Publications by authors named "Philippe K Zysset"

87 Publications

Prediction of the Inelastic Behaviour of Radius Segments: Damage-based Nonlinear Micro Finite Element Simulation vs Pistoia Criterion.

J Biomech 2021 02 2;116:110205. Epub 2021 Jan 2.

Institute of Lightweight Design and Structural Biomechanics, TU Wien, Austria; Division Biomechanics, Karl Landsteiner University, Austria.

The Pistoia criterion (PC) is widely used to estimate the failure load of distal radius segments based on linear micro Finite Element (μFE) analyses. The advantage of the PC is that a simple strain-threshold and a tissue volume fraction can be used to predict failure properties. In this study, the PC is compared to materially nonlinear μFE analyses, where the bone tissue is modelled as an elastic, damageable material. The goal was to investigate for which outcomes the PC is sufficient and when a nonlinear (NL) simulation is required. Three types of simulation results were compared: (1) prediction of the failure load, (2) load sharing of cortical and trabecular regions, and (3) distribution of local damaged/overstrained tissue at the maximum sustainable load. The failure load obtained experimentally could be predicted well with both the PC and the NL simulations using linear regression. Although the PC strongly overestimated the failure load, it was sufficient to predict adequately normalized apparent results. An optimised PC (oPC) was proposed which uses experimental data to calibrate the individual volume of overstrained tissue. The main areas of local over-straining predicted by the oPC were the same as estimated by the NL simulation, although the oPC predicted more diffuse regions. However, the oPC relied on an individual calibration requiring the experimental failure load while the NL simulation required no a priori knowledge of the experimental failure load.
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http://dx.doi.org/10.1016/j.jbiomech.2020.110205DOI Listing
February 2021

Empirical relationships between bone density and ultimate strength: A literature review.

J Mech Behav Biomed Mater 2020 10 3;110:103866. Epub 2020 Jun 3.

Institute for Biomechanics, ETH-Zürich, Zürich, Switzerland.

Introduction: Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

Methods: All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

Results: Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

Conclusions: Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.
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http://dx.doi.org/10.1016/j.jmbbm.2020.103866DOI Listing
October 2020

Conventional finite element models estimate the strength of metastatic human vertebrae despite alterations of the bone's tissue and structure.

Bone 2020 12 20;141:115598. Epub 2020 Aug 20.

ARTORG Center for Biomedical Engineering Research, University of Bern, Freiburgstrasse 3, 3010 Bern, Switzerland. Electronic address:

Introduction: Pathologic vertebral fractures are a major clinical concern in the management of cancer patients with metastatic spine disease. These fractures are a direct consequence of the effect of bone metastases on the anatomy and structure of the vertebral bone. The goals of this study were twofold. First, we evaluated the effect of lytic, blastic and mixed (both lytic and blastic) metastases on the bone structure, on its material properties, and on the overall vertebral strength. Second, we tested the ability of bone mineral content (BMC) measurements and standard FE methodologies to predict the strength of real metastatic vertebral bodies.

Methods: Fifty-seven vertebral bodies from eleven cadaver spines containing lytic, blastic, and mixed metastatic lesions from donors with breast, esophageal, kidney, lung, or prostate cancer were scanned using micro-computed tomography (μCT). Based on radiographic review, twelve vertebrae were selected for nanoindentation testing, while the remaining forty-five vertebrae were used for assessing their compressive strength. The μCT reconstruction was exploited to measure the vertebral BMC and to establish two finite element models. 1) a micro finite element (μFE) model derived at an image resolution of 24.5 μm and 2) homogenized FE (hFE) model derived at a resolution of 0.98 mm. Statistical analyses were conducted to measure the effect of the bone metastases on BV/TV, indentation modulus (E), ratio of plastic/total work (W/W), and in vitro vertebral strength (F). The predictive value of BMC, μFE stiffness, and hFE strength were evaluated against the in vitro measurements.

Results: Blastic vertebral bodies exhibit significantly higher BV/TV compared to the mixed (p = 0.0205) and lytic (p = 0.0216) vertebral bodies. No significant differences were found between lytic and mixed vertebrae (p = 0.7584). Blastic bone tissue exhibited a 5.8% lower median E (p< 0.001) and a 3.3% lower median W/W (p<0.001) compared to non-involved bone tissue. No significant differences were measured between lytic and non-involved bone tissues. F ranged from 1.9 to 13.8 kN, was strongly associated with hFE strength (R=0.78, p< 0.001) and moderately associated with BMC (R=0.66, p< 0.001) and μFE stiffness (R=0.66, p< 0.001), independently of the lesion type.

Discussion: Our findings show that tumour-induced osteoblastic metastases lead to slightly, but significantly lower bone tissue properties compared to controls, while osteolytic lesions appear to have a negligible impact. These effects may be attributed to the lower mineralization and woven nature of bone forming in blastic lesions whilst the material properties of bone in osteolytic vertebrae appeared little changed. The moderate association between BMC- and FE-based predictions to fracture strength suggest that vertebral strength is affected by the changes of bone mass induced by the metastatic lesions, rather than altered tissue properties. In a broader context, standard hFE approaches generated from CTs at clinical resolution are robust to the lesion type when predicting vertebral strength. These findings open the door for the development of FE-based prediction tools that overcomes the limitations of BMC in accounting for shape and size of the metastatic lesions. Such tools may help clinicians to decide whether a patient needs the prophylactic fixation of an impending fracture.
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http://dx.doi.org/10.1016/j.bone.2020.115598DOI Listing
December 2020

Finite element models can reproduce the effect of nucleotomy on the multi-axial compliance of human intervertebral discs.

Comput Methods Biomech Biomed Engin 2020 Oct 16;23(13):934-944. Epub 2020 Jun 16.

