Graphene-Based Nanoelectromechanical Periodic Array with Tunable Frequency.

Phononic crystals (PnCs) have attracted much attention due to their great potential for dissipation engineering and propagation manipulation of phonons. Notably, the excellent electrical and mechanical properties of graphene make it a promising material for nanoelectromechanical resonators. Transferring a graphene flake to a prepatterned periodic mechanical structure enables the realization of a PnC with on-chip scale. Here, we demonstrate a nanoelectromechanical periodic array by anchoring a graphene membrane to a 9 × 9 array of standing nanopillars. The device exhibits a quasi-continuous frequency spectrum with resonance modes distributed from ∼120 MHz to ∼980 MHz. Moreover, the resonant frequencies of these modes can be electrically tuned by varying the voltage applied to the gate electrode sitting underneath. Simulations suggest that the observed band-like spectrum provides an experimental evidence for PnC formation. Our architecture has large fabrication flexibility, offering a promising platform for investigations on PnCs with electrical accessibility and tunability.

Tunable parametric amplification of a graphene nanomechanical resonator in the nonlinear regime.

Parametric amplification is widely used in nanoelectro-mechanical systems to enhance the transduced mechanical signals. Although parametric amplification has been studied in different mechanical resonator systems, the nonlinear dynamics involved receives less attention. Taking advantage of the excellent electrical and mechanical properties of graphene, we demonstrate electrical tunable parametric amplification using a doubly clamped graphene nanomechanical resonator. By applying external microwave pumping with twice the resonant frequency, we investigate parametric amplification in the nonlinear regime. We experimentally show that the extracted coefficient of the nonlinear Duffing force α and the nonlinear damping coefficient η vary as a function of external pumping power, indicating the influence of higher-order nonlinearity beyond the Duffing (∼x 3) and van der Pol (∼[Formula: see text]) types in our device. Even when the higher-order nonlinearity is involved, parametric amplification still can be achieved in the nonlinear regime. The parametric gain increases and shows a tendency of saturation with increasing external pumping power. Further, the parametric gain can be electrically tuned by the gate voltage with a maximum gain of 10.2 dB achieved at the gate voltage of 19 V. Our results will benefit studies on nonlinear dynamics, especially nonlinear damping in graphene nanomechanical resonators that has been debated in the community over past decade.

Evaluation of the performance of three tenodesis techniques for the treatment of scapholunate instability: flexion-extension and radial-ulnar deviation.

Chronic scapholunate ligament (SL) injuries are difficult to treat and can lead to wrist dysfunction. Whilst several tendon reconstruction techniques have been employed in the management of SL instability, SL gap reappearance after surgery has been reported. Using a finite element model and cadaveric study data, we investigated the performance of the Corella, scapholunate axis (SLAM) and modified Brunelli tenodesis (MBT) techniques. Scapholunate dorsal and volar gap and angle were obtained following virtual surgery undertaken using each of the three reconstruction methods with the wrist positioned in flexion, extension, ulnar deviation and radial deviation, in addition to the ulnar-deviated clenched fist and neutral positions. From the study, it was found that, following simulated scapholunate interosseous ligament rupture, the Corella technique was better able to restore the SL gap and angle close to the intact ligament for all wrist positions investigated, followed by SLAM and MBT. The results suggest that for the tendon reconstruction techniques, the use of multiple junction points between scaphoid and lunate may be of benefit. Graphical abstract The use of multiple junction points between scaphoid and lunate may be of benefit for tendon reconstruction techniques.

Stress shielding in periprosthetic bone following a total knee replacement: Effects of implant material, design and alignment.

