Dynamics of the head-neck complex in response to the trunk horizontal vibration: modeling and identification

Although many studies exist concerning the influence of seat vibration on the head in the seated human body, the dynamic response of the head-neck complex (HNC) to the trunk vibration has not been well investigated. Little quantitative knowledge exists about viscoelastic parameters of the neck. In this study, the dynamics of the HNC is identified when it is exposed to the trunk horizontal (fore-and-aft) vibration. The frequency response functions between the HNC angular velocity and the trunk horizontal acceleration, corresponding to four volunteers, are obtained in the frequency range of 0.5 Hz to 10 Hz. A fourth-order mathematical model, derived by considering a double-inverted-pendulum model for the HNC, is designed to simulate the dynamic response of the HNC to the trunk horizontal vibration. The frequency domain identification method is used to determine the coefficients of the mathematical model of the HNC. Good agreement has been obtained between experimental and simulation results. This indicates that the system, similar to the designed fourth-order model, has mainly two resonance frequencies. The viscoelastic parameters of the neck, including the spring and damping coefficients, are then obtained by use of the optimization method.     

Trunk muscle electromyography and whole body vibration

By measuring the electromyographic (EMG) activity of the paraspinal muscles, we have estimated the average and peak-to-peak torque imposed on the spine during whole body vibration. Six subjects had surface electrodes placed on their erector spinae muscles at the L3 level. The EMG-torque relationship was estimated by having each subject perform isometric horizontal pulls in an upright seated posture. The subject was then vibrated vertically and sinusoidally in a controlled, flexed, slightly lordotic seated posture, in 1 Hz increments from 3 to 10 Hz at a 0.1 g RMS seat acceleration level. Between vibration readings taken at each frequency, a static reading was also taken with the subject maintaining the same posture. The entire vibration-static 3-10 Hz test was repeated for reliability purposes. Specialized digital signal processing techniques were developed for the EMG signals to enhance the measured cyclic muscle activity and to allow automatic measurement of the time relationship between the mechanical displacement and the estimated torque. We found significantly more average and peak-to-peak estimated torque at almost all frequencies for vibration vs static sitting.     

Effect of vibration magnitude, vibration spectrum and muscle tension on apparent mass and cross axis transfer functions during whole-body vibration exposure

Twelve seated male subjects were exposed to 15 vibration conditions to investigate the nature and mechanisms of the non-linearity in biomechanical response. Subjects were exposed to three groups of stimuli: Group A comprised three repeats of random vertical vibration at 0.5, 1.0 and 1.5 m s⁻² r.m.s. with subjects sitting in a relaxed upright posture. Group B used the same vibration stimuli as Group A, but with subjects sitting in a ‘tense’ posture. Group C used vibration where the vibration spectrum was dominated by either low-frequency motion (2–7 Hz), high-frequency motion (7–20 Hz) or a 1.0 m s⁻² r.m.s. sinusoid at the frequency of the second peak in apparent mass (about 10–14 Hz) added to 0.5 m s⁻² r.m.s. random vibration. In the relaxed posture, frequencies of the primary peak in apparent mass decreased with increased vibration magnitude. In the tense posture, the extent of the non-linearity was reduced. For the low-frequency dominated stimulus, the primary peak frequency was lower than that for the high-frequency dominated stimulus indicating that the frequency of the primary peak in the apparent mass is dominated by the magnitude of the vibration encompassing the peak. Cross-axis transfer functions showed peaks of about 15–20% and 5% of the magnitudes of the peaks in the apparent mass for x- and y-direction transfer functions, respectively, in the relaxed posture. In the tense posture, cross-axis transfer functions reduced in magnitude with increased vibration, likely indicating a reduced fore-aft pitching of the body with increased tension, supporting the hypothesis that pitching contributes to the non-linearity in apparent mass.     