Department of Orthopedic Surgery, Bern University Hospital, Bern, Switzerland.

Finite element (FE) models can unravel the link between intervertebral disc (IVD) degeneration and its mechanical behaviour. Nucleotomy may provide the data required for model verification. Three human IVDs were scanned with MRI and tested in multiple loading scenarios, prior and post nucleotomy. The resulting data was used to generate, calibrate, and verify the FE models. Nucleotomy increased the experimental range of motion by 26%, a result reproduced by the FE simulation within a 5% error. This work demonstrates the ability of FE models to reproduce the mechanical compliance of human IVDs prior and post nucleotomy.
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http://dx.doi.org/10.1080/10255842.2020.1773808DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7735477PMC
October 2020

Explicit finite element analysis can predict the mechanical response of conical implant press-fit in homogenized trabecular bone.

J Biomech 2020 06 16;107:109844. Epub 2020 May 16.

ARTORG Centre for Biomedical Engineering Research, University of Bern, Freiburgstrasse 3, 3010 Bern, Switzerland.

Prediction of primary stability is a major challenge in the surgical planning of dental and orthopedic implants. Computational methods become attractive to estimate primary stability from clinical CT images, but implicit finite element analysis of implant press-fit faces convergence issues due to contact and highly distorted elements. This study aims to develop and validate an explicit finite element method to simulate the insertion and primary stability of a rigid implant in a deformable bone while accounting for damage occurring at the bone-implant interface. Accordingly, a press-fit experiment of a conical implant into predrilled bovine trabecular bone was designed and realized for six samples. A displacement-driven cyclic protocol was used to quantify the reaction force and stiffness of the bone-implant system. Homogenized finite element analyses of the experiments were performed by modeling contact with friction and converting an existing constitutive model with elasto-plasticity and damage of bone tissue to be applicable to an explicit time integration scheme where highly distorted elements get deleted. The computed reaction forces and unloading stiffnesses showed high correlations (R = 0.95 and R = 0.94) with the experiment. Friction between bone and implant exhibited a strong influence on both reaction force and stiffness. In conclusion, the developed explicit finite element approach with frictional contact and element deletion accounts properly for bone damage during press-fit and will help optimizing dental or orthopedic implant design towards maximal primary stability.
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http://dx.doi.org/10.1016/j.jbiomech.2020.109844DOI Listing
June 2020

Finite element analysis of bone strength in osteogenesis imperfecta.

Bone 2020 04 22;133:115250. Epub 2020 Jan 22.

ARTORG Centre for Biomedical Engineering Research, University of Bern, Bern, Switzerland.

As a dedicated experimentalist, John Currey praised the high potential of finite element (FE) analysis but also recognized its critical limitations. The application of the FE methodology to bone tissue is reviewed in the light of his enthusiastic and colorful statements. In the past decades, FE analysis contributed substantially to the understanding of structure-function properties in the hierarchical organization of bone and to the simulation of bone adaptation. The systematic experimental validation of FE analysis of bone strength in anatomical locations at risk of fracture led to its application in clinical studies to evaluate efficacy of antiresorptive or anabolic treatment of bone fragility. Beyond the successful analyses of healthy or osteoporotic bone, FE analysis becomes increasingly involved in the investigation of other fragility-related bone diseases. The case of osteogenesis imperfecta (OI) is exposed, the multiscale alterations of the bone tissue and the effect of treatment summarized. A few FE analyses attempting to answer open questions in OI are then reported. An original study is finally presented that explored the structural properties of the Brtl/+ murine model of OI type IV subjected to sclerostin neutralizing antibody treatment using microFE analysis. The use of identical material properties in the four-point bending FE simulations of the femora reproduced not only the experimental values but also the statistical comparisons examining the effect of disease and treatment. Further efforts are needed to build upon the extraordinary legacy of John Currey and clarify the impact of different bone diseases on the hierarchical mechanical properties of bone.
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http://dx.doi.org/10.1016/j.bone.2020.115250DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7383936PMC
April 2020

Efficient materially nonlinear [Formula: see text]FE solver for simulations of trabecular bone failure.

Biomech Model Mechanobiol 2020 Jun 20;19(3):861-874. Epub 2019 Nov 20.

Institute of Lightweight Design and Structural Biomechanics, TU Wien, Vienna, Austria.

An efficient solver for large-scale linear [Formula: see text] simulations was extended for nonlinear material behavior. The material model included damage-based tissue degradation and fracture. The new framework was applied to 20 trabecular biopsies with a mesh resolution of [Formula: see text]. Suitable material parameters were identified based on two biopsies by comparison with axial tension and compression experiments. The good parallel performance and low memory footprint of the solver were preserved. Excellent correlation of the maximum apparent stress was found between simulations and experiments ([Formula: see text]). The development of local damage regions was observable due to the nonlinear nature of the simulations. A novel elasticity limit was proposed based on the local damage information. The elasticity limit was found to be lower than the 0.2% yield point. Systematic differences in the yield behavior of biopsies under apparent compression and tension loading were observed. This indicates that damage distributions could lead to more insight into the failure mechanisms of trabecular bone.
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http://dx.doi.org/10.1007/s10237-019-01254-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7203600PMC
June 2020

Prediction of insertion torque and stiffness of a dental implant in bovine trabecular bone using explicit micro-finite element analysis.

J Mech Behav Biomed Mater 2019 10 28;98:301-310. Epub 2019 Jun 28.

ARTORG Centre for Biomedical Engineering Research, University of Bern, Stauffacherstrasse 78, 3014, Bern, Switzerland.