Periprosthetic bone strain distributions in some of the typical cases of total knee replacement (TKR) were studied with regard to the selection of material, design and the alignments of tibial components to examine which conditions are more forgiving than the others to stress shielding post a TKR. Four tibial components with two implant designs (cruciate sacrificing and cruciate retaining) and material properties (metal-backed (MB) and all-polyethylene (AP)) were considered in a specimen-specific finite element tibia bone model loaded in a neutral position. The influence of tibial material and design on the periprosthetic bone strain response was investigated under the peak loads of walking and stair descending/ascending. Two of the models were also modified to examine the effect of selected implant malalignment conditions (7° posterior, 5° valgus and 5° varus) on stress shielding in the bone, where the medio-lateral load share ratios were adjusted accordingly. The predicted increases of bone density due to implantation for the selected cases studied were also presented. For the cases examined, the effect of stress shielding on the periprosthetic bone seems to be more significantly influenced by the implant material than by the implant geometry. Significant stress shielding is found in MB cases, as opposed to increase in bone density found in AP cases, particularly in the bones immediately beneath the baseplate. The effect of stress shielding is reduced somewhat for the MB components in the malaligned positions compared with the neutral case. In AP cases, the effect of stress shielding is mostly low except in the varus position, possibly due to off-loading of lateral condyle. Increases in bone density are found in both MB and AP cases for the malaligned conditions.

Stress shielding in bone of a bone-cement interface.

Cementation is one of the main fixation methods used in joint replacement surgeries such as Total Knee Replacement (TKR). This work was prompted by a recent retrieval study, which shows losses up to 75% of the bone stock at the bone-cement interface ten years post TKR. It aims to examine the effects of cementation on the stress shielding of the interfacing bone, when the influence of an implant is removed. A micromechanics finite element study of a generic bone-cement interface is presented here, where bone elements in the partially and the fully interdigitated regions were evaluated under selected load cases. The results revealed significant stress shielding effect in the bone of all bone-cement interface regions, particularly in fully interdigitated region. This finding may be useful in the studies of implant fixation and other related orthopedic treatment strategies.

Spatial resolution and measurement uncertainty of strains in bone and bone-cement interface using digital volume correlation.

The measurement uncertainty of strains has been assessed in a bone analogue (sawbone), bovine trabecular bone and bone-cement interface specimens under zero load using the Digital Volume Correlation (DVC) method. The effects of sub-volume size, sample constraint and preload on the measured strain uncertainty have been examined. There is generally a trade-off between the measurement uncertainty and the spatial resolution. Suitable sub-volume sizes have been be selected based on a compromise between the measurement uncertainty and the spatial resolution of the cases considered. A ratio of sub-volume size to a microstructure characteristic (Tb.Sp) was introduced to reflect a suitable spatial resolution, and the measurement uncertainty associated was assessed. Specifically, ratios between 1.6 and 4 appear to give rise to standard deviations in the measured strains between 166 and 620 µÎµ in all the cases considered, which would seem to suffice for strain analysis in pre as well as post yield loading regimes. A microscale finite element (µFE) model was built from the CT images of the sawbone, and the results from the µFE model and a continuum FE model were compared with those from the DVC. The strain results were found to differ significantly between the two methods at tissue level, consistent in trend with the results found in human bones, indicating mainly a limitation of the current DVC method in mapping strains at this level.

Microdamage assessment of bone-cement interfaces under monotonic and cyclic compression.

Bone-cement interface has been investigated under selected loading conditions, utilising experimental techniques such as in situ mechanical testing and digital image correlation (DIC). However, the role of bone type in the overall load transfer and mechanical behaviour of the bone-cement construct is yet to be fully quantified. Moreover, microdamage accumulation at the interface and in the cement mantle has only been assessed on the exterior surfaces of the samples, where no volumetric information could be obtained. In this study, some typical bone-cement interfaces, representative of different fixation scenarios for both hip and knee replacements, were constructed using mainly trabecular bone, a mixture of trabecular and cortical bone and mainly cortical bone, and tested under static and cyclic compression. Axial displacement and strain fields were obtained by means of digital volume correlation (DVC) and microdamage due to static compression was assessed using DVC and finite element (FE) analysis, where yielded volumes and strains (εzz) were evaluated. A significantly higher load was transferred into the cement region when mainly cortical bone was used to interdigitate with the cement, compared with the other two cases. In the former, progressive damage accumulation under cyclic loading was observed within both the bone-cement interdigitated and the cement regions, as evidenced by the initiation of microcracks associated with high residual strains (εzz_res).

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.

Characterisation of a metallic foam-cement composite under selected loading conditions.

