Probabilistic failure analysis of bone using a finite element model of mineral–collagen composites

Microdamage accumulation is a major pathway for energy dissipation during the post-yield deformation of bone. In this study, a two-dimensional probabilistic finite element model of a mineral–collagen composite was developed to investigate the influence of the tissue and ultrastructural properties of bone on the evolution of microdamage from an initial defect in tension. The probabilistic failure analyses indicated that the microdamage progression would be along the plane of the initial defect when the debonding at mineral–collagen interfaces was either absent or limited in the vicinity of the defect. In this case, the formation of a linear microcrack would be facilitated. However, the microdamage progression would be scattered away from the initial defect plane if interfacial debonding takes place at a large scale. This would suggest the possible formation of diffuse damage. In addition to interfacial debonding, the sensitivity analyses indicated that the microdamage progression was also dependent on the other material and ultrastructural properties of bone. The intensity of stress concentration accompanied with microdamage progression was more sensitive to the elastic modulus of the mineral phase and the nonlinearity of the collagen phase, whereas the scattering of failure location was largely dependent on the mineral to collagen ratio and the nonlinearity of the collagen phase. The findings of this study may help understanding the post-yield behavior of bone at the ultrastructural level and shed light on the underlying mechanism of bone fractures.     

A nonlinear homogenized finite element analysis of the primary stability of the bone–implant interface

Stability of an implant is defined by its ability to undergo physiological loading–unloading cycles without showing excessive tissue damage and micromotions at the interface. Distinction is usually made between the immediate primary stability and the long-term, secondary stability resulting from the biological healing process. The aim of this research is to numerically investigate the effect of initial implantation press-fit, bone yielding, densification and friction at the interface on the primary stability of a simple bone–implant system subjected to loading–unloading cycles. In order to achieve this goal, human trabecular bone was modeled as a continuous, elasto-plastic tissue with damage and densification, which material constants depend on bone volume fraction and fabric. Implantation press-fit related damage in the bone was simulated by expanding the drilled hole to the outer contour of the implant. The bone–implant interface was then modeled with unilateral contact with friction. The implant was modeled as a rigid body and was subjected to increasing off-axis loading cycles. This modeling approach is able to capture the experimentally observed primary stability in terms of initial stiffness, ultimate force and progression of damage. In addition, it is able to quantify the micromotions around the implant relevant for bone healing and osseointegration. In conclusion, the computationally efficient modeling approach used in this study provides a realistic structural response of the bone–implant interface and represents a powerful tool to explore implant design, implantation press-fit and the resulting risk of implant failure under physiological loading.     

Prediction of Colles’ fracture load in human radius using cohesive finite element modeling

Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles’ fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731–6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4–5% per decade based only on material level changes and by 6–20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r²=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.     

Can the modeling for simplification of a dental implant surface affect the accuracy of 3D finite element analysis?

The aim of this study was to assess stress/strain of different implant modeling simplifications by 3D-FEA. Three variation of external hexagon implant (Ø3.75?×?10 mm) supporting one molar crown were simulated: A (no threads); B (slightly threads simplification); C (original design). 200 N (axial) and 100 N (oblique) were applied. Cortical bone was evaluated by maximum principal stress and microstrain qualitatively and quantitatively (ANOVA and Tukey post hoc (p < 0.05)). Higher stress levels (p < 0.05) were observed in model A. Models B and C presented similar stress transmission. It was possible to conclude that slightly simplification should be used for studies evaluating stress transferring for bone tissue.     

