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.

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.

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.

Analysis of tenodesis techniques for treatment of scapholunate instability using the finite element method.

Chronic scapholunate ligament (SL) injury is a common disorder affecting the wrist. Despite advances in surgical techniques used to treat this injury, SL gap re-emergence may occur postoperatively. This paper presents an investigation into the performance of the Corella, schapolunate axis (SLAM), and modified Brunelli tenodesis (MBT) surgical reconstruction techniques used to treat scapholunate instability. Finite element (FE) models were used to undertake virtual surgery, and the resulting scapholunate (SL) gap and angle obtained using the 3 techniques were compared. The Corella technique was found to achieve the SL gap and angle closest to the intact (ligament) wrist, restoring SL gap and angle to within 5.6% and 0.6%, respectively. The MBT method resulted in an SL gap least close to the intact. The results of our study indicate that the contribution of volar scapholunate interosseous ligament to scapholunate stability could be important.

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.

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.

Prediction of inter-segment stability and osteophyte formation on the multi-segment C2-C7 after unilateral and bilateral facetectomy.

The objective of this study was to determine the intersegment stability, disc degeneration, and osteophytes formation on the multisegment cervical spine (C2-C7) after unilateral and bilateral facetectomy. A geometrically accurate non-linear three-dimensional model of the intact human cervical spine was created from the digitized coordinates of the dry vertebrae. The intact model was validated against the published results under physiological loading conditions. Eight surgically altered models were created from the intact model. The intact and surgical altered models were subjected to physiological loading. The inclusion of five levels in the present model allowed accurate determination of the intersegment responses and internal cortical bone and disc annulus stress in the adjacent spinal components. Results indicated that facetectomy performed on C5-C6 significantly affects the corresponding stress and intersegment motions at the corresponding C5-C6 levels. The maximum increases were 18 per cent for bilateral facetectomy and 7 per cent for unilateral facetectomy under lateral bending. Combined flexion-extension and axial rotation caused an approximately similar amount of increases after total facetectomy. In addition, adjacent segments (C4-C5 and C6-7) also experience a slight increase in the intersegment responses and internal stress after facetectomy. It has been shown that facetectomy of greater than 50 per cent resulted in segment hypermobility and substantial increase in the disc annulus and cortical bone stress. Increase in the stress may lead to osteophytes formation. This study revealed important information that will help clinicians identify the critical intersegment stability and to decide on the amount of facets resection.

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.

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).

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.

Influence of cervical disc degeneration after posterior surgical techniques in combined flexion-extension--a nonlinear analytical study.

Laminectomy and facetectomy are surgical techniques used for decompression of the cervical spinal stenosis. Recent in vitro and finite element studies have shown significant cervical spinal instability after performing these surgical techniques. However, the influence of degenerated cervical disk on the biomechanical responses of the cervical spine after these surgical techniques remains unknown. Therefore, a three-dimensional nonlinear finite element model of the human cervical spine (C2-C7) was created. Two types of disk degeneration grades were simulated. For each grade of disk degeneration, the intact as well as the two surgically altered models simulating C5 laminectomy with or without C5-C6 total facetectomies were exercised under flexion and extension. Intersegmental rotational motions, internal disk annulus, cancellous and cortical bone stresses were obtained and compared to the normal intact model. Results showed that the cervical rotational motion decreases with progressive disk degeneration. Decreases in the rotational motion due to disk degeneration were accompanied by higher cancellous and cortical bone stress. The surgically altered model showed significant increases in the rotational motions after laminectomies and facetectomies when compared to the intact model. However, the percentage increases in the rotational motions after various surgical techniques were reduced with progressive disk degeneration.

Vibration characteristics of the human spine under axial cyclic loads: effect of frequency and damping.

STUDY DESIGN: A nonlinear finite element model of lumbar spine segment L3-L5 was developed. The effects of upper body mass, nucleus injury, damping, and different vibration frequency loads were analyzed for the whole body vibration. OBJECTIVES: To analyze the influence of whole body vibration on facets of lumbar spine and to analyze the influence of nucleus injury, upper body mass, and damping on the dynamic characteristics of lumbar spine. SUMMARY OF BACKGROUND DATA: Many studies have investigated whole body vibration for lumbar spine. However, very few investigations analyzed the influence of whole body vibration on facets and vibration characteristics of the injured spine. METHODS: The nonlinear finite element model of the L3-L5 segment was constructed based on the embalmed vertebra geometry and validated. Besides static and modal analyses, transient dynamic analyses were also conducted on the model with an upper body mass under damping and different frequency cyclic loads. RESULTS: In the period of human spine vibration, the vibration effects of different regions of the lumbar spine are not the same. Anterior regions of the L3-L5 segment show small vibration amplitudes, but posterior regions show large amplitudes. The vibration amplitude of facet contact force is more than 2.0-fold as large as that of displacement and stress on vertebrae or discs. To decrease the weight of the upper body will increase the resonant frequency. To remove the nucleus will decrease the resonant frequencies. The vibration displacement, stress, and facet contact force will reduce generally by 50% using damping ratio 0.08. CONCLUSIONS: The posterior regions of intervertebral discs of the lumbar spine are easy to injure during long-term whole body vibration compared to anterior regions. The vibration of human spine is more dangerous to facets, especially during whole body vibration approximating a sympathetic vibration, which may lead to abnormal remodeling and disorder of the lumbar spine.