An open-cell metallic foam was employed as an analogue material for human trabecular bone to interface with polymethyl methacrylate (PMMA) bone cement to produce composite foam-cement interface specimens. The stress-displacement curves of the specimens were obtained experimentally under tension, shear, mixed tension and shear (mixed-mode), and step-wise compression loadings. In addition, under step-wise compression, an image-guided failure assessment (IGFA) was used to monitor the evolution of micro-damage of the interface. Microcomputed tomography (µCT) images were used to build a subject-specific model, which was then used to perform finite element (FE) analysis under tension, shear and compression. For tension-shear loading conditions, the strengths of the interface specimens were found to increase with the increase of the loading angle reaching the maximum under shear loading condition, and the results compare reasonably well with those from bone-cement interface. Under compression, however, the mechanical strength measured from the foam-cement interface is much lower than that from bone-cement interface. Furthermore, load transfer between the foam and the cement appears to be poor under both tension and compression, hence the use of the foam should be discouraged as a bone analogue material for cement fixation studies in joint replacements.

3D real-time micromechanical compressive behaviour of bone-cement interface: experimental and finite element studies.

The integrity of bone-cement interface is essential for the long-term stability of cemented total joint arthroplasty. Although several studies have been carried out on bone-cement interface at continuum level, micromechanics of the interface has been studied only recently for tensile and shear loading cases. Fundamental studies of bone-cement interface at microstructural level are critical to the understanding of the failure processes of the interface, where multiple factors may contribute to failure. Here we present a micromechanical study of bone-cement interface under compression, which utilised in situ mechanical testing, time-lapsed microcomputed tomography (CT) and finite element (FE) modelling. Bovine trabecular bone was used to interdigitate with bone cement to obtain bone-cement interface samples, which were tested in step-wise compression using a custom-made loading stage within the µCT chamber. A finite element model was built from the CT images of one of the tested samples and loaded similarly as in the experiment. The simulated stress-displacement response fell within the range of the experimental responses, and the predicted local strain distribution correlated well with the failure pattern in the subject-specific experimental model. Damage evolution with load in the samples was monitored both experimentally and numerically. The results from the FE simulations further revealed the development of damage in the regions of interest during compression, which may be useful towards a micromechanics understanding of the failure processes at bone-cement interface.

A subject-specific pelvic bone model and its application to cemented acetabular replacements.

A subject-specific three-dimensional finite element (FE) pelvic bone model has been developed and applied to the study of bone-cement interfacial response in cemented acetabular replacements. The pelvic bone model was developed from CT scan images of a cadaveric pelvis and validated against the experiment data obtained from the same specimen at a simulated single-legged stance. The model was then implanted with a cemented acetabular cup at selected positions to simulate some typical implant conditions due to the misplacement of the cup as well as a standard cup condition. For comparison purposes, a simplified FE model with homogeneous trabecular bone material properties was also generated and similar implant conditions were examined. The results from the homogeneous model are found to underestimate significantly both the peak von Mises stress and the area of the highly stressed region in the cement near the bone-cement interface, compared with those from the subject-specific model. Non-uniform cement thickness and non-standard cup orientation seem to elevate the highly stressed region as well as the peak stress near the bone-cement interface.

Evaluation of load transfer characteristics of a dynamic stabilization device on disc loading under compression.

In the current study, finite element analyses were conducted to examine the biomechanical capability of a newly design dynamic stabilization system, FlexPLUS, to restore the load transmission of degenerated intervertebral L4-L5 lumbar motion segment spine under compression. Detailed three-dimensional FE models of L4-L5 motion segment and the FlexPLUS were developed. Compressive loading up to 1000N was applied to the intact L4-L5 model, the L4-L5 models with slight and moderate degenerated disc, and the implanted L4-L5 model. Further more, the load transmission characteristics of Dynesys and a rigid rod was also simulated for comparison. The resultant load-displacement curves and the load transferred through annulus under various conditions were compared. The predicted axial displacement of L4 top surface against applied compressive force of the intact L4-L5 model agreed well with experimental data. The predicted results showed that degenerated disc has significant effect on the lumbar segment load bearing capacity. Not only the stiffness of the segment was greatly increased, the uniform nature of the disc stress distribution was also altered. The FlexPLUS can effectively reduce the disc loading of degenerated model. Although the non-uniform load distribution pattern through annulus was not improved, the overall stress magnitude was greatly reduced to the level of intact model for grade II degeneration.

