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Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker–Prager and eccentric–ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker–Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.

Nickel–titanium alloys are commonly adopted for producing cardiovascular minimally invasive devices such as self-expandable stents, aortic valves and stent-grafts. These devices are subjected to cyclic loads (due to blood pulsatility, leg or heart movements), that can induce fatigue fracture, and may also be subjected to very large deformations (due to crimping procedure, a tortuous physiological path or overloads), that can induce material yield. Recently, the authors developed a new constitutive model that considers inelastic strains due to not-completed reverse phase transformation (not all the stress-induced martensite turns back to austenite) or/and plasticity and their accumulation during cyclic loads. In this article, the model is implemented in the finite element code ABAQUS/Standard and it is used to investigate the effects of inelastic strain accumulation on endovascular nickel–titanium devices. In particular, the behavior of a transcatheter aortic valve is studied considering the following steps: (1) crimping, (2) expansion in a tube resembling a durability test chamber and (3) cyclic loads due to pressure variation applied on the inner surface of the tube. The analyses are performed twice, activating and not activating that part of the new model which describes the development of irreversible strain. From the results, it is interesting to note that plasticity has a very significant effect on the local material response, inducing stress modification from compression to tension. However, permanent deformations are concentrated in few zones of the stent frame and their presence does not affect the global behavior of the device that maintains its capability of recovering the original shape. In conclusion, this work suggests that at least for cardiovascular devices where the crimping is high (local strain may reach values of 8%–9%), taking into account inelastic effects due to plasticity and not-completed reverse phase transformation can be important, and hence using a suitable constitutive model is recommended.

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

Cement augmentation in vertebrae (vertebroplasty) is usually used to restore mechanical strength after spinal fracture but could also be used as a prophylactic treatment. So far, the mechanical competence has been determined immediately post-treatment, without considering long-term effects of bone adaptation. In this work, we investigated such long-term effects of vertebroplasty on the stiffness of the augmented bone by means of computational simulation of bone adaptation. Using micro-finite element analysis, we determined sites of increased mechanical stress (stress raisers) and stress shielding and, based on the simulations, regions with increased or decreased bone loss due to augmentation. Cement volumes connecting the end plates led to increased stress shielding and bone loss. The increased stiffness due to the augmentation, however, remained constant over the simulation time of 30 years. If the intervention was performed at an earlier time point, it did lead to more bone loss, but again, it did not affect long-term stability as this loss was compensated by bone gains in other areas. In particular, around the augmentation cement, bone structures were preserved, suggesting a long-term integration of the cement in the augmented bone. We conclude that, from a biomechanical perspective, the impact of vertebroplasty on the bone at the microstructural level is less detrimental than previously thought.

Bifurcation aneurysms account for a large fraction of cerebral aneurysms and often present morphologies that render traditional endovascular treatments, such as coiling, challenging and problematic. Flow-diverter stents offer a potentially elegant treatment option for such aneurysms, but clinical use of these devices remains controversial. Specifically, the deployment of a flow-diverter device in a bifurcation entails jailing one or more potentially vital vessels with a low-porosity mesh designed to restrict the flow. When multiple device placement configurations exist, the most appropriate clinical decision becomes increasingly opaque. In this study, three bifurcation aneurysm geometries were virtually treated by flow-diverter device. Each aneurysm was selected to offer two possible device deployment positions. Flow-diverters similar to commercially available designs were deployed with a fast-deployment algorithm before transient and steady state computational fluid dynamics simulations were performed. Reductions in aneurysm inflow, mean wall shear stress and maximum wall shear stress, all factors often linked with aneurysm treatment outcome, were compared for different device configurations in each aneurysm. In each of the three aneurysms modelled, a particular preferential device placement was shown to offer superior performance with the greatest reduction in the flow metrics considered. In all the three aneurysm geometries, substantial variations in inflow reduction (up to 25.3%), mean wall shear stress reduction (up to 14.6%) and maximum wall shear stress reduction (up to 12.1%) were seen, which were all attributed to device placement alone. Optimal device placement was found to be non-trivial and highly aneurysm specific; in only one-third of the simulated geometries, the best overall performance was achieved by deploying a device in the daughter vessel with the highest flow rate. Good correspondence was seen between transient results and steady state computations that offered a significant reduction in simulation run time. If accurate steady state computations are combined with the fast-deployment algorithm used, the modest run time and corresponding hardware make a virtual treatment pipeline in the clinical setting a meaningful possibility.