Mechanical principles of effects of botulinum toxin on muscle length–force characteristics: An assessment by finite element modeling

Recent experiments involving muscle force measurements over a range of muscle lengths show that effects of botulinum toxin (BTX) are complex e.g., force reduction varies as a function of muscle length. We hypothesized that altered conditions of sarcomeres within active parts of partially paralyzed muscle is responsible for this effect. Using finite element modeling, the aim was to test this hypothesis and to study principles of how partial activation as a consequence of BTX affects muscle mechanics. In order to model the paralyzing effect of BTX, only 50% of the fascicles (most proximal, or middle, or most distal) of the modeled muscle were activated. For all muscle lengths, a vast majority of sarcomeres of these BTX-cases were at higher lengths than identical sarcomeres of the BTX-free muscle. Due to such “longer sarcomere effect”, activated muscle parts show an enhanced potential of active force exertion (up to 14.5%). Therefore, a muscle force reduction originating exclusively from the paralyzed muscle fiber populations, is compromised by the changes of active sarcomeres leading to a smaller net force reduction. Moreover, such “compromise to force reduction” varies as a function of muscle length and is a key determinant of muscle length dependence of force reduction caused by BTX. Due to longer sarcomere effect, muscle optimum length tends to shift to a lower muscle length. Muscle fiber–extracellular matrix interactions occurring via their mutual connections along full peripheral fiber lengths (i.e., myofascial force transmission) are central to these effects. Our results may help improving our understanding of mechanisms of how the toxin secondarily affects the muscle mechanically.     

Numerical modeling of bone tissue adaptation—A hierarchical approach for bone apparent density and trabecular structure

In this work, a three-dimensional model for bone remodeling is presented, taking into account the hierarchical structure of bone. The process of bone tissue adaptation is mathematically described with respect to functional demands, both mechanical and biological, to obtain the bone apparent density distribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone is assumed as a continuum material characterized by equivalent (homogenized) mechanical properties. At local scale a periodic cellular material model approaches bone trabecular anisotropy as well as bone surface area density. For each scale there is a material distribution problem governed by density-based design variables which at the global level can be identified with bone relative density. In order to show the potential of the model, a three-dimensional example of the proximal femur illustrates the distribution of bone apparent density as well as microstructural designs characterizing both anisotropy and bone surface area density. The bone apparent density numerical results show a good agreement with Dual-energy X-ray Absorptiometry (DXA) exams. The material symmetry distributions obtained are comparable to real bone microstructures depending on the local stress field. Furthermore, the compact bone porosity is modeled giving a transversal isotropic behavior close to the experimental data. Since, some computed microstructures have no permeability one concludes that bone tissue arrangement is not a simple stiffness maximization issue but biological factors also play an important role.     

Sensitivity analysis of the Poisson Nernst–Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model

Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst–Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred experimentally. It is crucial to understand how the mathematical model (and resulting simulations) depend on specific values of these parameters. Here we develop a rigorous approach based on the sensitivity equation for the electrodiffusion model. To illustrate the proposed methodology, we investigate the sensitivity of the electrical response of a node of Ranvier with respect to ionic diffusion coefficients and the membrane dielectric permittivity.

     

Search for critical loading condition of the spine–A meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2–L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Does screw–bone interface modelling matter in finite element analyses?

The effect of screw-bone interface modelling strategies was evaluated in the setting of a tibial mid-shaft fracture stabilised using locking plates. Three interface models were examined: fully bonded interface; screw with sliding contact with bone; and screw with sliding contact with bone in an undersized pilot hole. For the simulation of the last interface condition we used a novel thermal expansion approach to generate the pre-stress that the bone would be exposed to during screw insertion. The study finds that the global load-deformation response is not influenced by the interface modelling approach employed; the deformation varied by less than 1% between different interaction models. However, interface modelling is found to have a considerable impact on the local stress-strain environment within the bone in the vicinity of the screws. Frictional and tied representations did not have significantly different peak strain values (<5% difference); the frictional interface had higher peak compressive strains while the tied interface had higher tensile strains. The undersized pilot hole simulation produced the largest strains. The peak minimum principal strains for the frictional interface were 26% of those for the undersized pilot hole simulation at a load of 770 N. It is concluded that the commonly used tie constraint can be used effectively when the only interest is the global load-deformation behaviour. Different contact interface models, however, alter the mechanical response around screw holes leading to different predictions for screw loosening, bone damage and stress shielding.     