The assessment of dental implant performance is dominated by the concept of mechanical stability. Primary stability is defined as the capacity of a bone-implant structure to bear loads without occurrence of excessive damage and loosening. In order to achieve the highest primary stability, dental implants are inserted into bone using a press-fit procedure. Pre- and postoperative evaluation of primary stability using implantation torque and resonance frequency analysis are valid approaches but do not allow the systematic comparison of different protocols in similar situations. The aim of this research is to develop and validate an explicit, micro-finite element (μFE) methodology to study the effect of different amounts of initial press-fit on implantation torque and initial stiffness of a dental implant. Ten bovine trabecular bone samples were prepared that cover a wide range of bone volume fraction. A dental implant was inserted using two implantation protocols named soft (small initial drilled hole) and dense (increased initial drilled hole). The implantation torque was measured and the stiffness was calculated using an infinitesimal off-axis loading. Finite element simulations of the implant insertion and subsequent loading were performed on micro-computed tomography (μCT) reconstructions of the samples using an explicit solver. Bone was defined as an elasto-plastic material with von Mises yield criteria and hardening. Element deletion was triggered by a threshold in cumulated plastic strains. A sensitivity analysis was performed on friction, hardening and fracture strain to provide a better insight into the effects of these parameters on the results. The implantation torque required for the soft protocol was higher compared to the dense approach in both experiment and simulation due to the higher amount of bone compaction in the first approach. Interestingly, stiffness did not show a significant dependency on the drilling protocol in both experiment and simulation. In conclusion, the explicit microFE methodology developed in this study was able to capture the outcome of two drilling protocols in terms of torque and stiffness and represents a powerful tool to explore the effect of different parameters on primary stability of dental implants.
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http://dx.doi.org/10.1016/j.jmbbm.2019.06.024DOI Listing
October 2019

Compressive behaviour of uniaxially aligned individual mineralised collagen fibres at the micro- and nanoscale.

Acta Biomater 2019 04 8;89:313-329. Epub 2019 Mar 8.

Institute of Mechanical, Process and Energy Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK. Electronic address:

The increasing incidence of osteoporotic bone fractures makes fracture risk prediction an important clinical challenge. Computational models can be utilised to facilitate such analyses. However, they critically depend on bone's underlying hierarchical material description. To understand bone's irreversible behaviour at the micro- and nanoscale, we developed an in situ testing protocol that allows us to directly relate the experimental data to the mechanical behaviour of individual mineralised collagen fibres and its main constitutive phases, the mineralised collagen fibrils and the mineral nanocrystals, by combining micropillar compression of single fibres with small angle X-ray scattering (SAXS) and X-ray diffraction (XRD). Failure modes were assessed by SEM. Strain ratios in the elastic region at fibre, fibril and mineral levels were found to be approximately 22:5:2 with strain ratios at the point of compressive strength of 0.23 ± 0.11 for fibril-to-fibre and 0.07 ± 0.01 for mineral-to-fibre levels. Mineral-to-fibre levels showed highest strain ratios around the apparent yield point, fibril-to-fibre around apparent strength. The mineralised collagen fibrils showed a delayed mechanical response, contrary to the mineral phase, which points towards preceding deformations of mineral nanocrystals in the extrafibrillar matrix. No damage was measured at the level of the mineralised collagen fibre which indicates an incomplete separation of the mineral and collagen, and an extrafibrillar interface failure. The formation of kink bands and the gradual recruitment of fibrils upon compressive loading presumably led to localised strains. Our results from a well-controlled fibrillar architecture provide valuable input for micromechanical models and computational non-linear bone strength analyses that may provide further insights for personalised diagnosis and treatment as well as bio-inspired implants for patients with bone diseases. STATEMENT OF SIGNIFICANCE: Musculoskeletal diseases such as osteoporosis, osteoarthritis or bone cancer significantly challenge health care systems and make fracture risk prediction and treatment optimisation important clinical goals. Computational methods such as finite element models have the potential to optimise analyses but highly depend on underlying material descriptions. We developed an in situ testing set-up to directly relate experimental data to the mechanical behaviour of bone's fundamental building block, the individual mineralised collagen fibre and its main constituents. Low multilevel strain ratios suggest high deformations in the extrafibrillar matrix and energy dissipation at the interfaces, the absence of damage indicates both an incomplete separation between mineral and collagen and an extrafibrillar interface failure. The formation of kink bands in the fibril-reinforced composite presumably led to localised strains. The deformation behaviour of a well-controlled fibrillar architecture provides valuable input for non-linear bone strength analyses.
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http://dx.doi.org/10.1016/j.actbio.2019.02.053DOI Listing
April 2019

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations.

Int J Numer Method Biomed Eng 2019 05 13;35(5):e3188. Epub 2019 Mar 13.

ARTORG Center for Biomedical Engineering Research, University of Bern, Stauffacherstr. 78, CH-3014, Bern, Switzerland.

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.
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http://dx.doi.org/10.1002/cnm.3188DOI Listing
May 2019

"Peroperative estimation of bone quality and primary dental implant stability".

J Mech Behav Biomed Mater 2019 04 28;92:24-32. Epub 2018 Dec 28.

Institute for Surgical Technology and Biomechanics, University of Bern, Stauffacherstrasse 78, 3014 Bern, Switzerland; Institute for Mechanical, Process and Energy Engineering, Heriot-Watt University, UK EH14 4AS, Edinburgh, United Kingdom.

Objectives: Dental implants are widely used to restore function and appearance. It may be essential to choose the appropriate drilling protocol and implant design in order to optimise primary stability. This could be achieved based on an assessment of the implantation site with respect to bone quality and objective biomechanical descriptors such as stiffness and strength of the bone-implant system. The aim of this ex vivo study is to relate these descriptors with bone quality, with a pre-implantation indicator of implant stability: pilot-hole drilling force (F), and with two post-implantation indicators: maximal implantation torque (T) and resonance frequency analysis (RFA).

