Cortical and trabecular mechanical properties in the femoral neck vary differently with changes in bone mineral density.

Graphical Abstract.

Critical loss of primary implant stability in osteosynthesis locking screws under cyclic overloading.

Primary implant stability, which refers to the stability of the implant during the initial healing period is a crucial factor in determining the long-term success of the implant and lays the foundation for secondary implant stability achieved through osseointegration. Factors affecting primary stability include implant design, surgical technique, and patient-specific factors like bone quality and morphology. In vivo, the cyclic nature of anatomical loading puts osteosynthesis locking screws under dynamic loads, which can lead to the formation of micro cracks and defects that slowly degrade the mechanical connection between the bone and screw, thus compromising the initial stability and secondary stability of the implant. Monotonic quasi-static loading used for testing the holding capacity of implanted screws is not well suited to capture this behavior since it cannot capture the progressive deterioration of peri­implant bone at small displacements. In order to address this issue, this study aims to determine a critical point of loss of primary implant stability in osteosynthesis locking screws under cyclic overloading by investigating the evolution of damage, dissipated energy, and permanent deformation. A custom-made test setup was used to test implanted 2.5 mm locking screws under cyclic overloading test. For each loading cycle, maximum forces and displacement were recorded as well as initial and final cycle displacements and used to calculate damage and energy dissipation evolution. The results of this study demonstrate that for axial, shear, and mixed loading significant damage and energy dissipation can be observed at approximately 20 % of the failure force. Additionally, at this load level, permanent deformations on the screw-bone interface were found to be in the range of 50 to 150 mm which promotes osseointegration and secondary implant stability. This research can assist surgeons in making informed preoperative decisions by providing a better understanding of the critical point of loss of primary implant stability, thus improving the long-term success of the implant and overall patient satisfaction.

The 2-layer elasto-visco-plastic rheological model for the material parameter identification of bone tissue extended by a damage law.

The response of bone tissue to mechanical load is complex and includes plastic hardening, viscosity and damage. The quantification of these effects plays a mayor role in bone research and in biomechanical clinical trials as to better understand related diseases. In this study, the damage growth in individual wet human trabeculae subjected to cyclic overloading is quantified by inverse rheological modeling. Therefore, an already published rheological material model, that includes linear elasticity, plasticity and viscosity is extended by a damage law. The model is utilized in an optimization process to identify the corresponding material parameters and damage growth in single human trabeculae under tensile load. Results show that the damage model is leading to a better fit of the test data with an average root-mean-square-error (RMSE) of 2.52 MPa compared to the non-damage model with a RMSE of 3.03 MPa. Although this improvement is not significant, the damage model qualitatively better represents the data as it accounts for the visible stiffness reduction along the load history. It returns realistic stiffness values of 11.92 GPa for the instantaneous modulus and 5.73 GPa for the long term modulus of wet trabecular human bone. Further, the growth of damage in the tissue along the load history is substantial, with values above 0.8 close to failure. The relative loss of stiffness per cycle is in good agreement with comparable literature. Inverse rheological modeling proves to be a valuable tool for quantifying complex constitutive behavior from a single mechanical measurement. The evolution of damage in the tissue can be identified continuously over the load history and separated from other effects.

A mechanically validated open-source silicone model for the training of gastric perforation sewing.

BACKGROUND: Gastrointestinal perforation is commonly seen in emergency departments. The perforation of the stomach is an emergency situation that requires immediate surgical treatment. The necessary surgical skills require regular practical training. Owing to patient`s safety, in vivo training opportunities in medicine are restricted. Animal tissue especially porcine tissue, is commonly used for surgical training. Due to its limiting factors, artificial training models are often to be preferred. Many artificial models are on the market but to our knowledge, none that mimic the haptic- and sewing properties of a stomach wall at the same time. In this study, an open source silicone model of a gastric perforation for training of gastric sewing was developed that attempts to provide realistic haptic- and sewing behaviour. METHODS: To simulate the layered structure of the human stomach, different silicone materials were used to produce three different model layups. The production process was kept as simple as possible to make it easily reproducible. A needle penetration setup as well as a systematic haptic evaluation were developed to compare these silicone models to a real porcine stomach in order to identify the most realistic model. RESULTS: A silicone model consisting of three layers was identified as being the most promising and was tested by clinical surgeons. CONCLUSIONS: The presented model simulates the sewing characteristics of a human stomach wall, is easily reproducible at low-costs and can be used for practicing gastric suturing techniques. TRIAL REGISTRATIONS: Not applicable.