Frequency response of Pinus Pinea L. for selective cone harvesting by vibration

The stone pine (Pinus pinea L.) is exploited for wood production and its edible kernels. Cones take 3 years to mature, while other newer cones are growing on the tree. Currently, mechanical cone harvesting by tree vibration drives the profitability and development of this crop in forest ecosystems. However, the adaptation of vibration parameters is necessary to avoid damage to the tree and for the implementation of good harvesting practices. Direct measurements of acceleration transmissibility along fruit-bearing branches under controlled laboratory conditions showed that vibrations in the frequency range of 18.0 ± 5.3 Hz were capable of producing resonance phenomena in mature cones. Morphological changes produced in the mature cones, especially in the stalk and total weight, amplified the acceleration transmissibility, providing more favourable conditions for fruit detachment. Field tests with stone pines and a trunk shaker confirmed the potential of selective mechanical harvesting, which is conditional on the vibration parameters applied. The frequency range of the resonance of the mature cone proved to be suitable for vibration of the tree at its trunk. The quality and efficiency of the mechanical harvesting were determined to be inversely related parameters during harvesting by vibration. Trunk vibration at a frequency of 18 Hz and approximate acceleration of 65 m/s² achieved a high harvest quality, with limited detachment of shoots and unripe cones, and a harvesting efficiency near 85%.     

Neuromuscular response of the trunk to inertial based sudden perturbations following whole body vibration exposure

The effects of whole body vibration exposure on the neuromuscular responses following inertial-based trunk perturbations were examined. Kinematic and surface EMG (sEMG) data were collected while subjects were securely seated on a robotic platform. Participants were either exposed to 10 min of vibration or not, which was followed by sudden inertial trunk perturbations with and without timing and direction knowledge. Amplitude of sEMG was analyzed for data collected during the vibration protocol, whereas the onset of sEMG activity and lumbar spine angle were analyzed for the perturbation protocol. Data from the vibration protocol did not show a difference in amplitude of sEMG for participants exposed to vibration and those not. The perturbation protocol data showed that those not exposed to vibration had a 14% faster muscle onset, despite data showing no difference in fatigue level.     

The mechanical role of the trunk and lower extremities in a seated weight-moving task in the sagittal plane

A two-dimensional, sagittally-symmetric biomechanical model was developed to analyze the joint moments required to stabilize the trunk in a seated, dynamic, weight-moving task. Kinematic and reaction force data were measured while subjects moved a hand-held weight (0-4 kgf) at shoulder level to and fro at 1 Hz. These data were then used for model input and validation purposes. A second, simpler model was used to simulate how joint loads varied with weight held, trunk inclination, and movement frequency. The results for this seated task demonstrate a) significant trunk, hip, knee, and ankle joint moments (37, 13, 4, 13 percent of maximum strength values, respectively) were required, b) considerable intersubject differences in mean joint moments (more than 66 percent) were found, which primarily were due to subtle differences in body segment kinematics and lower extremities use, and c) the important role of the lower extremities in stabilizing the trunk in the seated posture.     

Reliability of assessing postural control during seated balancing using a physical human-robot interaction

This study evaluated the within- and between-visit reliability of a seated balance test for quantifying trunk motor control using input–output data. Thirty healthy subjects performed a seated balance test under three conditions: eyes open (EO), eyes closed (EC), and eyes closed with vibration to the lumbar muscles (VIB). Each subject performed three trials of each condition on three different visits. The seated balance test utilized a torque-controlled robotic seat, which together with a sitting subject resulted in a physical human-robot interaction (pHRI) (two degrees-of-freedom with upper and lower body rotations). Subjects balanced the pHRI by controlling trunk rotation in response to pseudorandom torque perturbations applied to the seat in the coronal plane. Performance error was expressed as the root mean square (RMSE) of deviations from the upright position in the time domain and as the mean bandpass signal energy (E_mb) in the frequency domain. Intra-class correlation coefficients (ICC) quantified the between-visit reliability of both RMSE and E_mb. The empirical transfer function estimates (ETFE) from the perturbation input to each of the two rotational outputs were calculated. Coefficients of multiple correlation (CMC) quantified the within- and between-visit reliability of the averaged ETFE. ICCs of RMSE and E_mb for all conditions were ≥0.84. The mean within- and between-visit CMCs were all ≥0.96 for the lower body rotation and ≥0.89 for the upper body rotation. Therefore, our seated balance test consisting of pHRI to assess coronal plane trunk motor control is reliable.     