Structure–activity relationships of the thujaplicins for inhibition of human tyrosinase

Tyrosinase inhibitors have become increasingly critical agents in cosmetic, agricultural, and medicinal products. Although a large number of tyrosinase inhibitors have been reported, almost all the inhibitors were unfortunately evaluated by using commercial available mushroom tyrosinase. Here, we examined the inhibitory effects of three isomers of thujaplicin (α, β, and γ) on human tyrosinase and analyzed their binding modes using homology model and docking studies. As the results, γ-thujaplicin was found to strongly inhibit human tyrosinase with the IC₅₀ of 1.15 μM, extremely superior to a well-known tyrosinase inhibitor kojic acid (IC₅₀ = 571.17 μM). MM-GB/SA binding free energy decomposition analyses suggested that the potent inhibitory activity of γ-thujaplicin may be due to the interactions with His367, Ile368, and Val377 (hot spot amino acid residues) in human tyrosinase. Furthermore, the binding mode of α-thujaplicin indicated that Val377 and Ser380 may cause van der Waals clashes with the isopropyl group of α-thujaplicin. These results provide a novel structural insight into the hot spot of human tyrosinase for the specific binding of γ-thujaplicin and a way to optimize not only thujaplicins but also other lead compounds as specific inhibitors for human tyrosinase in a rational manner.     

Three-dimensional finite element analysis of stress distribution in retention screws of different crown–implant ratios

The retaining screw of the implant-supported dental prosthesis is the weakest point of the crown/implant system. Furthermore, crown height is another important factor that may increase the lever arm. Therefore, the aim of this study was to assess the stress distribution in implant prosthetic screws with different heights of the clinical crown of the prosthesis using the method of three-dimensional finite element analysis. Three models were created with implants (3.75 mm × 10 mm) and crowns (heights of 10, 12.5 and 15 mm). The results were visualised by means of von Mises stress maps that increased the crown heights. The screw structure exhibited higher levels of stresses in the oblique load. The oblique loading resulted in higher stress concentration when compared with the axial loading. It is concluded that the increase of the crown was damaging to the stress distribution on the screw, mainly in oblique loading.     

Production of human platelet lysate by use of ultrasound for ex vivo expansion of human bone marrow–derived mesenchymal stromal cells

Background aimsA medium supplemented with fetal bovine serum (FBS) is of common use for the expansion of human mesenchymal stromal cells (MSCs). However, its use is discouraged by regulatory authorities because of the risk of zoonoses and immune reactions. Human platelet lysate (PL) obtained by freezing/thawing disruption of platelets has been proposed as a possible substitute of FBS. The process is time-consuming and not well standardized. A new method for obtaining PL that is based on the use of ultrasound is proposed.MethodsPlatelet sonication was performed by submerging platelet-containing plastic bags in an ultrasonic bath. To evaluate platelet lysis we measured platelet-derived growth factor-AB release. PL efficiency was tested by expanding bone marrow (BM)-MSCs, measuring population doubling time, differentiation capacity and immunogenic properties. Safety was evaluated by karyotyping expanded cells.ResultsAfter 30 minutes of sonication, 74% of platelet derived growth factor-AB was released. PL enhanced BM-MSC proliferation rate compared with FBS. The mean cumulative population doubling (cPD) of cells growth in PL at 10%, 7.5% and 5% was better compared with cPD obtained with 10% FBS. PD time (hours) of MSCs with PL obtained by sonication was shorter than for cPD with PL obtained by freezing/thawing (18.9 versus 17.4, P < 0.01). BM mononucleated cells expressed MSC markers and were able to differentiate into adipogenic, osteogenic and chondrogenic lineages. When BM-MSCs and T cells were co-cultured in close contact, immunosuppressive activity of BM-MSCs was maintained. Cell karyotype showed no genetic alterations.ConclusionsThe proposed method for the production of PL by sonication could be a safe, efficient and fast substitute of FBS, without the potential risks of FBS.     