The predictive ability of a QCT-FE model of the proximal femoral stiffness under multiple load cases is strongly influenced by experimental uncertainties.

Despite significant improvements in terms of the predictive ability of Quantitative Computed Tomography based Finite Element (QCT-FE) models in estimating femoral strength (fracture load and stiffness), no substantial clinical adoption of this method has taken place to date. Narrowing the wide variability of FE results by standardizing the methodology and validation protocols, as well as reducing the uncertainties in the FEA process have been proposed as routes towards improved reliability. The aim of this study was to: First, validate a QCT-FE model of proximal femoral stiffness in multiple stance load cases, and second, using a parametric approach, determine the influence of select experimental and modeling parameters on the predictive ability of our model. Ten fresh frozen human femoral samples were tested in neutral stance, 15° adducted and 15° abducted load cases. Voxel-based linear-elastic QCT-FE models of the samples were generated to predict the models' stiffness values in all load cases. The base FE models were validated against the experimental results using linear regression. Thirty six deviated models were created using the minimum and maximum values of experiment-based "plausible range" for 18 parameters in 4 categories of embedding, loading, material, and segmentation. The predictive ability of the models were compared in terms of the coefficient of determination (R2) of the linear regression between the measured and predicted stiffness values in all load cases. Our model was capable of capturing 90% of the variation in the experimental stiffness of the samples in neutral stance position (R2 = 0.9, concordance correlation coefficient (CCC) = 0.93, percent root mean squared error (RMSE%) = 8.4%, slope and intercept not significantly different from unity and zero, respectively). Embedding and loading categories strongly affected the predictive ability of the models with an average percent difference in R2 of 4.36% ± 2.77 and 2.96% ± 1.69 for the stance-neutral load case, respectively. The performance of the models were significantly different in adducted and abducted load cases with their R2 dropping to 71% and 70%, respectively. Similarly, off-axes load cases were affected by the parameters differently compared to the neutral load case, with the loading parameter category imposing more than 10% difference on their R2, larger than all other categories. We also showed that automatically selecting the best performing plausible value for each parameter and each sample would result in a perfectly linear correlation (R2> 0.99) between the "tuned" model's predicted stiffness and experimental results. Based on our results, high sensitivity of the model performance to experimental parameters requires extra diligence in modeling the embedding geometry and the loading angles since these sources of uncertainty could dwarf the effects of material modeling and image processing parameters. The results of this study could help in improving the robustness of the QCT-FE models of proximal femur by limiting the uncertainties in the experimental and modeling steps.

The biomechanical behavior of 3D printed human femoral bones based on generic and patient-specific geometries.

BACKGROUND: Bone is a highly complex composite material which makes it hard to find appropriate artificial surrogates for patient-specific biomechanical testing. Despite various options of commercially available bones with generic geometries, these are either biomechanically not very realistic or rather expensive. METHODS: In this work, additive manufacturing was used for the fabrication of artificial femoral bones. These were based on CT images of four different commercially available femoral bone surrogates and three human bones with varying bone density. The models were 3D printed using a low-budget fused deposition modeling (FDM) 3D printer and PLA filament. The infill density was mechanically calibrated and varying cortical thickness was used. Compression tests of proximal femora simulating stance were performed and the biomechanical behavior concerning ultimate force, spring stiffness, and fracture pattern were evaluated as well as compared to the results of commercial and cadaveric bones. RESULTS: Regarding the ultimate forces and spring stiffness, the 3D printed analogs showed mechanical behavior closer to their real counterparts than the commercially available polyurethan-based surrogates. Furthermore, the increase in ultimate force with increasing bone density observed in human femoral bones could be reproduced well. Also, the fracture patterns observed match well with fracture patterns observed in human hip injuries. CONCLUSION: Consequently, the methods presented here show to be a promising alternative for artificial generic surrogates concerning femoral strength testing. The manufacturing is straightforward, cheap, and patient-specific geometries are possible.

Biomechanical finite element analysis of short-implant-supported, 3-unit, fixed CAD/CAM prostheses in the posterior mandible.