Tibiofemoral contact forces in total knee replacement have been measured at the medial and lateral sites respectively using an instrumented prosthesis, and predicted from musculoskeletal multibody dynamics models with a reasonable accuracy. However, it is uncommon that the medial and lateral forces are applied separately to replace a total axial load according to the ISO standard in the majority of current finite element analyses. In this study, we quantified the different effects of applying the medial and lateral loads separately versus the traditional total axial load application on contact mechanics and wear prediction of a patient-specific knee prosthesis. The load application position played an important role under the medial–lateral load application. The loading set which produced the closest load distribution to the multibody dynamics model was used to predict the contact mechanics and wear for the prosthesis and compared with the total axial load application. The medial–lateral load distribution using the present method was found to be closer to the multibody dynamics prediction than the traditional total axial load application, and the maximum contact pressure and contact area were consistent with the corresponding load variation. The predicted total volumetric wear rate and area were similar between the two load applications. However, the split of the predicted wear volumes on the medial and the lateral sides was different. The lateral volumetric wear rate was 31.46% smaller than the medial from the traditional load application prediction, while from the medial–lateral load application, the lateral side was only 11.8% smaller than the medial. The medial–lateral load application could provide a new and more accurate method of load application for patient-specific preclinical contact mechanics and wear prediction of knee implants.

Atherogenesis, the formation of plaques in the wall of blood vessels, starts as a result of lipid accumulation (low-density lipoprotein cholesterol) in the vessel wall. Such accumulation is related to the site of endothelial mechanotransduction, the endothelial response to mechanical stimuli and haemodynamics, which determines biochemical processes regulating the vessel wall permeability. This interaction between biomechanical and biochemical phenomena is complex, spanning different biological scales and is patient-specific, requiring tools able to capture such mathematical and biological complexity in a unified framework. Mathematical models offer an elegant and efficient way of doing this, by taking into account multifactorial and multiscale processes and mechanisms, in order to capture the fundamentals of plaque formation in individual patients. In this study, a mathematical model to understand plaque and calcification locations is presented: this model provides a strong interpretability and physical meaning through a multiscale, complex index or metric (the penetration site of low-density lipoprotein cholesterol, expressed as volumetric flux). Computed tomography scans of the aortic bifurcation and iliac arteries are analysed and compared with the results of the multifactorial model. The results indicate that the model shows potential to predict the majority of the plaque locations, also not predicting regions where plaques are absent. The promising results from this case study provide a proof of concept that can be applied to a larger patient population.

Respiratory disease is a significant problem worldwide, and it is a problem with increasing prevalence. Pathology in the upper airways and lung is very difficult to diagnose and treat, as response to disease is often heterogeneous across patients. Computational models have long been used to help understand respiratory function, and these models have evolved alongside increases in the resolution of medical imaging and increased capability of functional imaging, advances in biological knowledge, mathematical techniques and computational power. The benefits of increasingly complex and realistic geometric and biophysical models of the respiratory system are that they are able to capture heterogeneity in patient response to disease and predict emergent function across spatial scales from the delicate alveolar structures to the whole organ level. However, with increasing complexity, models become harder to solve and in some cases harder to validate, which can reduce their impact clinically. Here, we review the evolution of complexity in computational models of the respiratory system, including successes in translation of models into the clinical arena. We also highlight major challenges in modelling the respiratory system, while making use of the evolving functional data that are available for model parameterisation and testing.