The apparent mass of the seated human body: vertical vibration

Apparent mass frequency response functions of the seated human body have been measured with random vibration in the vertical direction at frequencies up to 20 Hz. A group of eight subjects was used to investigate some factors (footrest, backrest, posture, muscle tension, vibration magnitude) that may affect the apparent mass of a person; a group of 60 subjects (24 men, 24 women and 12 children) was used to investigate variability between people. Relative movement between the feet and the seat was found to affect the apparent mass at frequencies below resonance, particularly near zero-frequency. The resonance frequency generally increased with the use of a back rest, an erect posture and, in particular, increased muscle tension; but there was considerable intersubject variability in the changes. The magnitude of the vibration had a consistent effect: the resonance frequency decreased from about 6 to 4 Hz when the magnitude of the vibration was increased from 0.25 to 2.0 ms-2 r.m.s. The apparent masses of all the subjects were remarkably similar when normalized with respect to sitting weight. However, there were statistically significant correlations between apparent mass and some body characteristics (such as weight and age).     

Non-linear characteristics in the dynamic responses of seated subjects exposed to vertical whole-body vibration

The effect of the magnitude of vertical vibration on the dynamic response of the seated human body has been investigated. Eight male subjects were exposed to random vibration in the 0.5 to 20 Hz frequency range at five magnitudes: 0.125, 0.25, 0.5, 1.0 and 2.0 ms(-2) r.m.s. The dynamic responses of the body were measured at eight locations: at the first, fifth, and tenth thoracic vertebrae (T1, T5, T10), at the first, third, and fifth lumbar vertebrae (L1, L3, L5) and at the pelvis (the posterior-superior iliac spine). At each location, the motions on the body surface were measured in the three orthogonal axes within the sagittal plane (i.e., the vertical, fore-and-aft, and pitch axes). The force at the seat surface was also measured. Frequency response functions (i.e., transmissibilities and apparent mass) were used to represent the responses of the body. Non-linear characteristics were observed in the apparent mass and in the transmissibilities to most measurement locations. Resonance frequencies in the frequency response functions decreased with increases in the vibration magnitude (e.g. for the vertical transmissibility to L3, a reduction from 6.25 to 4.75 Hz when the vibration magnitude increased from 0.125 to 2.0 ms(-2) r.m.s.). The transmission of vibration within the spine also showed some evidence of a non-linear characteristic. It can be concluded from this study that the dynamic responses of seated subjects are clearly non-linear with respect to vibration magnitude, whereas previous studies have reported inconsistent conclusions. More understanding of the dependence on vibration magnitude of both the dynamic responses of the soft tissues of the body and the muscle activity (voluntary and involuntary) is required to identify the causes of the non-linear characteristics observed in this study.     

The apparent mass of the human body exposed to non-orthogonal horizontal vibration

Apparent masses of 15 male and 15 female subjects have been measured during exposure to various directions of horizontal vibration. Twenty vibration conditions were used in the experiment. In each of five directions (0, 22.5, 45, 67.5 and 90° to the mid-sagittal plane) subjects were exposed to random vibration in the frequency range of 1.5–20 Hz at 0.25, 0.5 and 1.0 m s⁻² r.m.s. The five remaining conditions were selected to give measurements whereby the magnitude of the x-component of the vibration was fixed and the y-component changed and vice-versa. Two peaks were observed in the apparent masses. The first peak occurred at about 3 Hz and reduced in frequency with increases in vibration magnitude. The frequency of the first peak also reduced as the direction of vibration changed from 0 to 90°. The magnitude of the peak increased as the vibration magnitude and direction increased. The second peak occurred at about 5 Hz and decreased in both frequency and magnitude with increases in vibration magnitude. There was no change in the frequency of the second peak with vibration direction, although the magnitude of the peak decreased as the angle of vibration to the mid-sagittal plane increased. Increasing the magnitude of the x-component of vibration whilst using a fixed y-component changed the magnitude of the first peak but did not change the frequency of the first or any characteristics of the second peak. In contrast, increasing the y-component of vibration whilst using a fixed x-component changed the frequencies and magnitudes of both peaks. Predictions of the response at 45° by applying the principle of superposition to data measured at 0 and 90° showed that the response of the body with direction was not linear. This implies that the apparent mass in non-orthogonal axes cannot be predicted from the apparent masses measured in orthogonal directions.     

