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Concept: Torsion


Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Concepts: Interval finite element, Finite element method, Model, Biomechanics, Solid mechanics, Beam, Torsion, Structural analysis


To validate torsional analysis, based on finite elements, of WaveOne instruments against in vitro tests and to model the effects of different nickel titanium materials METHODOLOGY: WaveOne reciprocating instruments (Small, Primary and Large, n=8 each, M-Wire) were tested under torsion according to standard ISO 3630-1. Torsional profiles including torque and angle at fracture were determined. Test conditions were reproduced through Finite Element Analysis (FEA) simulations based on micro CT scans at 10μm resolution; results were compared to experimental data using analysis of variance and two-sided one sample t-tests. The same simulation was performed on virtual instruments with identical geometry and load condition, based on M-Wire or conventional NiTi alloy.

Concepts: Engineering, Finite element method, Hilbert space, Normal distribution, Analysis of variance, Standard, Partial differential equation, Torsion


Open reduction internal fixation technique has been generally accepted for treatment of midshaft clavicle fractures. Both superior and anterior clavicle plates have been reported in clinical or biomechanical researches, while presently the spiral clavicle plate design has been introduced improved biomechanical behavior over conventional designs. In order to objectively realize the multi-directional biomechanical performances among the three geometries for clavicle plate designs, a current conceptual finite element study has been conducted with identical cross-sectional features for clavicle plates. The conceptual superior, anterior, and spiral clavicle plate models were constructed for virtual reduction and fixation to an OTA 15-B1.3 midshaft transverse fracture of clavicle. Mechanical load cases including cantilever bending, axial compression, inferior bending, and axial torsion have been applied for confirming the multi-directional structural stability and implant safety in biomechanical perspective. Results revealed that the anterior clavicle plate model represented lowest plate stress under all loading cases. The superior clavicle plate model showed greater axial compressive stiffness, while the anterior clavicle plate model performed greater rigidity under cantilever bending load. Three model represented similar structural stiffness under axial torsion. Played as a transition structure between superior and anterior clavicle plate, the spiral clavicle plate model revealed comparable results with acceptable multi-directional biomechanical behavior. The concept of spiral clavicle plate design is worth considering in practical application in clinics. Implant safety should be further investigated by evidences in future mechanical tests and clinical observations.

Concepts: Bone fracture, Fracture, Orthopedic surgery, Clavicle fracture, Elasticity, Clavicle, Torsion, Superiority complex


Insight into crumpling or compaction of one-dimensional objects is important for understanding biopolymer packaging and designing innovative technological devices. By compacting various types of wires in rigid confinements and characterizing the morphology of the resulting crumpled structures, here, we report how friction, plasticity and torsion enhance disorder, leading to a transition from coiled to folded morphologies. In the latter case, where folding dominates the crumpling process, we find that reducing the relative wire thickness counter-intuitively causes the maximum packing density to decrease. The segment size distribution gradually becomes more asymmetric during compaction, reflecting an increase of spatial correlations. We introduce a self-avoiding random walk model and verify that the cumulative injected wire length follows a universal dependence on segment size, allowing for the prediction of the efficiency of compaction as a function of material properties, container size and injection force.

Concepts: Fundamental physics concepts, Force, Space, Materials science, Classical mechanics, Point, Wire, Torsion


The mechanical flexibility of coordination frameworks can lead to a range of highly anomalous structural behaviours. Here, we demonstrate the extreme compressibility of the LnFe(CN)6 frameworks (Ln = Ho, Lu or Y), which reversibly compress by 20% in volume under the relatively low pressure of 1 GPa, one of the largest known pressure responses for any crystalline material. We delineate in detail the mechanism for this high compressibility, where the LnN6 units act like torsion springs synchronized by rigid Fe(CN)6 units performing the role of gears. The materials also show significant negative linear compressibility via a cam-like effect. The torsional mechanism is fundamentally distinct from the deformation mechanisms prevalent in other flexible solids and relies on competition between locally unstable metal coordination geometries and the constraints of the framework connectivity, a discovery that has implications for the strategic design of new materials with exceptional mechanical properties.