Methods: Eighty trabecular bone specimens were cored from human vertebrae and bovine tibiae. Bone volume fraction (BV/TV), a representative for bone quality, was obtained through micro-computed tomography scans. Implants were kept in controlled laboratory conditions following standard surgical procedures. Forces and torques were recorded and RFA was assessed after implantation. Off-axis compression tests were conducted on the implants until failure. Implant stability was identified by stiffness and ultimate force (F). The relationships between BV/TV, Stiffness, F and F, T, RFA were established.

Results: F correlated well with BV/TV of the implantation site (r = 0.81), stiffness (r = 0.75) and F (r = 0.80). T correlated better with stiffness (r = 0.86) and F (r = 0.94) than RFA (r = 0.77 and r = 0.74, respectively).

Conclusion: Our results indicate that BV/TV and bone-implant stability can be directly estimated by the force needed for the pilot drilling that occurs during the site preparation before implantation. Moreover, implantation torque outperforms RFA for evaluating the mechanical competence of the bone-implant system.
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http://dx.doi.org/10.1016/j.jmbbm.2018.12.035DOI Listing
April 2019

Integrating MRI-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc.

J Mech Behav Biomed Mater 2018 09 17;85:37-42. Epub 2018 May 17.

Institute of Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland.

Intervertebral disc degeneration is a common disease that is often related to impaired mechanical function, herniations and chronic back pain. The degenerative process induces alterations of the disc's shape, composition and structure that can be visualized in vivo using magnetic resonance imaging (MRI). Numerical tools such as finite element analysis (FEA) have the potential to relate MRI-based information to the altered mechanical behavior of the disc. However, in terms of geometry, composition and fiber architecture, current FE models rely on observations made on healthy discs and might therefore not be well suited to study the degeneration process. To address the issue, we propose a new, more realistic FE methodology based on diffusion tensor imaging (DTI). For this study, a human disc joint was imaged in a high-field MR scanner with proton-density weighted (PD) and DTI sequences. The PD image was segmented and an anatomy-specific mesh was generated. Assuming accordance between local principal diffusion direction and local mean collagen fiber alignment, corresponding fiber angles were assigned to each element. Those element-wise fiber directions and PD intensities allowed the homogenized model to smoothly account for composition and fibrous structure of the disc. The disc's in vitro mechanical behavior was quantified under tension, compression, flexion, extension, lateral bending and rotation. The six resulting load-displacement curves could be replicated by the FE model, which supports our approach as a first proof of concept towards patient-specific disc modeling.
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http://dx.doi.org/10.1016/j.jmbbm.2018.05.005DOI Listing
September 2018

Ultimate force and stiffness of 2-piece zirconium dioxide implants with screw-retained monolithic lithium-disilicate reconstructions.

J Prosthodont Res 2018 Apr 15;62(2):258-263. Epub 2017 Dec 15.

Department of Prosthodontics & Dental Materials, School of Dental Medicine, University of Siena, Italy; Dental Trial Clinical Research Unit [DenTCRU], School of Dentistry, University of Leeds, United Kingdom.

Purpose: The aims were to analyze stiffness, ultimate force, and failure modes of a 2-piece zirconium dioxide (ZrO) implant system.

Methods: Eleven 2-piece ZrO implants, each mounted with ZrO abutments plus bonded monolithic lithium disilicate (LS) restorations, were grouped for 3.3mm (A) and 4.1mm (B) diameter samples. Quasi-static load was monotonically applied under a standardized test set-up (loading configuration according to DIN ISO 14801). The ultimate force was defined as the maximum force that implants are able to carry out until fracture; stiffness was measured as the maximum slope during loading. An unpaired t-test was performed between group A and B for ultimate force and stiffness (p<0.05).

Results: Force-displacement curves revealed statistically homogenous inner-group results for all samples. Failure modes showed characteristic fractures at the neck configuration of the implants independent of the diameter. Mean stiffness was 1099N/mm (±192) for group A, and significantly lower compared to group B with 1630N/mm (±274) (p<0.01); whereas mean ultimate force was 348N (±53) for group A, and significantly increased for group B with 684N (±29) (p<0.0001).

Conclusions: The examined 2-piece ZrO implant system mounted to LS-restorations seems to be a stable unit under in-vitro conditions with mechanical properties compared to loading capacity of physiological force. The metal-free implant reconstructions demonstrated high stiffness and ultimate force under quasi-static load for single tooth replacement under consideration of the dental indication of narrow and standard diameter implants.
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http://dx.doi.org/10.1016/j.jpor.2017.11.002DOI Listing
April 2018

A rate-independent continuum model for bone tissue with interaction of compressive and tensile micro-damage.

J Mech Behav Biomed Mater 2017 10 8;74:448-462. Epub 2017 Jul 8.

Institute for Mechanical, Process and Energy Engineering, Heriot-Watt University, Edinburgh, United Kingdom.

Low bone strength is a major risk factor for osteoporotic fractures and is only partially determined by clinical densitometry. Accumulated micro-damage induces residual strains, degrades elastic modulus and reduces bone strength independently of bone mineral density. Histologically, overloading of bone in compression and tension leads to distinct crack size, distribution and orientation which interact during combined loading scenarios. Statistics of rheological models can describe this process and reproduce experimental stress-strain curves with an unprecedented realism, but are computationally expensive and therefore difficult to generalize to 3D. Accordingly, the aim of this work is to formulate a continuum damage model that describes the key features of bone micro-damage, namely the accumulation of residual strains, the degradation of elastic modulus and the reduction of strength in compression, tension and especially in their sequential application. The promising qualitative agreement of the model with the experiments will motivate a generalization to 3D and allow the biomechanical investigation of bones and bone-implant systems subjected to cyclic overloading in tension and/or compression.
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http://dx.doi.org/10.1016/j.jmbbm.2017.07.008DOI Listing
October 2017

Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses.