OBJECTIVE: To assess the biomechanical effects of different prosthetic/implant configurations and load directions on 3-unit fixed prostheses supported by short dental implants in the posterior mandible using validated 3-D finite element (FE) models. METHODS: Models represented an atrophic mandible, missing the 2nd premolar, 1st and 2nd molars, and rehabilitated with either two short implants (implant length-IL = 8 mm and 4 mm) supporting a 3-unit dental bridge or three short implants (IL = 8 mm, 6 mm and 4 mm) supporting zirconia prosthesis in splinted or single crowns design. Load simulations were performed in ABAQUS (Dassault Systèmes, France) under axial and oblique (30°) force of 100 N to assess the global stiffness and forces within the implant prosthesis. Local stresses within implant/prosthesis system and strain energy density (SED) within surrounding bone were determined and compared between configurations. RESULTS: The global stiffness was around 1.5 times higher in splinted configurations vs. single crowns, whereby off-axis loading lead to a decrease of 39%. Splinted prostheses exhibited a better stress distribution than single crowns. Local stresses were larger and distributed over a larger area under oblique loads compared to axial load direction. The forces on each implant in the 2-implant-splinted configurations increased by 25% compared to splinted crowns on 3 implants. Loading of un-splinted configurations resulted in increased local SED magnitude. CONCLUSION: Splinting of adjacent short implants in posterior mandible by the prosthetic restoration has a profound effect on the magnitude and distribution of the local stress peaks in peri-implant regions. Replacing each missing tooth with an implant is recommended, whenever bone supply and costs permit.

A parameter reduced adaptive quasi-linear viscoelastic model for soft biological tissue in uniaxial tension.

Mechanical characterisation of soft viscous materials is essential for many applications including aerospace industries, material models for surgical simulation, and tissue mimicking materials for anatomical models. Constitutive material models are, therefore, necessary to describe soft biological tissues in physiologically relevant strain ranges. Hereby, the adaptive quasi-linear viscoelastic (AQLV) model enables accurate modelling of the strain-dependent non-linear viscoelastic behaviour of soft tissues with a high flexibility. However, the higher flexibility produces a large number of model parameters. In this study, porcine muscle and liver tissue samples were modelled in the framework of the originally published AQLV (3-layers of Maxwell elements) model using four incremental ramp-hold experiments in uniaxial tension. AQLV model parameters were reduced by decreasing model layers (M) as well as the number of experimental ramp-hold steps (N). Leave One out cross validation tests show that the original AQLV model (3M4N) with 19 parameters, accurately describes porcine muscle tissue with an average R2 of 0.90 and porcine liver tissue, R2 of 0.86. Reducing the number of layers (N) in the model produced acceptable model fits for 1-layer (R2 of 0.83) and 2-layer models (R2 of 0.89) for porcine muscle tissue and 1-layer (R2 of 0.84) and 2-layer model (R2 of 0.85) for porcine liver tissue. Additionally, a 2 step (2N) ramp-hold experiment was performed on additional samples of porcine muscle tissue only to further reduce model parameters. Calibrated spring constant values for 2N ramp-hold tests parameters k1 and k2 had a 16.8% and 38.0% deviation from those calibrated for a 4 step (4N) ramp hold experiment. This enables further reduction of material parameters by means of step reduction, effectively reducing the number of parameters required to calibrate the AQLV model from 19 for a 3M4N model to 8 for a 2M2N model, with the added advantage of reducing the time per experiment by 50%. This study proposes a 'reduced-parameter' AQLV model (2M2N) for the modelling of soft biological tissues at finite strain ranges. Sequentially, the comparison of model parameters of soft tissues is easier and the experimental burden is reduced.

Material design of soft biological tissue replicas using viscoelastic micromechanical modelling.

Anatomical models for research and education are often made of artificial materials that attempt to mimic biological tissues in terms of their mechanical properties. Recent developments in additive manufacturing allow tuning mechanical properties with microstructural designs. We propose a strategy for designing material microstructures to mimic soft tissue viscoelastic behaviour, based on a micromechanical Mori-Tanaka model. The model was applied to predict homogenised viscoelastic properties of materials, exhibiting a matrix-inclusion microstructure with varying inclusion volume fractions. The input properties were thereby obtained from compression relaxation tests on silicone elastomers. Validation of the model was done with experimental results for composite samples. Finally, different combinations of silicones were compared to mechanical properties of soft tissues (hepatic, myocardial, adipose, cervical, and prostate tissue), found in literature, in order to design microstructures for replicating these tissues in terms of viscoelasticity. The viscoelastic Mori-Tanaka model showed good agreement with the corresponding experimental results for low inclusion volume fractions, while high fractions lead to underestimation of the complex modulus by the model. Predictions for the loss tangent were reasonably accurate, even for higher inclusion volume fractions. Based on the model, designs for 3D printed microstructures can be extracted in order to replicate the viscoelastic properties of soft tissues.

