Vibration modes of injured spine at resonant frequencies under vertical vibration

The porous cantilever beam as a model for spinal implants: Experimental, analytical and finite element analysis of dynamic properties

Investigation of the dynamic properties of implants is essential to ensure safety and compatibility with the host's natural spinal tissue. This paper presents a simplified model of a cantilever beam to investigate the effects of holes/pores on the structures. Free vibration test is one of the most effective methods to measure the dynamic response of a cantilever beam, such as natural frequency and damping ratio. In this study, the natural frequencies of cantilever beams made of polycarbonate (PC) containing various circular open holes were investigated numerically, analytically, and experimentally. The experimental data confirmed the accuracy of the natural frequencies of the cantilever beam with open holes calculated by finite element and analytical models. In addition, two finite element simulation methods, the dynamic explicit and modal dynamic methods, were applied to determine the damping ratios of cantilever beams with open holes. Finite element analysis accurately simulated the damped vibration behavior of cantilever beams with open holes when known material damping properties were applied. The damping behavior of cantilever beams with random pores was simulated, highlighting a completely different relationship between porosity, natural frequency and damping response. The latter highlights the potential of finite element methods to analyze the dynamic response of arbitrary and complex structures, towards improved implant design.

Study on the process of intervertebral disc disease by the theory of continuum damage mechanics

BACKGROUND

Recently, more and more people suffer from low back pain triggered by lumbar degenerative disc disease. The mechanical factor is one of the most significant causes of disc degeneration. This study aims to explore the biomechanical responses of the intervertebral disc, and investigate the process of disc injury by the theory of continuum damage mechanics.

METHODS

A finite element model of the L4-L5 lumbar spine was developed and validated. The model not only considered changes in permeability coefficient with strain, but also included physiological factors such as osmotic pressure. Three loading conditions were simulated: (A) static loads, (B) vibration loads, (C) injury process.

FINDINGS

The simulation results revealed that the facet joints shared massive stresses of the intervertebral discs, and prevented excessive lumbar spine movement. However, their asymmetrical position may have led to degeneration. The von Mises stress and pore pressure of annulus fibrosus showed significantly different trends under static loads and vibration loads. The von Mises stress of nucleus pulposus was not sensitive to vibration loads, but its pore pressure was conspicuously influenced by vibration loads. The injury first appeared at the posterior centre, and then, it gradually expanded along the edge of the intervertebral disc. With an increase in the loading steps, the damage rate of the intervertebral disc increased logarithmically.

INTERPRETATION

The variation in the biomechanical performance of the intervertebral disc could be attributed to the periodic movement of internal fluids. This study might be helpful for understanding the mechanism of intervertebral disc degeneration.

Finite element analysis of the lumbar spine in adolescent idiopathic scoliosis subjected to different loads

OBJECTIVE

To explore the biomechanical changes of the lumbar spine segment of idiopathic scoliosis under different loads by simulating six kinds of lumbar spine motions based on a three-dimensional finite element (FE) model. Methods According to the plain CT scan data of L1-L5 segment of an AIS patient, a three-dimensional FE model was established to simulate the biomechanics of lumbar scoliosis under different loads. The lumbar model was reconstructed using Mimics20.0, smoothed in Geomagic2013, assembled in Solidworks 2020, with FE analysis performed using Workbench19.0. Results The completed model had a total of 119029 C3D4 solid elements, 223805 nodes, including finely reconstructed tissue structures. In patients with AIS, the range of motion (ROM) is reduced under all loads. Under flexion loads, the vertebral concave stress distribution is greater; under extension lateral bending, and rotation load at the posterior side of the vertebral body, the stress is concentrated in the L3 vertebral arch. The buffering effect of intervertebral disc on the rotational load is the weakest. Different loads of AIS cause corresponding changes in the force and displacement of different positions of the vertebral body or intervertebral discs. Conclusions The change in physiological shape of the lumbar vertebrae limits the ROM of the lumbar vertebrae. The stress showed a trend of local concentration which located in the concave side of the scoliosis. The stress on the lumbar vertebrae comprising the greatest curvature is the most excessive. The stress in the intervertebral disc under the rotating load is greater than that under other kinds of loads, and the intervertebral disc is more likely to be injured because of the rotating load.