Dynamic head-neck stabilization and modulation with perturbation bandwidth investigated using a multisegment neuromuscular model

The human head-neck system requires continuous stabilization in the presence of gravity and trunk motion. We investigated contributions of the vestibulocollic reflex (VCR), the cervicocollic reflex (CCR), and neck muscle co-contraction to head-in-space and head-on-trunk stabilization, and investigated modulation of the stabilization strategy with the frequency content of trunk perturbations and the presence of visual feedback.We developed a multisegment cervical spine model where reflex gains (VCR and CCR) and neck muscle co-contraction were estimated by fitting the model to the response of young healthy subjects, seated and exposed to anterior-posterior trunk motion, with frequency content from 0.3 up to 1, 2, 4 and 8 Hz, with and without visual feedback.The VCR contributed to head-in-space stabilization with a strong reduction of head rotation (<8 Hz) and a moderate reduction of head translation (>1 Hz). The CCR contributed to head-on-trunk stabilization with a reduction of head rotation and head translation relative to the trunk (<2 Hz). The CCR also proved essential to stabilize the individual intervertebral joints and prevent neck buckling. Co-contraction was estimated to be of minor relevance. Control strategies employed during low bandwidth perturbations most effectively reduced head rotation and head relative displacement up to 3 Hz while control strategies employed during high bandwidth perturbations reduced head global translation between 1 and 4 Hz. This indicates a shift from minimizing head-on-trunk rotation and translation during low bandwidth perturbations to minimizing head-in-space translation during high bandwidth perturbations. Presence of visual feedback had limited effects suggesting increased usage of vestibular feedback.     

Dynamic analysis of olive trees in intensive orchards under forced vibration

The mechanical harvesting of fruit for oil production in an intensive olive tree orchard is generally accomplished by applying vibration to the tree’s trunk. This vibration is consequently transmitted to the branches, causing the fruit to detach. Although this practice is commonly used, the effects on tree behavior under forced vibration are not firmly established. Dynamic analysis was performed on 17 olive trees (Olea europaea L.) growing in an intensively-managed orchard using modal testing techniques. Modal parameter identification was focused inside the range excitation frequency used by the most commonly available trunk shakers on the market. The olive trees featuring a low morphological variability and modal parameters were obtained for a representative olive tree. The first two modes of vibration of the main tree frame were identified with damping ratios of 26.9 and 17.1% and natural frequencies of 20.2 and 37.7 Hz, respectively. A third mode of vibration of less importance was found at a higher frequency. Therefore, many local modes of vibration were detected near these natural frequencies, primarily located on secondary branches. During the testing, the olive trees behaved like a damped harmonic oscillator with predominantly mass damping in these modes.     

Experimental model for stimulation of cultured human osteoblast-like cells by high frequency vibration

Reliable and reproducible experimental methods for studying enhancement of osteoblast proliferation and metabolic activity in vitro provide invaluable tools for the research of biochemical processes involved in bone turnover in vivo. Some of the current methods used for this purpose are based on the ability of the osteoblasts to react metabolically to mechanical stimulation. These methods are based on the hypothesis that intracellular metabolic pathways could be influenced by the excitation of cytoskeletal components by mechanical cell deformation. Based on the same assumptions we developed a new experimental approach of biomechanical stimulation of cultured osteoblast-like cells by vibration. This method is based on the use of a specially designed vibration device that consists of an electric shaker with horizontally mounted well plate containing cell cultures. We used a first passage explant outgrowth of human osteoblast-like cell cultures, originating from samples of cancelous bone, collected from femoral necks of six donors during surgical arthroplasties of osteoarthritic hips. Well plates with replicates of cultured cells were exposed to a sine shaped vibration protocol in a frequency range of 20–60 Hz with displacement amplitude of 25 (±5) μm. We found that vibration at a distinct set of mechanical parameters of 20 Hz frequency and peak to peak acceleration of 0.5 ± 0.1 m/sec² is optimal for cell proliferation, and at 60 Hz frequency with peak to peak acceleration of 1.3 ± 0.1 m/sec² for metabolic activity. The presented easily reproducible experimental model should improve and simplify further research on the interactions between mechanical stimuli and intracellular biochemical pathways in osteoblasts. This revised version was published online in September 2006 with corrections to the Cover Date.     