A numerical study of the effect of axial acceleration on the responses of the cervical spine during low-speed rear-end impact.

A detailed, three-dimensional, head-neck (vertebral segments CO to C7) finite element model - developed and validated previously on the basis of the actual geometry of a cadaveric specimen - was used to evaluate the effect of cranial acceleration on the response of the cervical spine during low-speed, rear-end impact. Analyses were carried out to compare the predicted overall and segmental rotations, peak disc stresses, and capsular ligament strains of each motion segment during whiplash with or without cranial acceleration applied on the C7 inferior surface. The results show that, in the first 150 ms, the variation curves of predicted segmental rotational angles, disc stresses, and capsular strains for each motion segment overlapped well under the two conditions. However, after 150 ms, the capsular strains of C2 to C6 without cranial acceleration applied on C7 were all obviously lower than those with cranial acceleration applied, but the segmental rotational angles and disc stresses remain unaffected. It was implied that, although without cranial acceleration applied on C7, the relatively simple head-neck model could be used to reflect effectively the biomechanical response of the cervical spine during the initial stage (i.e. 150 ms) under low-speed, rear-end impact as well as the whole-human-body dummy model.

Finite element analysis of head-neck kinematics under simulated rear impact at different accelerations.

The information on the variation of ligament strains over time after rear impact has been seldom investigated. In the current study, a detailed three-dimensional C0-C7 finite element model of the whole head-neck complex developed previously was modified to include T1 vertebra. Rear impact of half sine-pulses with peak values of 3.5g, 5g, 6.5g and 8g respectively were applied to the inferior surface of the T1 vertebral body to validate the simulated variations of the intervertebral segmental rotations and to investigate the ligament tensions of the cervical spine under different levels of accelerations. The simulated kinematics of the head-neck complex showed relatively good agreement with the experimental data with most of the predicted peak values falling within one standard deviation of the experimental data. Under rear impact, the whole C0-T1 structure formed an S-shaped curvature with flexion at the upper levels and extension at the lower levels at early stage after impact, during which the lower cervical levels might experience hyperextensions. The predicted high resultant strain of the capsular ligaments, even at low impact acceleration compared with other ligament groups, suggests their susceptibility to injury. The peak impact acceleration has a significant effect on the potential injury of ligaments. Under higher accelerations, most ligaments will reach failure strain in a much shorter time immediately after impact.

Finite element application in implant research for treatment of lumbar degenerative disc disease.

Surgical treatment for disc degeneration can be roughly grouped as fusion, disc replacement and dynamic stabilization. The clinical efficacy and biomechanical features of the implants used for disc degenerations can be evaluated through short- or long-term follow up observation, in vitro and in vivo experiments and computational simulations. Finite element models are already making an important contribution to our understanding of the spine and its components. Models are being used to reveal the biomechanical function of the spine and its behavior when healthy, diseased or damaged. They are also providing support in the design and application of spinal instrumentation. The article reviewed the most recent studies in the application of FE models that address the issue of implant research for treatment of low back pain. The published studies were grouped and reviewed thoroughly based on the function of implants investigated. The considerations of the finite element analysis in these studies were further discussed.

Finite element analysis of head-neck kinematics during motor vehicle accidents: analysis in multiple planes.

In this study, a detailed three-dimensional head-neck (C0-C7) finite element (FE) model developed previously based on the actual geometry of a human cadaver specimen was used. Five simulation analyses were performed to investigate the kinematic responses of the head-neck complex under rear-end, front, side, rear- and front-side impacts. Under rear-end and front impacts, it was predicted that the global and intervertebral rotations of the head-neck in the sagittal plane displayed nearly symmetric curvatures about the frontal plane. The primary sagittal rotational angles of the neck under direct front and rear-end impact conditions were higher than the primary frontal rotational angles under other side impact conditions. The analysis predicted early S-shaped and subsequent C-shaped curvatures of the head-neck complex in the sagittal plane under front and rear-end impact, and in the frontal plane under side impact. The head-neck complex flexed laterally in one direction with peak magnitude of larger than 22 degrees and a duration of about 130 ms before flexing in the opposite direction under both side and rear-side impact, compared to the corresponding values of about 15 degrees and 105 ms under front-side impact. The C0-C7 FE model has reasonably predicted the effects of impact direction in the primary sagittal and frontal segmental motion and curvatures of the head-neck complex under various impact conditions.