Concepts: Crystal, Torque, Thermodynamics, Metal, Materials science, Pressure, Torsion, Torsion spring


Interbody fusion with posterior instrumentation is a common method for treating lumbar degenerative disc diseases. However, the high rigidity of the fusion construct may produce abnormal stresses at the adjacent segment and lead to adjacent segment degeneration (ASD). As such, biodegradable implants are becoming more popular for use in orthopaedic surgery. These implants offer sufficient stability for fusion but at a reduced stiffness. Tailored to degrade over a specific timeframe, biodegradable implants could potentially mitigate the drawbacks of conventional stiff constructs and reduce the loading on adjacent segments. Six finite element models were developed in this study to simulate a spine with and without fixators. The spinal fixators used both titanium rods and biodegradable rods. The models were subjected to axial loading and pure moments. The range of motion (ROM), disc stresses, and contact forces of facet joints at adjacent segments were recorded. A 3-point bending test was performed on the biodegradable rods and a dynamic bending test was performed on the spinal fixators according to ASTM F1717-11a. The finite element simulation showed that lumbar spinal fusion using biodegradable implants had a similar ROM at the fusion level as at adjacent levels. As the rods degraded over time, this produced a decrease in the contact force at adjacent facet joints, less stress in the adjacent disc and greater loading on the anterior bone graft region. The mechanical tests showed the initial average fatigue strength of the biodegradable rods was 145 N, but this decreased to 115N and 55N after 6 months and 12 months of soaking in solution. Also, both the spinal fixator with biodegradable rods and with titanium rods was strong enough to withstand 5,000,000 dynamic compression cycles under a 145 N axial load. The results of this study demonstrated that biodegradable rods may present more favourable clinical outcomes for lumbar fusion. These polymer rods could not only provide sufficient initial stability, but the loss in rigidity of the fixation construct over time gradually transfers loading to adjacent segments.

Concepts: Bone fracture, Finite element method, Force, Orthopedic surgery, Finite element method in structural mechanics, Spinal fusion, Torsion, Direct stiffness method


Conical implant-abutment connections are popular for their excellent connection stability, which is attributable to frictional resistance in the connection. However, conical angles, the inherent design parameter of conical connections, exert opposing effects on 2 influencing factors of the connection stability: frictional resistance and abutment rigidity. This pilot study employed an optimization approach through the finite element method to obtain an optimal conical angle for the highest connection stability in an Ankylos-based conical connection system. A nonlinear 3D finite element parametric model was developed according to the geometry of the Ankylos system (conical half angle = 5.7°) by using the ANSYS 11.0 software. Optimization algorithms were conducted to obtain the optimal conical half angle and achieve the minimal value of maximum von Mises stress in the abutment, which represents the highest connection stability. The optimal conical half angle obtained was 10.1°. Compared with the original design (5.7°), the optimal design demonstrated an increased rigidity of abutment (36.4%) and implant (25.5%), a decreased microgap at the implant-abutment interface (62.3%), a decreased contact pressure (37.9%) with a more uniform stress distribution in the connection, and a decreased stress in the cortical bone (4.5%). In conclusion, the methodology of design optimization to determine the optimal conical angle of the Ankylos-based system is feasible. Because of the heterogeneity of different systems, more studies should be conducted to define the optimal conical angle in various conical connection designs.

Concepts: Finite element method, Operations research, Methodology, Computational fluid dynamics, Optimization, Numerical analysis, Yield surface, Torsion


The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3-L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

Concepts: Spinal disc herniation, Finite element method, Human body, Model, Intervertebral disc, Finite element method in structural mechanics, Torsion, Direct stiffness method


The objectives of this study were to describe fracture morphology resulting from common loading mechanisms such as bending and torsion in immature bone and to identify differences in the energy required to produce various fracture types under these two loading mechanisms using an immature porcine animal model.

Concepts: Bone, Hip fracture, Torque, Mechanics, Torsion, Polar moment of inertia


De-rotational osteotomies are indicated in patients with pathologic femoral torsion. However, there is disagreement whether an osteotomy should be performed proximally or distally. Conventionally only the total torsion is measured, which does not allow differentiation between a torsional deformity located in the proximal or distal metaphysis or the diaphysis. The aim of this study is to validate a new multi-level measurement protocol for evaluation of the magnitude of torsion of the respective femoral segments in CT.

Concepts: Measurement, Psychometrics, Vector space, Tomography, Torsion, Torsion spring