An active head-neck model in whole-body vibration: vibration magnitude and softening

An active head-neck model is introduced in this work to predict human-dynamic response to different vibration magnitudes during fore-aft whole-body vibration. The proposed model is a rigid-link dynamic system augmented with passive spring-damper tissue-like elements and additional active dampers that resemble the active part of the muscles. The additional active dampers are functions of the input displacement, velocity, and acceleration and are based on active control theories and a kd-tree data-searching scheme. Five human subjects exposed to random fore-aft vibration with frequency content of 0.5-10 Hz were tested under different vibration with magnitudes of 0.46 m/s(2), 1.32 m/s(2), and 1.66 m/s(2) rms. The results showed that the proposed model was able to reasonably capture the softening characteristics of the human head-neck response during fore-aft whole-body vibration of different magnitudes.     

Direction-dependent neck and trunk postural reactions during sitting

Postural reactions in healthy individuals in the seated position have previously been described and have been shown to depend on the direction of the perturbation; however the neck response following forward and backward translations has not been compared. The overall objective of the present study was to compare neck and trunk kinematic, kinetic and electromyographic (EMG) stabilization patterns of seated healthy individuals to forward and backward translations. Ten healthy individuals, seated on a chair fixed onto a movable platform, were exposed to forward and backward translations (distance = 0.15 m, peak acceleration = 1.2 m/s²). The head and trunk kinematics as well as the EMG activity of 16 neck and trunk muscles were recorded. Neck and trunk angular displacements were computed in the sagittal plane. The centers of mass (COMs) of the head (HEAD), upper thorax (UPTX), lower thorax (LOWTX) and abdomen (ABDO) segments were also computed. Moments of force at the C7-T1 and L5-S1 levels were calculated using a top-down, inverse dynamics approach. Forward translations provoked greater overall COM peak displacements. The first peak of moment of force was also reached earlier following forward translations which may have played a role in preventing the trunk from leaning backwards. These responses can be explained by the higher postural threat imposed by a forward translation.     

Experimental Evidence of the Tonic Vibration Reflex during Whole-Body Vibration of the Loaded and Unloaded Leg

Increased muscle activation during whole-body vibration (WBV) is mainly ascribed to a complex spinal and supraspinal neurophysiological mechanism termed the tonic vibration reflex (TVR). However, TVR has not been experimentally demonstrated during low-frequency WBV, therefore this investigation aimed to determine the expression of TVR during WBV.  Whilst seated, eight healthy males were exposed to either vertical WBV applied to the leg via the plantar-surface of the foot, or Achilles tendon vibration (ATV) at 25Hz and 50Hzfor 70s. Ankle plantar-flexion force, tri-axial accelerations at the shank and vibration source, and surface EMG activity of m. soleus (SOL) and m. tibialis anterior (TA) were recorded from the unloaded and passively loaded leg to simulate body mass supported during standing.  Plantar flexion force was similarly augmented by WBV and ATV and increased over time in a load- and frequency dependent fashion. SOL and TA EMG amplitudes increased over time in all conditions independently of vibration mode. 50Hz WBV and ATV resulted in greater muscle activation than 25Hz in SOL when the shank was loaded and in TA when the shank was unloaded despite the greater transmission of vertical acceleration from source to shank with 25Hz and WBV, especially during loading. Low-amplitude WBV of the unloaded and passively loaded leg produced slow tonic muscle contraction and plantar-flexion force increase of similar magnitudes to those induced by Achilles tendon vibration at the same frequencies. This study provides the first experimental evidence supporting the TVR as a plausible mechanism underlying the neuromuscular response to whole-body vibration.     

Combined effects of vibration and noise on palmar sweating in healthy subjects

The combined effects of vibration and noise on palmar sweating were studied experimentally in healthy subjects. Ten subjects were exposed to vibration at an acceleration of 100 m.sec-2 root mean square at a frequency of 125 Hz, a noise level of 105 dB(A) at a frequency of 1000 Hz and both stimuli together. Vibration was applied to the right hand and noise to both ears from headphones. Palmar sweating was measured by the ventilated capsule method. Vibration caused a marked increase in palmar sweating of the right hand directly exposed to vibration and also of the left hand not exposed to vibration. Simultaneous vibration and noise caused a greater increase in palmar sweating than by each of the factors separately. The combined effects tended to be greater in subjects who were more susceptible to vibration or noise.     