Effect of bilateral facetectomy of thoracolumbar spine T11-L1 on spinal stability.

Spinal stenosis can be found in any part of the spine, though it is most commonly located on the lumbar and cervical areas. It has been documented in the literature that bilateral facetectomy in a lumbar motion segment to increase the space induces an increase in flexibility at the level at which the surgery was performed. However, the result of bilateral facetectomy on the stability of the thoracolumbar spine has not been studied. A nonlinear three-dimensional finite element (FE) model of thoracolumbar T11-L1 was built to explore the influence of bilateral facetectomy. The FE model of T11-L1 was validated against published experimental results under various physiological loadings. The FE model with bilateral facetectomy was evaluated under flexion, extension, lateral bending and axial rotation to determine alterations in kinematics. Results show that bilateral facetectomy causes increase in motion, considerable increase in axial rotation and least increase in lateral bending. Removal of facets did not result in significant change in the sagittal motion in flexion and extension.

Comparison of kinematics between thoracolumbar T11-t12 and T12-L1 functional spinal units.

The purpose of this study was to compare the kinematics in terms of the locations and loci of instantaneous axes of rotation (IARs) at levels T11-T12 and T12-L1 of thoracolumbar junction (TLJ). The LAR is one of the kinematics characteristics of a functional spinal unit (FSU) in a plane under load. There is little information about loci of IARs in the TLJ. Validated finite element (FE) models of T11-T12 and T12-L1 FSUs were used to determine the locations and loci of IARs in three anatomical planes. In the sagittal plane, the locations and loci of the IARs were located below the intervertebral disc for T11-T12, and situated in the intervertebral disc for T12-L1. In the frontal plane, they were all located around the mid-sagittal plane for T11-T12 and T12-L1. In the transverse plane, they fell in the medio-anterior region of the movable vertebra T11 for T11-T12, and located near the cortical shell of the upper vertebra T12 for T12-L1. These findings may offer an insight to better understanding the kinematics of the human thoracolumbar spine and provide clinically relevant information for the evaluation of spinal stability and functionality of implant devices.

Effects of bone materials on the screw pull-out strength in human spine.

A three-dimensional finite element model simulating the threaded connections including detailed helix curve for the bone and surgical screw was constructed. Validation of the FE model was conducted by comparing the predicted screw pull-out strength in different foam materials against experimental study. The FE model was then further analyzed to investigate the interaction of bone material and purchase length on the screw pull-out strength. The results show that failure of the connection was due to bone shearing which occurred along a cylindrical surface determined by the outer perimeter of the screw. The cortical shell resists around 50% of the pull-out strength for a screw of 4mm in major diameter and 22 mm in length. The effects of purchase length on the pull-out strength were different for different bone material. It is the bone material that determines the stability of the inserted surgical screw. The significance of the purchase length on the pull-out strength of cortical screw will be much lower than that in cancellous bone screw.

Finite element analysis of moment-rotation relationships for human cervical spine.

A comprehensive, geometrically accurate, nonlinear C0-C7 FE model of head and cervical spine based on the actual geometry of a human cadaver specimen was developed. The motions of each cervical vertebral level under pure moment loading of 1.0 Nm applied incrementally on the skull to simulate the movements of the head and cervical spine under flexion, tension, axial rotation and lateral bending with the inferior surface of the C7 vertebral body fully constrained were analysed. The predicted range of motion (ROM) for each motion segment were computed and compared with published experimental data. The model predicted the nonlinear moment-rotation relationship of human cervical spine. Under the same loading magnitude, the model predicted the largest rotation in extension, followed by flexion and axial rotation, and least ROM in lateral bending. The upper cervical spines are more flexible than the lower cervical levels. The motions of the two uppermost motion segments account for half (or even higher) of the whole cervical spine motion under rotational loadings. The differences in the ROMs among the lower cervical spines (C3-C7) were relatively small. The FE predicted segmental motions effectively reflect the behavior of human cervical spine and were in agreement with the experimental data. The C0-C7 FE model offers potentials for biomedical and injury studies.