Experimental validation of a micro-CT finite element model of a human cadaveric mandible rehabilitated with short-implant-supported partial dentures.

PURPOSE: This study aimed to address the predictive value of a micro-computed tomography (µCT)-based finite element (µFE) model of a human cadaveric edentulous posterior mandible, rehabilitated by short dental implants. Hereby, three different prosthetic/implant configurations of fixed partial dentures ("Sp"-3 splinted crowns on 3 implants, "Br" - Bridge: 3 splinted crowns on 2 implants, and "Si"- 3 single crowns) were analysed by comparing the computational predictions of the global stiffness with experimental data. METHODS: Experimental displacement of the bone/implant/prosthesis system was measured under axial and oblique loads of 100 N using an optical deformation system (GOM Aramis) and the overall movement of the testing machine (Zwick Z030). Together with the measured machine force, an "Aramis" (optical markers) and "Zwick" (test machine) stiffness were calculated. FE models were created based on µCT-scans of the cadaveric mandible sample (n = 1) before and after implantation and using stl-files of the crowns. The same load tests and boundary conditions were simulated on the models and the µFE-results were compared to experimental data using linear regression analysis. RESULTS: The regression line through a plot of pooled stiffness values (N/mm) for the optical displacement recording (true local displacement) and the test machine (machine compliance included) had a slope of 0.57 and a correlation coefficient R2 of 0.82. The average pooled correlation of global stiffness between the experiment and FE-analysis (FEA) showed a R2 of 0.80, but the FEA-stiffness was 7.2 times higher. The factor was highly dependent on the test configuration. Sp-configuration showed the largest stiffness followed by Br-configuration (17% difference in experiment and 21% in FEA). CONCLUSIONS: The current study showed good qualitative agreement between the experimental and predicted global stiffness of different short implant configurations. It could be deduced that 1:1 splinting of the short implants by the crowns is most favorable for the stiffness of the implant/prosthesis system. However, in the clinical context, the absolute in silico readings must be interpreted cautiously, as the FEA showed a considerable overestimation of the values.

Which experimental procedures influence the apparent proximal femoral stiffness? A parametric study.

BACKGROUND: Experimental validation is the gold standard for the development of FE predictive models of bone. Employing multiple loading directions could improve this process. To capture the correct directional response of a sample, the effect of all influential parameters should be systematically considered. This study aims to determine the impact of common experimental parameters on the proximal femur's apparent stiffness. METHODS: To that end, a parametric approach was taken to study the effects of: repetition, pre-loading, re-adjustment, re-fixation, storage, and µCT scanning as random sources of uncertainties, and loading direction as the controlled source of variation in both stand and side-fall configurations. Ten fresh-frozen proximal femoral specimens were prepared and tested with a novel setup in three consecutive sets of experiments. The neutral state and 15-degree abduction and adduction angles in both stance and fall configurations were tested for all samples and parameters. The apparent stiffness of the samples was measured using load-displacement data from the testing machine and validated against marker displacement data tracked by DIC cameras. RESULTS: Among the sources of uncertainties, only the storage cycle affected the proximal femoral apparent stiffness significantly. The random effects of setup manipulation and intermittent µCT scanning were negligible. The 15∘ deviation in loading direction had a significant effect comparable in size to that of switching the loading configuration from neutral stance to neutral side-fall. CONCLUSION: According to these results, comparisons between the stiffness of the samples under various loading scenarios can be made if there are no storage intervals between the different load cases on the same samples. These outcomes could be used as guidance in defining a highly repeatable and multi-directional experimental validation study protocol.

A novel specimen shape for measurement of linear strain fields by means of digital image correlation.

