genes were increasingly expressed in periodontal fibroblasts. CONCLUSIONS The present work is a pioneer study on the paracrine activity of bone grafts. The findings suggest that cortical bone chips release soluble signals that can modulate differentiation of mesenchymal cells in vitro at least partially involving TGF-β signaling.

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.

Morphology–elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations

With improving clinical CT scanning technology, the accuracy of CT-based finite element (FE) models of the human skeleton may be ameliorated by an enhanced description of apparent level bone mechanical properties. Micro-finite element (μFE) modeling can be used to study the apparent elastic behavior of human cancellous bone. In this study, samples from the femur, radius and vertebral body were investigated to evaluate the predictive power of morphology–elasticity relationships and to compare them across different anatomical regions. μFE models of 701 trabecular bone cubes with a side length of 5.3 mm were analyzed using kinematic boundary conditions. Based on the FE results, four morphology–elasticity models using bone volume fraction as well as full, limited or no fabric information were calibrated for each anatomical region. The 5 parameter Zysset–Curnier model using full fabric information showed excellent predictive power with coefficients of determination ( r2adj ) of 0.98, 0.95 and 0.94 of the femur, radius and vertebra data, respectively, with mean total norm errors between 14 and 20%. A constant orthotropy model and a constant transverse isotropy model, where the elastic anisotropy is defined by the model parameters, yielded coefficients of determination between 0.90 and 0.98 with total norm errors between 16 and 25%. Neglecting fabric information and using an isotropic model led to r2adj between 0.73 and 0.92 with total norm errors between 38 and 49%. A comparison of the model regressions revealed minor but significant (p<0.01) differences for the fabric–elasticity model parameters calibrated for the different anatomical regions. The proposed models and identified parameters can be used in future studies to compute the apparent elastic properties of human cancellous bone for homogenized FE models.

Das Paradox der Wahlbeteiligung, das keines ist. Eine theoretische Rekonstruktion und empirische Anwendung des Ansatzes von Downs aus der Perspektive der Theorie subjektiver Werterwartung

Seit der richtungweisenden wie einflußreichen Arbeit von Downs (1957) wird in der empirischen Wahlforschung das „Paradox der Wahlbeteiligung“ kontrovers diskutiert. Kritiker des ökonomischen Ansatzes führen gerade dieses Paradox an, um die Grenzen von Rational-Choice-Theorien aufzuzeigen (z.B. Green und Shapiro 1994). Ausgangspunkt dieser Debatte ist zunächst der Versuch von Downs, die Beteiligung von Individuen an politischen Wahlen mit der Theorie rationaler Entscheidung zu erklären: Demnach beteiligen sich Wahlberechtigte an Wahlen, wenn aus ihrer Sicht der erwartete Nutzen der Wahlbeteiligung (etwa persönliche Vorteile nach dem Wahlsieg der präferierten Partei) die anfallenden Kosten der Wahlbeteiligung (etwa zeitlicher Aufwand für Beschaffung, Auswertung und Analyse von Informationen über das Politikangebot) übersteigt. Wahlberechtigte diskontieren den zu maximierenden Nutzen aus ihrer Wahlbeteiligung mit der Wahrscheinlichkeit, daß ihre eigene Stimme der präferierten Partei zum Wahlsieg verhilft. Allerdings tendiert diese Wahrscheinlichkeit, den Wahlausgang alleine zu entscheiden, mit der anwachsenden Größe des Elektorats gegen Null. Da aber aus Sicht des einzelnen Wählers die eigene Stimme so gut wie keinen entscheidenden Einfluß auf den Wahlausgang hat, aber mit Sicherheit Informations-, Opportunitäts- und Teilnahmekosten anfallen, die dann immer größer als die mit der Erfolgswahrscheinlichkeit gewichteten Nutzeneinkommen sind, ist es höchst unwahrscheinlich, daß sich ein instrumentell rationaler Akteur an politischen Wahlen beteiligt (Downs 1957: 244–245). Jedoch sind in modernen Demokratien die Beteiligungen an politischen Wahlen mitunter beträchtlich, und diese empirische Beobachtung widerspricht der ökonomischen Theorie des Wählens von Downs (1957)1. Es stellt sich also die Frage, warum sich Wahlberechtigte an politischen Wahlen beteiligen und warum die Wahlbeteiligungen zumeist recht hoch sind (vgl. Palfrey und Rosenthal 1993).

Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a Gradient Structure Tensor (GST) and a Sobel Structure Tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28°), and the error was inversely correlated to the degree of transverse isotropy (r=−0.34, p<0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p<0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p<0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone.

Syntheses, receptor bindings, in vitro and in vivo stabilities and biodistributions of DOTA-neurotensin(8-13) derivatives containing β-amino acid residues - a lesson about the importance of animal experiments

Neurotensin(8-13) (NTS(8-13)) analogs with C- and/or N-terminal β-amino acid residues and three DOTA derivatives thereof have been synthesized (i.e., 1-6). A virtual docking experiment showed almost perfect fit of one of the 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA) derivatives, 6a, into a crystallographically identified receptor NTSR1 (Fig.1). The affinities for the receptors of the NTS analogs and derivatives are low, when determined with cell-membrane homogenates, while, with NTSR1-exhibiting cancer tissues, affinities in the single-digit nanomolar range can be observed (Table 2). Most of the β-amino acid-containing NTS(8-13) analogs (Table 1 and Fig.2), including the (68) Ga complexes of the DOTA-substituted ones (6; Figs.2 and 5), are stable for ca. 1 h in human serum and plasma, and in murine plasma. The biodistributions of two (68) Ga complexes (of 6a and 6b) in HT29 tumor-bearing nude mice, in the absence and in the presence of a blocking compound, after 10, 30, and 60 min (Figs. 3 and 4) lead to the conclusion that the amount of specifically bound radioligand is rather low. This was confirmed by PET-imaging experiments with the tumor-bearing mice (Fig.6). Comparison of the in vitro plasma stability (after 1 h) with the ex vivo blood content (after 10-15 min) of the two (68) Ga complexes shows that they are rapidly cleaved in the animals (Fig.5).