The effect of direct and indirect force transmission on peri-implant bone stress – a contact finite element analysis

In almost all finite element (FE) studies in dentistry, virtual forces are applied directly to dentures. The purpose of this study was to develop a FE model with non-linear contact simulation using an antagonist as force transmitter and to compare this with a similar model that uses direct force transmission. Furthermore, five contact situations were created in order to examine their influence on the peri-implant bone stresses, which are relevant to the survival rate of implants. It was found that the peri-implant bone stresses were strongly influenced by the kind of force transmission and contact number.     

Micro-mechanical damage of trabecular bone–cement interface under selected loading conditions: a finite element study

In this study, two micro finite element models of trabecular bone–cement interface developed from high resolution computed tomography (CT) images were loaded under compression and validated using the in situ experimental data. The models were then used under tension and shear to examine the load transfer between the bone and cement and the micro damage development at the bone–cement interface. In addition, one models was further modified to investigate the effect of cement penetration on the bone–cement interfacial behaviour. The simulated results show that the load transfer at the bone–cement interface occurred mainly in the bone cement partially interdigitated region, while the fully interdigitated region seemed to contribute little to the mechanical response. Consequently, cement penetration beyond a certain value would seem to be ineffective in improving the mechanical strength of trabecular bone–cement interface. Under tension and shear loading conditions, more cement failures were found in denser bones, while the cement damage is generally low under compression.     

Finite element modeling of superelastic nickel–titanium orthodontic wires

Thanks to its good corrosion resistance and biocompatibility, superelastic Ni–Ti wire alloys have been successfully used in orthodontic treatment. Therefore, it is important to quantify and evaluate the level of orthodontic force applied to the bracket and teeth in order to achieve tooth movement. In this study, three dimensional finite element models with a Gibbs-potential-based-formulation and thermodynamic principles were used. The aim was to evaluate the influence of possible intraoral temperature differences on the forces exerted by NiTi orthodontic arch wires with different cross sectional shapes and sizes. The prediction made by this phenomenological model, for superelastic tensile and bending tests, shows good agreement with the experimental data. A bending test is simulated to study the force variation of an orthodontic NiTi arch wire when it loaded up to the deflection of 3 mm, for this task one half of the arch wire and the 3 adjacent brackets were modeled. The results showed that the stress required for the martensite transformation increases with the increase of cross-sectional dimensions and temperature. Associated with this increase in stress, the plateau of this transformation becomes steeper. In addition, the area of the mechanical hysteresis, measured as the difference between the forces of the upper and lower plateau, increases.     

Response analysis of the lumbar spine during regular daily activities—A finite element analysis

A non-linear poroelastic finite element model of the lumbar spine was developed to investigate spinal response during daily dynamic physiological activities. Swelling was simulated by imposing a boundary pore pressure of 0.25 MPa at all external surfaces. Partial saturation of the disc was introduced to circumvent the negative pressures otherwise computed upon unloading. The loading conditions represented a pre-conditioning full day followed by another day of loading: 8 h rest under a constant compressive load of 350 N, followed by 16 h loading phase under constant or cyclic compressive load varying in between 1000 and 1600 N. In addition, the effect of one or two short resting periods in the latter loading phase was studied.The model yielded fairly good agreement with in-vivo and in-vitro measurements. Taking the partial saturation of the disc into account, no negative pore pressures were generated during unloading and recovery phase. Recovery phase was faster than the loading period with equilibrium reached in only ～3 h. With time and during the day, the axial displacement, fluid loss, axial stress and disc radial strain increased whereas the pore pressure and disc collagen fiber strains decreased. The fluid pressurization and collagen fiber stiffening were noticeable early in the morning, which gave way to greater compression stresses and radial strains in the annulus bulk as time went by. The rest periods dampened foregoing differences between the early morning and late in the afternoon periods. The forgoing diurnal variations have profound effects on lumbar spine biomechanics and risk of injury.