Strains on the surface of engineering structures or biological tissues are non-homogeneous. These strain fields can be captured by means of Digital Image Correlation (DIC). However, DIC strain field measurements are prone to noise and filtering of these fields influences measured strain gradients. This study aims to design a novel tensile test specimen showing two linear gradients, to measure full-field linear strain measurements on the surface of test specimens, and to investigate the accuracy of DIC strain measurements globally (full-field) and locally (strain gauges' positions), with and without filtering of the DIC strain fields. Three materials were employed for this study: aluminium, polymer, and bovine bone. Normalized strain gradients were introduced that are load independent and evaluated at two local positions showing 3.6 and 6.9% strain change per mm. Such levels are typically found in human bones. At these two positions, two strain gauges were applied to check the experimental strain magnitudes. A third strain gauge was applied to measure the strain in a neutral position showing no gradient. The accuracy of the DIC field measurement was evaluated at two deformation stages (at [Formula: see text] 500 and 1750 µstrain) using the root mean square error (RMSE). The RMSE over the two linear strain fields was less than 500 µstrain for both deformation stages and all materials. Gaussian low-pass filter (LPF) reduced the DIC noise between 25% and 64% on average. As well, filtering improved the accuracy of the local normalized strain gradients measurements with relative difference less than 20% and 12% for the high- and low-gradient, respectively. In summary, a novel specimen shape and methodological approach are presented which are useful for evaluating and improving the accuracy of the DIC measurement where non-homogeneous strain fields are expected such as on bone tissue due to their hierarchical structure.

Effects of Osteoporosis on Bone Morphometry and Material Properties of Individual Human Trabeculae in the Femoral Head.

Osteoporosis is the most common bone disease and is conventionally classified as a decrease of total bone mass. Current diagnosis of osteoporosis is based on clinical risk factors and dual energy X-ray absorptiometry (DEXA) scans, but changes in bone quantity (bone mass) and quality (trabecular structure, material properties, and tissue composition) are not distinguished. Yet, osteoporosis is known to cause a deterioration of the trabecular network, which might be related to changes at the tissue scale-the material properties. The goal of the current study was to use a previously established test method to perform a thorough characterization of the material properties of individual human trabeculae from femoral heads in cyclic tensile tests in a close to physiologic, wet environment. A previously developed rheological model was used to extract elastic, viscous, and plastic aspects of material behavior. Bone morphometry and tissue mineralization were determined with a density calibrated micro-computed tomography (µCT) set-up. Osteoporotic trabeculae neither showed a significantly changed material or mechanical behavior nor changes in tissue mineralization, compared with age-matched healthy controls. However, donors with osteopenia indicated significantly reduced apparent yield strain and elastic work with respect to osteoporosis, suggesting possible initial differences at disease onset. Bone morphometry indicated a lower bone volume to total volume for osteoporotic donors, caused by a smaller trabecular number and a larger trabecular separation. A correlation of age with tissue properties and bone morphometry revealed a similar behavior as in osteoporotic bone. In the range studied, age does affect morphometry but not material properties, except for moderately increased tissue strength in healthy donors and moderately increased hardening exponent in osteoporotic donors. Taken together, the distinct changes of trabecular bone quality in the femoral head caused by osteoporosis and aging could not be linked to suspected relevant changes in material properties or tissue mineralization. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Effects of anti-resorptive treatment on the material properties of individual canine trabeculae in cyclic tensile tests.

Osteoporosis is defined as a decrease of bone mass and strength, as well as an increase in fracture risk. It is conventionally treated with antiresorptive drugs, such as bisphosphonates (BPs) and selective estrogen receptor modulators (SERMs). Although both drug types successfully decrease the risk of bone fractures, their effect on bone mass and strength is different. For instance, BP treatment causes an increase of bone mass, stiffness and strength of whole bones, whereas SERM treatment causes only small (4%) increases of bone mass, but increased bone toughness. Such improved mechanical behavior of whole bones can be potentially related to the bone mass, bone structure or material changes. While bone mass and architecture have already been investigated previously, little is known about the mechanical behavior at the tissue/material level, especially of trabecular bone. As such, the goal of the work presented here was to fill this gap by performing cyclic tensile tests in a wet, close to physiologic environment of individual trabeculae retrieved from the vertebrae of beagle dogs treated with alendronate (a BP), raloxifene (a SERM) or without treatments. Identification of material properties was performed with a previously developed rheological model and of mechanical properties via fitting of envelope curves. Additionally, tissue mineral density (TMD) and microdamage formation were analyzed. Alendronate treatment resulted in a higher trabecular tissue stiffness and strength, associated with higher levels of TMD. In contrast, raloxifene treatment caused a higher trabecular toughness, pre-dominantly in the post-yield region. Microdamage formation during testing was not affected by either anti-resorptive treatment regimens. These findings highlight that the improved mechanical behavior of whole bones after anti-resorptive treatment is at least partly caused by improved material properties, with different mechanisms for alendronate and raloxifene. This study further shows the power of performing a mechanical characterization of trabecular bone at the level of individual trabeculae for better understanding of clinically relevant mechanical behavior of bone.