Finite element investigation on the dynamic mechanical properties of low-frequency vibrations on human L2-L3 spinal motion segments with different degrees of degeneration

Exposure to low-frequency vibration is harmful to human lumbar health. However, the dynamic mechanical properties of lumbar spines with varying degrees of degeneration during time-dependent vibration remain incompletely understood. In this study, four poroelastic finite element models of human L2-L3 spinal motion segments, including the non-degeneration and the mild, moderate, and serious degeneration, were established. One-hour low-frequency vibrations with different frequencies were applied. Then, the dynamic mechanical properties of different degenerated lumbar models under the same vibration and the same lumbar model under vibrations at different frequencies were investigated. The results indicated and implied that the negative influences of 1-h vibration on the dynamic mechanical properties of the non-degenerated and mildly degenerated models were similar, but became obvious for the moderately and seriously degenerated models with time. Therefore, the damage caused by low-frequency vibration on the degenerated spinal motion segments was more serious compared with that on the healthy one. Meanwhile, the dynamic mechanical properties of the same lumbar model under vibrations at different frequencies expressed the negligible differences when the vibration frequency was not close to the lumbar natural frequency. Thus, the effects of the 1-h vibrations at different frequencies on one spinal motion segment were similar. Vibration frequency sensitivity analysis on the dynamic characteristics of human L2-L3 spinal motion segments with different degrees of degeneration.

Presentation of an Approach on Determination of the Natural Frequency of Human Lumbar Spine Using Dynamic Finite Element Analysis

Occurring resonance may negatively affect the health of the human lumbar spine. Hence, vibration generated in working and living environments should be optimized to avoid resonance when identifying the natural frequency of the human lumbar spine. The range of the natural frequency of the human lumbar spine has been investigated, but its specific numerical value has not been determined yet. This study aimed at presenting an approach based on resonance for predicting the specific numerical value of the natural frequency of the human lumbar spine. The changes in the numerical fluctuation amplitudes and the cycles of lumbar mechanical parameters during resonance are greater than those during nonresonant vibration. Given that the range of the natural frequency has been identified, vibrations at different excitation frequencies within this range can be applied in a human lumbar finite element model for dynamic finite element analysis. When the excitation frequency is close to the natural frequency, resonance occurs, causing great changes in the numerical fluctuation amplitudes and the cycles of lumbar mechanical parameters. Therefore, the natural frequency of the lumbar finite element model could be back-calculated. Results showed that the natural frequency of the established model was 3.5 Hz. Meanwhile, the closer the excitation frequency was to the natural frequency, the greater the changes in the numerical fluctuation amplitudes and cycles in the parameters would be. This study presented an approach for predicting the specific numerical value of the natural frequency of the human lumbar spine. Identifying the natural frequency assists in finding preventive measures for lumbar injury caused by vibration and in designing the vibration source in working and living environments to avoid approximating to the natural frequency of the human lumbar spine.

The Use of Body Worn Sensors for Detecting the Vibrations Acting on the Lower Back in Alpine Ski Racing

This study explored the use of body worn sensors to evaluate the vibrations that act on the human body in alpine ski racing from a general and a back overuse injury prevention perspective. In the course of a biomechanical field experiment, six male European Cup-level athletes each performed two runs on a typical giant slalom (GS) and slalom (SL) course, resulting in a total of 192 analyzed turns. Three-dimensional accelerations were measured by six inertial measurement units placed on the right and left shanks, right and left thighs, sacrum, and sternum. Based on these data, power spectral density (PSD; i.e., the signal's power distribution over frequency) was determined for all segments analyzed. Additionally, as a measure expressing the severity of vibration exposure, root-mean-square (RMS) acceleration acting on the lower back was calculated based on the inertial acceleration along the sacrum's longitudinal axis. In both GS and SL skiing, the PSD values of the vibrations acting at the shank were found to be largest for frequencies below 30 Hz. While being transmitted through the body, these vibrations were successively attenuated by the knee and hip joint. At the lower back (i.e., sacrum sensor), PSD values were especially pronounced for frequencies between 4 and 10 Hz, whereas a corresponding comparison between GS and SL revealed higher PSD values and larger RMS values for GS. Because vibrations in this particular range (i.e., 4 to 10 Hz) include the spine's resonant frequency and are known to increase the risk of structural deteriorations/abnormalities of the spine, they may be considered potential components of mechanisms leading to overuse injuries of the back in alpine ski racing. Accordingly, any measure to control and/or reduce such skiing-related vibrations to a minimum should be recognized and applied. In this connection, wearable sensor technologies might help to better monitor and manage the overall back overuse-relevant vibration exposure of athletes in regular training and or competition settings in the near future.

The degenerative state of the intervertebral disk independently predicts the failure of human lumbar spine to high rate loading: an experimental study

BACKGROUND

In the elderly, 30%-50% of patients report a fall event to precede the onset of vertebral fractures. The dynamic characteristics of the spine determine the peak forces on the vertebrae in a fall. However, we know little about the effect of intervertebral disk degeneration on the failure of human spines under the high loading rates associated with such falls. We hypothesized that MR estimates of disk hydration and viscoelastic properties will provide better estimates of failure strength than bone density alone.