Biomech Model Mechanobiol 2017 Dec 22;16(6):1925-1936. Epub 2017 Jun 22.

Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland.

Micro-finite element ([Formula: see text]FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone ("embedded configuration"). Thirteen cubic volumes (10.6 mm side length) were collected from [Formula: see text]CT reconstructions of human vertebrae and femora and converted into [Formula: see text]FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear [Formula: see text]FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (-10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.
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http://dx.doi.org/10.1007/s10237-017-0928-0DOI Listing
December 2017

New approaches for cement-based prophylactic augmentation of the osteoporotic proximal femur provide enhanced reinforcement as predicted by non-linear finite element simulations.

Clin Biomech (Bristol, Avon) 2017 May 2;44:7-13. Epub 2017 Mar 2.

AO Research Institute Davos, Switzerland.

Background: High incidence and increased mortality related to secondary, contralateral proximal femoral fractures may justify invasive prophylactic augmentation that reinforces the osteoporotic proximal femur to reduce fracture risk. Bone cement-based approaches (femoroplasty) may deliver the required strengthening effect; however, the significant variation in the results of previous studies calls for a systematic analysis and optimization of this method. Our hypothesis was that efficient generalized augmentation strategies can be identified via computational optimization.

Methods: This study investigated, by means of finite element analysis, the effect of cement location and volume on the biomechanical properties of fifteen proximal femora in sideways fall. Novel cement cloud locations were developed using the principles of bone remodeling and compared to the "single central" location that was previously reported to be optimal.

Findings: The new augmentation strategies provided significantly greater biomechanical benefits compared to the "single central" cement location. Augmenting with approximately 12ml of cement in the newly identified location achieved increases of 11% in stiffness, 64% in yield force, 156% in yield energy and 59% in maximum force, on average, compared to the non-augmented state. The weaker bones experienced a greater biomechanical benefit from augmentation than stronger bones. The effect of cement volume on the biomechanical properties was approximately linear. Results of the "single central" model showed good agreement with previous experimental studies.

Interpretation: These findings indicate enhanced potential of cement-based prophylactic augmentation using the newly developed cementing strategy. Future studies should determine the required level of strengthening and confirm these numerical results experimentally.
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http://dx.doi.org/10.1016/j.clinbiomech.2017.03.001DOI Listing
May 2017

μCT-based trabecular anisotropy can be reproducibly computed from HR-pQCT scans using the triangulated bone surface.

Bone 2017 04 18;97:114-120. Epub 2017 Jan 18.

Institute for Surgical Technology and Biomechanics, University of Bern, Stauffacherstr. 78, CH-3014 Bern, Switzerland.

The trabecular structure can be assessed at the wrist or tibia via high-resolution peripheral quantitative computed tomography (HR-pQCT). Yet on this modality, the performance of the existing methods, evaluating trabecular anisotropy is usually overlooked, especially in terms of reproducibility. We thus proposed to compare the TRI routine used by SCANCO Medical AG (Brüttisellen, Switzerland), the classical mean intercept length (MIL), and the grey-level structure tensor (GST) to the mean surface length (MSL), a new method for evaluating a second-order fabric tensor based on the triangulation of the bone surface. The distal radius of 24 fresh-frozen human forearms was scanned three times via HR-pQCT protocols (61μm, 82μm nominal voxel size), dissected, and imaged via micro computed tomography (μCT) at 16μm nominal voxel size. After registering the scans, we compared for each resolution the fabric tensors, determined by the mentioned techniques for 182 trabecular regions of interest. We then evaluated the reproducibility of the fabric information measured by HR-pQCT via precision errors. On μCT, TRI and GST were respectively the best and worst surrogates for MIL (MIL computed on μCT) in terms of eigenvalues and main direction of anisotropy. On HR-pQCT, however, MSL provided the best approximation of MIL. Surprisingly, surface-based approaches (TRI, MSL) also proved to be more precise than both MIL and GST. Our findings confirm that MSL can reproducibly estimate MIL, the current gold standard. MSL thus enables the direct mapping of the fabric-dependent material properties required in homogenised HR-pQCT-based finite element models.
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http://dx.doi.org/10.1016/j.bone.2017.01.016DOI Listing
April 2017

Fast estimation of Colles' fracture load of the distal section of the radius by homogenized finite element analysis based on HR-pQCT.

Bone 2017 04 7;97:65-75. Epub 2017 Jan 7.

Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland. Electronic address:

Fractures of the distal section of the radius (Colles' fractures) occur earlier in life than other osteoporotic fractures. Therefore, they can be interpreted as a warning signal for later, more deleterious fractures of vertebral bodies or the femoral neck. In the past decade, the advent of HR-pQCT allowed a detailed architectural analysis of the distal radius and an automated but time-consuming estimation of its strength with linear micro-finite element (μFE) analysis. Recently, a second generation of HR-pQCT scanner (XtremeCT II, SCANCO Medical, Switzerland) with a resolution beyond 61 μm became available for even more refined biomechanical investigations in vivo. This raises the question how biomechanical outcome variables compare between the original (LR) and the new (HR) scanner resolution. Accordingly, the aim of this work was to validate experimentally a patient-specific homogenized finite element (hFE) analysis of the distal section of the human radius for the fast prediction of Colles' fracture load based on the last generation HR-pQCT. Fourteen pairs of fresh frozen forearms (mean age = 77.5±9) were scanned intact using the high (61 μm) and the low (82 μm) resolution protocols that correspond to the new and original HR-pQCT systems. From each forearm, the 20mm most distal section of the radius were dissected out, scanned with μCT at 16.4 μm and tested experimentally under compression up to failure for assessment of stiffness and ultimate load. Linear and nonlinear hFE models together with linear micro finite element (μFE) models were then generated based on the μCT and HR-pQCT reconstructions to predict the aforementioned mechanical properties of 24 sections. Precision errors of the short term reproducibility of the FE analyses were measured based on the repeated scans of 12 sections. The calculated failure loads correlated strongly with those measured in the experiments: accounting for donor as a random factor, the nonlinear hFE provided a marginal coefficient of determination (R) of 0.957 for the high resolution (HR) and 0.948 for the low resolution (LR) protocols, the linear hFE with R of 0.957 for the HR and 0.947 for the LR protocols. Linear μFE predictions of the ultimate load were similar with an R of 0.950 for the HR and 0.954 for the LR protocols, respectively. Nonlinear hFE strength computation led to precision errors of 2.2 and 2.3% which were higher than the ones calculated based on the linear hFE (1.6 and 1.9%) and linear μFE (1.2 and 1.6%) for the HR and LR protocols respectively. Computation of the fracture load with nonlinear hFE demanded in average 6h of CPU time which was 3 times faster than with linear μFE, while computation with linear hFE took only a few minutes. This study delivers an extensive experimental and numerical validation for the application of an accurate and fast hFE diagnostic tool to help in identifying individuals who may be at risk of an osteoporotic wrist fracture and to follow up pharmacological and other treatments in such patients.
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http://dx.doi.org/10.1016/j.bone.2017.01.003DOI Listing
April 2017

European Society of Biomechanics S.M. Perren Award 2016: A statistical damage model for bone tissue based on distinct compressive and tensile cracks.

J Biomech 2016 11 25;49(15):3616-3625. Epub 2016 Oct 25.

Institute for Mechanical, Process and Energy Engineering, Heriot-Watt University, United Kingdom.

Osteoporosis leads to bone fragility and represents a major health problem in our aging societies. Bone is a quasi-brittle hierarchical composite that exhibits damage with distinct crack morphologies in compression and tension when overloaded. A recent study reported the complex damage response of bovine compact bone under four different cyclic overloading experiments combining compression and tension. The aim of the present work is to propose a mechanistic model by which cracking bone accumulates residual strain and reduces elastic modulus in distinct compressive and tensile overloading modes. A simple rheological unit of bone with two types of cracks is formulated in the framework of continuum damage mechanics. A statistics of these rheological units is then assembled in parallel to compute the response of a macroscopic bone sample in which compressive and tensile cracks are opened, closed or propagated towards failure. The resulting constitutive model reproduces the key macroscopic features of bone tissue damage and delivers an excellent agreement with the four cyclic overloading experiments. The remarkable predictions of the model support the presence of (1) friction between the crack surfaces producing hystereses, (2) an incomplete closure of cracks leading to residual strains, (3) a bridging mechanism of collagen fibrils which failure reduces elastic modulus, and (4) two distinct classes of cracks where compressive cracks have a strong influence on tensile damage and tensile cracks have a limited impact on compressive damage. This work is expected to help improve our understanding of the bone damage mechanisms contributing to skeletal fragility and to foster a proper generalization of this damage behavior in 3D for computational analysis of bone and bone-implant systems.
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http://dx.doi.org/10.1016/j.jbiomech.2016.09.045DOI Listing
November 2016

Head-Neck Osteoplasty has Minor Effect on the Strength of an Ovine Cam-FAI Model: In Vitro and Finite Element Analyses.

Clin Orthop Relat Res 2016 Dec 17;474(12):2633-2640. Epub 2016 Aug 17.

Musculoskeletal Research Unit, Vetsuisse Faculty, University of Zurich, Zürich, Switzerland.

Background: Osteochondroplasty of the head-neck region is performed on patients with cam femoroacetabular impingement (FAI) without fully understanding its repercussion on the integrity of the femur. Cam-type FAI can be surgically and reproducibly induced in the ovine femur, which makes it suitable for studying corrective surgery in a consistent way. Finite element models built on quantitative CT (QCT) are computer tools that can be used to predict femoral strength and evaluate the mechanical effect of surgical correction.

Questions/purposes: We asked: (1) What is the effect of a resection of the superolateral aspect of the ovine femoral head-neck junction on failure load? (2) How does the failure load after osteochondroplasty compare with reported forces from activities of daily living in sheep? (3) How do failure loads and failure locations from the computer simulations compare with the experiments?

Methods: Osteochondroplasties (3, 6, 9 mm) were performed on one side of 18 ovine femoral pairs with the contralateral intact side as a control. The 36 femurs were scanned via QCT from which specimen-specific computer models were built. Destructive compression tests then were conducted experimentally using a servohydraulic testing system and numerically via the computer models. Safety factors were calculated as the ratio of the maximal force measured in vivo by telemeterized hip implants during the sheep's walking and running activities to the failure load. The simulated failure loads and failure locations from the computer models were compared with the experimental results.

Results: Failure loads were reduced by 5% (95% CI, 2%-8%) for the 3-mm group (p = 0.0089), 10% (95% CI, 6%-14%) for the 6-mm group (p = 0.0015), and 19% (95% CI, 13%-26%) for the 9-mm group (p = 0.0097) compared with the controls. Yet, the weakest specimen still supported more than 2.4 times the peak load during running. Strong correspondence was found between the simulated and experimental failure loads (R = 0.83; p < 0.001) and failure locations.

Conclusions: The resistance of ovine femurs to fracture decreased with deeper resections. However, under in vitro testing conditions, the effect on femoral strength remains small even after 9 mm correction, suggesting that femoral head-neck osteochondroplasty could be done safely on the ovine femur. QCT-based finite element models were able to predict weakening of the femur resulting from the osteochondroplasty.