Comparison of Thiel preserved, fresh human, and animal liver tissue in terms of mechanical properties.

BACKGROUND: In medical training and research fresh human tissue is often replaced by preserved human or fresh animal tissue, due to availability and ethical reasons. Newer preservation approaches, such as the Thiel method, promise more realistic mechanical properties than conventional formaldehyde fixation. Concerning animal substitute material, porcine and bovine tissue is often chosen, as it is easily obtainable and certain similarity to human tissue is assumed. However, it has not been thoroughly investigated how Thiel preservation changes non-linear and viscoelastic behaviour of soft organ tissues. Furthermore, differences in these properties between animal tissue and human tissue have not been previously corroborated. METHODS: We conducted ramp and relaxation tensile tests on fresh human and Thiel preserved hepatic tissue, extracting strain-specific elastic moduli, and viscoelastic properties. The results for fresh human liver were then compared to corresponding results for Thiel preserved liver, as well as previously published results for porcine and bovine liver. RESULTS: Our results showed that Thiel preservation seems to be associated with increased stiffness as well as decreased viscoelastic damping behaviour. Porcine liver was stiffer than human liver with similar viscoelastic properties. Bovine liver exhibited similar stiffness as human liver, however lower viscoelastic damping. CONCLUSIONS: The differences between human and animal liver tissue, concerning their mechanical properties, can be explained by their characteristic histology. Changes in mechanical properties due to Thiel preservation might stem from altered protein cross-linking and dehydration. The results illustrate that appropriate materials for medical training systems must be selected based on which mechanical properties are relevant for the respective application.

A Review on Recent Advances in the Constitutive Modeling of Bone Tissue.

PURPOSE OF REVIEW: Image-based finite element analysis (FEA) to predict and understand the biomechanical response has become an essential methodology in musculoskeletal research. An important part of such simulation models is the constitutive material model of which recent advances are summarized in this review. RECENT FINDINGS: The review shows that existing models from other fields were introduced, such as cohesion zone (cortical bone) or phase-field models (trabecular bone). Some progress has been made in describing cortical bone involving physical mechanisms such as microcracks. Problems with validations at different length scales remain a problem. The improvement of recent constitutive models is partially obscured by uncertainties that affect overall predictions, such as image quality and calibration or boundary conditions. Nevertheless, in vivo CT-based FEA simulations based on a sophisticated constitutive behavior are a very valuable tool for clinical-related osteoporosis research.

Hyperelastic and viscoelastic characterization of hepatic tissue under uniaxial tension in time and frequency domain.

In order to create accurate anatomical models for medical training and research, mechanical properties of biological tissues need to be studied. However, non-linear and viscoelastic behaviour of most soft biological tissues complicates the evaluation of their mechanical properties. In the current study, a method for measuring hyperelasticity and viscoelasticity of bovine and porcine hepatic parenchyma in tension is presented. First, non-linear stress-stretch curves resulting from ramp loading and unloading, were interpreted based on a hyperelastic framework, using a Veronda-Westmann strain energy function. Strain-specific elastic moduli, such as initial stiffness EI, were thereupon defined in certain parts of the stress-stretch curves. Furthermore, dissipated and stored energy density were calculated. Next, the viscoelastic nature of liver tissue was examined with two different methods: stress relaxation and dynamic cyclic testing. Both tests yielded dissipated and stored energy density, as well as loss tangent (tanδ), storage modulus (E'), and loss modulus (E''). In tension, stress relaxation was experimentally more convenient than dynamic cyclic testing. Thus we considered whether relaxation could be used for approximating the results of the cyclic tests. Regarding the resulting elastic moduli, initial stiffness was similar for porcine and bovine liver (EI∼30kPa), while porcine liver was stiffer for higher strains. Comparing stress relaxation with dynamic cyclic testing, tanδ of porcine and bovine liver was the same for both methods (tanδ=0.05-0.25 at 1 Hz). Storage and loss moduli matched well for bovine, but not as well for porcine tissue. In conclusion, the utilized Veronda-Westmann model was appropriate for representing the hyperelasticity of liver tissue seen in ramp tests. Concerning viscoelasticity, both chosen testing methods - stress relaxation and dynamic cyclic testing - yielded comparable results for E', E'', and tanδ, as long as elasticity non-linearities were heeded. The here presented method provides novel insight into the tensile viscoelastic properties of hepatic tissue, and provides guidelines for convenient evaluation of soft tissue mechanical properties.