Non-linearities in apparent mass and transmissibility during exposure to whole-body vertical vibration

The causes of low back pain associated with prolonged exposure to whole-body vibration are not understood. An understanding of non-linearities in the biomechanical responses is required to identify the mechanisms responsible for the dynamic characteristics of the body, to allow for the non-linearities when predicting the influence of seating dynamics, and to predict the adverse effects caused by various magnitudes of vibration. Twelve subjects were exposed to six magnitudes, 0.25-2.5ms(-2) rms, of vertical random vibration in the frequency range 0.2-20Hz. The apparent masses of the subjects were determined together with transmissibilities measured from the seat to various locations on the body surface: the upper and lower abdominal wall, at L3, over the posterior superior iliac spine and the iliac crest. There were significant reductions in resonance frequencies for both the apparent mass and the transmissibilities to the lower abdomen with increases in vibration magnitude. The apparent mass resonance frequency reduced from 5.4-4. 2Hz as the magnitude of the vibration increased from 0.25-2.5ms(-2) rms. Vertical motion of the lumbar spine and pelvis showed resonances at about 4Hz and between 8 and 10Hz. When exposed to vertical vibration, the human body shows appreciable non-linearities in its biodynamic responses. Biodynamic models should be developed to reflect the non-linearity.     

Dynamic forces over the interface between a seated human body and a rigid seat during vertical whole-body vibration

Biodynamic responses of the seated human body are usually measured and modelled assuming a single point of vibration excitation. With vertical vibration excitation, this study investigated how forces are distributed over the body-seat interface. Vertical and fore-and-aft forces were measured beneath the ischial tuberosities, middle thighs, and front thighs of 14 subjects sitting on a rigid flat seat in three postures with different thigh contact while exposed to random vertical vibration at three magnitudes. Measures of apparent mass were calculated from transfer functions between the vertical acceleration of the seat and the vertical or fore-and-aft forces measured at the three locations, and the sum of these forces. When sitting normally or sitting with a high footrest, vertical forces at the ischial tuberosities dominated the vertical apparent mass. With feet unsupported to give increased thigh contact, vertical forces at the front thighs were dominant around 8 Hz. Around 3–7 Hz, fore-and-aft forces at the middle thighs dominated the fore-and-aft cross-axis apparent mass. Around 8–10 Hz, fore-and-aft forces were dominant at the ischial tuberosities with feet supported but at the front thighs with feet unsupported. All apparent masses were nonlinear: as the vibration magnitude increased the resonance frequencies decreased. With feet unsupported, the nonlinearity in the apparent mass was greater at the front thighs than at the ischial tuberosities. It is concluded that when the thighs are supported on a seat it is not appropriate to assume the body has a single point of vibration excitation.     

Energy Expenditure and Substrate Oxidation in Response to Side-Alternating Whole Body Vibration across Three Commonly-Used Vibration Frequencies

MethodsEE and RQ were measured in 8 healthy young adults by indirect calorimetry at rest, and subsequently during side-alternating WBV at one of 3 VFs (30, 40, and 50 Hz). Each frequency was assessed over 5 cycles of intermittent WBV (30s vibration/30s rest), separated by 5 min seated rest. During the WBV participants stood on the platform with knees flexed sufficiently to maintain comfort, prevent transmission of vibration to the upper body, and minimise voluntary physical exertion. Repeatability was assessed across 3 separate days in a subset of 4 individuals. In order to assess any sequence/habituation effect, an additional group of 6 men underwent 5 cycles of intermittent WBV (30s vibration/30s rest) at 40 Hz, separated by 5 min seated rest.ResultsSide-alternating WBV increased EE relative to standing, non-vibration levels (+36%, p<0.001). However, no differences in EE were observed across VFs. Similarly, no effect of VF on RQ was found, nor did WBV alter RQ relative to standing without vibration.ConclusionNo relationship could be demonstrated between EE and VF in the range of 30-50Hz, and substrate oxidation did not change in response to WBV. Furthermore, the thermogenic effect of intermittent WBV, whilst robust, was quantitatively small (<2 METS).