METHODS

Seventeen L1-L3 human spine segments were imaged (magnetic resonance imaging, dual-energy X-ray absorptiometry), their dynamic responses quantified using pendulum based impact, and the spines tested to failure under high rate loading simulating a fall event. The spines' stiffness and damping constants were computed (Kelvin-Voigt model) with disk hydration and geometry assessed from T2 and proton density images.

FINDINGS

Under impact, the spines exhibited a second-order underdamped response with stiffness and damping ranging (17.9-754.5) kN/m and (133.6-905.3) Ns/m respectively. Damping, but not stiffness, was negatively correlated with higher ultimate strength (P<0.05). Higher bone mineral density and MR-estimated disk hydration correlated with higher ultimate strength (P<0.01 for both). No such correlations were observed for the T2 values. Adding disk hydration yielded a 20% increase in the model's association with failure load compared to bone density alone (MANOVA, P<0.001).

INTERPRETATION

The strong correlation between disk viscoelastic properties and MR-estimated hydration with the spine segments' ultimate strength clearly demonstrates the need to include disk degeneration as part of fracture risk assessment in the elderly spine.

Resonance in the mouse tibia as a predictor of frequencies and locations of loading-induced bone formation

To enhance new bone formation for the treating of patients with osteopenia and osteoporosis, various mechanical loading regimens have been developed. Although a wide spectrum of loading frequencies is proposed in those regimens, a potential linkage between loading frequencies and locations of loading-induced bone formation is not well understood. In this study, we addressed a question: Does mechanical resonance play a role in frequency-dependent bone formation? If so, can the locations of enhanced bone formation be predicted through the modes of vibration? Our hypothesis is that mechanical loads applied at a frequency near the resonant frequencies enhance bone formation, specifically in areas that experience high principal strains. To test the hypothesis, we conducted axial tibia loading using low, medium, or high frequency to the mouse tibia, as well as finite element analysis. The experimental data demonstrated dependence of the maximum bone formation on location and frequency of loading. Samples loaded with the low-frequency waveform exhibited peak enhancement of bone formation in the proximal tibia, while the high-frequency waveform offered the greatest enhancement in the midshaft and distal sections. Furthermore, the observed dependence on loading frequencies was correlated to the principal strains in the first five resonance modes at 8.0-42.9 Hz. Collectively, the results suggest that resonance is a contributor to the frequencies and locations of maximum bone formation. Further investigation of the observed effects of resonance may lead to the prescribing of personalized mechanical loading treatments.

Effect of the Degenerative State of the Intervertebral Disk on the Impact Characteristics of Human Spine Segments

Models of the dynamic response of the lumbar spine have been used to examine vertebral fractures (VFx) during falls and whole body vibration transmission in the occupational setting. Although understanding the viscoelastic stiffness or damping characteristics of the lumbar spine are necessary for modeling the dynamics of the spine, little is known about the effect of intervertebral disk degeneration on these characteristics at high loading rates. We hypothesize that disk degeneration significantly affects the viscoelastic response of spinal segments to high loading rate. We additionally hypothesize the lumbar spine stiffness and damping characteristics are a function of the degree of preload. A custom, pendulum impact tester was used to impact 19 L1-L3 human spine segments with an end mass of 20.9 kg under increasing preloads with the resulting force response measured. A Kelvin-Voigt model, fitted to the frequency and decay response of the post-impact oscillations was used to compute stiffness and damping constants. The spine segments exhibited a second-order, under-damped response with stiffness and damping values of 17.9-754.5 kN/m and 133.6-905.3 Ns/m respectively. Regression models demonstrated that stiffness, but not damping, significantly correlated with preload (p < 0.001). Degenerative disk disease, reflected as reduction in magnetic resonance T2 relaxation time, was weakly correlated with change in stiffness at low preloads. This study highlights the need to incorporate the observed non-linear increase in stiffness of the spine under high loading rates in dynamic models of spine investigating the effects of a fall on VFx and those investigating the response of the spine to vibration.

Is vibration truly an injurious stimulus in the human spine?

Epidemiological data at one time was taken to suggest that chronic vibrations--for example operating vehicles with low-quality seats--contributed to intervertebral disc degeneration and lower back pain. More recent discussions, based in part upon extended twin studies, have cast doubt upon this interpretation, and question how much of the vibration is actually transmitted to the spine during loading. This review summarizes our recent survey of the current state of knowledge. In particular, we note that current studies are lacking a detailed factorial exploration of frequency, amplitude, and duration; this may be the primary cause for inconclusive and/or contradictory studies. It is our conclusion that vibrations are still an important consideration in discogenic back pain, and further controlled studies are warranted to definitively examine the underlying hypothesis: that chronic vibration can influence IVD cell biology and tissue mechanics.