Correction to: A two­layer elasto­visco­plastic rheological model for the material parameter identification of bone tissue.

In the original publication of the article.

A two-layer elasto-visco-plastic rheological model for the material parameter identification of bone tissue.

The ability to measure bone tissue material properties plays a major role in diagnosis of diseases and material modeling. Bone's response to loading is complex and shows a viscous contribution to stiffness, yield and failure. It is also ductile and damaging and exhibits plastic hardening until failure. When performing mechanical tests on bone tissue, these constitutive effects are difficult to quantify, as only their combination is visible in resulting stress-strain data. In this study, a methodology for the identification of stiffness, damping, yield stress and hardening coefficients of bone from a single cyclic tensile test is proposed. The method is based on a two-layer elasto-visco-plastic rheological model that is capable of reproducing the specimens' pre- and postyield response. The model's structure enables for capturing the viscously induced increase in stiffness, yield, and ultimate stress and for a direct computation of the loss tangent. Material parameters are obtained in an inverse approach by optimizing the model response to fit the experimental data. The proposed approach is demonstrated by identifying material properties of individual bone trabeculae that were tested under wet conditions. The mechanical tests were conducted according to an already published methodology for tensile experiments on single trabeculae. As a result, long-term and instantaneous Young's moduli were obtained, which were on average 3.64 GPa and 5.61 GPa, respectively. The found yield stress of 16.89 MPa was lower than previous studies suggest, while the loss tangent of 0.04 is in good agreement. In general, the two-layer model was able to reproduce the cyclic mechanical test data of single trabeculae with an root-mean-square error of 2.91 ± 1.77 MPa. The results show that inverse rheological modeling can be of great advantage when multiple constitutive contributions shall be quantified based on a single mechanical measurement.

Cortical thinning and accumulation of large cortical pores in the tibia reflect local structural deterioration of the femoral neck.

INTRODUCTION: Cortical bone thinning and a rarefaction of the trabecular architecture represent possible causes of increased femoral neck (FN) fracture risk. Due to X-ray exposure limits, the bone microstructure is rarely measurable in the FN of subjects but can be assessed at the tibia. Here, we studied whether changes of the tibial cortical microstructure, which were previously reported to be associated with femur strength, are also associated with structural deteriorations of the femoral neck. METHODS: The cortical and trabecular architectures in the FN of 19 humans were analyzed ex vivo on 3D microcomputed tomography images with 30.3 µm voxel size. Cortical thickness (Ct.Thtibia), porosity (Ct.Potibia) and pore size distribution in the tibiae of the same subjects were measured using scanning acoustic microscopy (12 µm pixel size). Femur strength during sideways falls was simulated with homogenized voxel finite element models. RESULTS: Femur strength was associated with the total (vBMDtot; R2 = 0.23, p < 0.01) and trabecular (vBMDtrab; R2 = 0.26, p < 0.01) volumetric bone mineral density (vBMD), with the cortical thickness (Ct.ThFN; R2 = 0.29, p < 0.001) and with the trabecular bone volume fraction (Tb.BV/TVFN; R2 = 0.34, p < 0.001), separation (Tb.SpFN; R2 = 0.25, p < 0.01) and number (Tb.NFN; R2 = 0.32, p < 0.001) of the femoral neck. Moreover, smaller Ct.Thtibia was associated with smaller Ct.ThFN (R2 = 0.31, p < 0.05), lower Tb.BV/TVFN (R2 = 0.29, p < 0.05), higher Tb.SpFN (R2 = 0.33, p < 0.05) and lower Tb.NFN (R2 = 0.42, p < 0.01). A higher prevalence of pores with diameter > 100 µm in tibial cortical bone (relCt.Po100µm-tibia) indicated higher Tb.SpFN (R2 = 0.36, p < 0.01) and lower Tb.NFN (R2 = 0.45, p < 0.01). CONCLUSION: Bone resorption and structural decline of the femoral neck may be identified in vivo by measuring cortical bone thickness and large pores in the tibia.