Clinical Relevance: The ovine femur provides a seemingly safe platform for scientific evaluation of FAI. It also appears that computer models based on preoperative CT scans may have the potential to provide patient-specific guidelines for preventing overcorrection of cam FAI.
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http://dx.doi.org/10.1007/s11999-016-5024-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5085938PMC
December 2016

Not only stiffness, but also yield strength of the trabecular structure determined by non-linear µFE is best predicted by bone volume fraction and fabric tensor.

J Mech Behav Biomed Mater 2017 01 14;65:808-813. Epub 2016 Oct 14.

Institute for Surgical Technology and Biomechanics, University of Bern, Switzerland.

The micro-architecture of cancellous bone is considered a major determinant of the fracture risk. Yet, if morphometry tells about alterations of the trabecular network, its elastic behaviour is best described by bone volume fraction (BV/TV) and the fabric tensor, which gives the anisotropy of the trabecular structure. This remains to be proven for yield strength, the onset of bone failure. The microstructure of 126 samples extracted from femoral heads of two female subjects was evaluated on micro-computed tomography scans via 25 structural indices. Parameters such as plate and rod decomposition via ITS and textural analyses by ISV, similar to the trabecular bone score, were also examined. The degree of collinearity between indices was assessed. The indices considered sufficiently independent were included in multi-linear regression models predicting stiffness or yield strength measured via nonlinear micro finite element analyses. The models' accuracy was checked and the contributions of all explanatory variables to the prediction were compared. Our results show that BV/TV alone explained most of the predicted yield strength (76%) and stiffness (89%). BV/TV together with the fabric tensor explained more than 98% of both measures! The fabric tensor also had a larger impact on yield strength (23%) than on the stiffness predictions (9%). On the other hand, the predictive value of the other independent factors (Tb.Th.SD, Tb.Sp.SD, rTb.Th, RR.Junc.D, ISV) was negligible (<1%). In conclusion, just as stiffness, yield strength of femoral trabecular bone is also best explained by BV/TV and trabecular anisotropy, the latter being even more relevant in its post-elastic behaviour.
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http://dx.doi.org/10.1016/j.jmbbm.2016.10.004DOI Listing
January 2017

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements.

Biomech Model Mechanobiol 2017 06 26;16(3):731-742. Epub 2016 Oct 26.

Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland.

Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.
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http://dx.doi.org/10.1007/s10237-016-0849-3DOI Listing
June 2017

Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly.

Bone 2016 12 4;93:196-211. Epub 2015 Dec 4.

Institute for Surgical Technology and Biomechanics, University of Bern, Switzerland; School of Engineering and Physical Science, Institute for Mechanical, Process and Energy Engineering, Heriot-Watt University, Edinburgh, United Kingdom. Electronic address:

The growing incidence of skeletal fractures poses a significant challenge to ageing societies. Since a major part of physiological loading in the lower limbs is carried by cortical bone, it would be desirable to better understand the structure-mechanical property relationships and scale effects in this tissue. This study aimed at assessing whether microindentation properties combined with chemical and morphological information are usable to predict macroscopic elastic and strength properties in a donor- and site-matched manner. Specimens for quasi-static macroscopic tests in tension, compression, and torsion and microindentation were prepared from a cohort of 19 male and 20 female donors (46 to 99 years). All tests were performed under fully hydrated conditions. The chemical composition of the extra-cellular matrix was investigated with Raman spectroscopy. The results of the micro-mechanical tests were combined with morphological and compositional properties using a power law relationship to predict the macro-mechanical results. Microindentation properties were not gender dependent, remarkably constant over age, and showed an overall small variation with standard deviations of approximately 10 %. Similar results were obtained for chemical tissue composition. Macro-mechanical stiffness and strength were significantly related to porosity for all load cases (p<0.05). In case of macroscopic yield strain and work-to-failure this was only true in torsion and compression, respectively. The correlations of macro-mechanical with micro-mechanical, morphological, and chemical properties showed no significance for cement line density, mineralisation, or variations in the microindentation results and were dominated by porosity with a moderate explanatory power of predominately less than 50 %. The results confirm that age, with minor exceptions gender, and small variations in average mineralisation have negligible effect on the tissue microindentation properties of human lamellar bone in the elderly. Furthermore, our findings suggest that microindentation experiments are suitable to predict macroscopic mechanical properties in the elderly only on average and not on a one to one basis. The presented data may help to form a better understanding of the mechanisms of ageing in bone tissue and of the length scale at which they are active. This may be used for future prediction of fracture risk in the elderly.
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http://dx.doi.org/10.1016/j.bone.2015.11.018DOI Listing
December 2016

Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images.

Curr Osteoporos Rep 2016 12;14(6):374-385

Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland.

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.
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http://dx.doi.org/10.1007/s11914-016-0335-yDOI Listing
December 2016

Response to the commentary on mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly.

Bone 2017 12 3;105:312-314. Epub 2016 Oct 3.

School of Engineering and Physical Science, Institute for Mechanical, Process and Energy Engineering, Heriot-Watt University, Edinburgh, United Kingdom. Electronic address:

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http://dx.doi.org/10.1016/j.bone.2016.09.025DOI Listing
December 2017

Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup.

J Mech Behav Biomed Mater 2016 Apr 3;57:116-27. Epub 2015 Dec 3.

AO Research Institute Davos, Switzerland.

Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation.
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http://dx.doi.org/10.1016/j.jmbbm.2015.11.026DOI Listing
April 2016

A finite element analysis of two novel screw designs for scaphoid waist fractures.

Med Eng Phys 2016 Feb 2;38(2):131-9. Epub 2015 Dec 2.

Department of Trauma Surgery, Medical University of Vienna, Austria.

The scaphoid is the most often fractured carpal bone. Scaphoid fracture repair with a headless compression screw allows for early functional recovery. The rotational stability of a single screw may be limited, having a potential negative impact on the healing process. Two novel screws have been designed to provide improved rotational stability compared to the existing ones. Using a computational finite element model of a scaphoid osteotomy, we compared the efficacy of one simple screw and the two new screws in restricting inter-fragmentary motion (IFM) in three functional positions of the wrist and as a function of inter-fragmentary compression force. The in-plane IFM was primary rotational and was better restricted by the new screws compared to the conventional one when the inter-fragmentary compression force was below 15-20 N, but provided no clear benefit in total flexion independently of the compression force. To better understand the differences in the non-compressed case, we analyzed the acting moments and investigated the effects of the bending and torsional screw stiffness on IFM. By efficiently restricting the inter-fragmentary shear, the new screws may be clinically advantageous when the inter-fragmentary compression force is partially or completely lost and may provide further benefits toward earlier and better healing of transverse waist fractures of the scaphoid.
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http://dx.doi.org/10.1016/j.medengphy.2015.11.006DOI Listing
February 2016

The Initial Slope of the Variogram, Foundation of the Trabecular Bone Score, Is Not or Is Poorly Associated With Vertebral Strength.

J Bone Miner Res 2016 Feb 3;31(2):341-6. Epub 2015 Sep 3.

Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland.

Trabecular bone score (TBS) rests on the textural analysis of dual-energy X-ray absorptiometry (DXA) to reflect the decay in trabecular structure characterizing osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible because prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly owing to an unrealistic setup and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings were used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation ("full vertebra"); 2) via the classical endplate embedding ("vertebral body"); or 3) via a ball joint to induce anterior wedge failure ("vertebral section"). High-resolution peripheral quantitative computed tomography (HR-pQCT) scans acquired from prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (F(exp)) and apparent failure stress (σexp) was assessed, and their relative contribution to a multilinear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with F(exp) and σexp , except for the "vertebral body" case (r(2) = 0.396, p = 0.028). Aside from the "vertebra section" setup where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing setup, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk.
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http://dx.doi.org/10.1002/jbmr.2610DOI Listing
February 2016

Continuum damage interactions between tension and compression in osteonal bone.

J Mech Behav Biomed Mater 2015 Sep 19;49:355-69. Epub 2015 May 19.

Institute for Surgical Technology and Biomechanics, University of Bern, Stauffacherstrasse 78, CH-3014 Bern, Switzerland. Electronic address:

Skeletal diseases such as osteoporosis impose a severe socio-economic burden to ageing societies. Decreasing mechanical competence causes a rise in bone fracture incidence and mortality especially after the age of 65 y. The mechanisms of how bone damage is accumulated under different loading modes and its impact on bone strength are unclear. We hypothesise that damage accumulated in one loading mode increases the fracture risk in another. This study aimed at identifying continuum damage interactions between tensile and compressive loading modes. We propose and identify the material constants of a novel piecewise 1D constitutive model capable of describing the mechanical response of bone in combined tensile and compressive loading histories. We performed several sets of loading-reloading experiments to compute stiffness, plastic strains, and stress-strain curves. For tensile overloading, a stiffness reduction (damage) of 60% at 0.65% accumulated plastic strain was detectable as stiffness reduction of 20% under compression. For compressive overloading, 60% damage at 0.75% plastic strain was detectable as a stiffness reduction of 50% in tension. Plastic strain at ultimate stress was the same in tension and compression. Compression showed softening and tension exponential hardening in the post-yield regime. The hardening behaviour in compression is unaffected by a previous overload in tension but the hardening behaviour in tension is affected by a previous overload in compression as tensile reloading strength is significantly reduced. This paper demonstrates how damage accumulated under one loading mode affects the mechanical behaviour in another loading mode. To explain this and to illustrate a possible implementation we proposed a theoretical model. Including such loading mode dependent damage and plasticity behaviour in finite element models will help to improve fracture risk analysis of whole bones and bone implant structures.
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http://dx.doi.org/10.1016/j.jmbbm.2015.05.007DOI Listing
September 2015

An over-nonlocal implicit gradient-enhanced damage-plastic model for trabecular bone under large compressive strains.

Int J Numer Method Biomed Eng 2015 Nov 14;31(11). Epub 2015 Jun 14.

Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Zikova 1903/4, Praha 6, 166 36, Czech Republic.

Purpose: Investigation of trabecular bone strength and compaction is important for fracture risk prediction. At 1-2% compressive strain, trabecular bone undergoes strain softening, which may lead to numerical instabilities and mesh dependency in classical local damage-plastic models. The aim of this work is to improve our continuum damage-plastic model of bone by reducing the influence of finite element mesh size under large compression.

Methodology: This spurious numerical phenomenon may be circumvented by incorporating the nonlocal effect of cumulated plastic strain into the constitutive law. To this end, an over-nonlocal implicit gradient model of bone is developed and implemented into the finite element software ABAQUS using a user element subroutine. The ability of the model to detect the regions of bone failure is tested against experimental stepwise loading data of 16 human trabecular bone biopsies.

Findings: The numerical outcomes of the nonlocal model revealed reduction of finite element mesh dependency compared with the local damage-plastic model. Furthermore, it helped reduce the computational costs of large-strain compression simulations.

Originality: To the best of our knowledge, the proposed model is the first to predict the failure and densification of trabecular bone up to large compression independently of finite element mesh size. The current development enables the analysis of trabecular bone compaction as in osteoporotic fractures and implant migration, where large deformation of bone plays a key role.
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http://dx.doi.org/10.1002/cnm.2728DOI Listing
November 2015
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