Muscle activity damps the soft tissue resonance that occurs in response to pulsed and continuous vibrations.

This study tested the hypotheses that when the excitation frequency of mechanical stimuli to the foot was close to the natural frequency of the soft tissues of the lower extremity, the muscle activity increases 1) the natural frequency and 2) the damping to minimize resonance. Soft tissue vibrations were measured with triaxial accelerometers, and muscle activity was measured by using surface electromyography from the quadriceps, hamstrings, tibialis anterior, and triceps surae groups from 20 subjects. Subjects were presented vibrations while standing on a vibrating platform. Both continuous vibrations and pulsed bursts of vibrations were presented, across the frequency range of 10-65 Hz. Elevated muscle activity and increased damping of vibration power occurred when the frequency of the input was close to the natural frequency of each soft tissue. However, the natural frequency of the soft tissues did not change in a manner that correlated with the frequency of the input. It is suggested that soft tissue damping may be the mechanism by which resonance is minimized at heel strike during running.     

Modification of soft tissue vibrations in the leg by muscular activity.

Vibration characteristics were recorded for the soft tissues of the triceps surae, tibialis anterior, and quadriceps muscles. The frequency and damping of free vibrations in these tissues were measured while isometric and isotonic contractions of the leg were performed. Soft tissue vibration frequency and damping increased with both the force produced by and the shortening velocity of the underlying muscle. Both frequency and damping were greater in a direction normal to the skin surface than in a direction parallel to the major axis of each leg segment. Vibration characteristics further changed with the muscle length and between the individuals tested. The range of the measured vibration frequencies coincided with typical frequencies of impact forces during running. However, observations suggest that soft tissue vibrations are minimal during running. These results support the strategy that increases in muscular activity may be used by some individuals to move the frequency and damping characteristics of the soft tissues away from those of the impact force and thus minimize vibrations during walking and running.     

Changes in muscle activity in response to different impact forces affect soft tissue compartment mechanical properties

Electromyographic (EMG) activity is associated with several tasks prior to landing in walking and running including positioning the leg, developing joint stiffness and possibly control of soft tissue compartment vibrations. The concept of muscle tuning suggests one reason for changes in muscle activity pattern in response to small changes in impact conditions, if the frequency content of the impact is close to the natural frequency of the soft tissue compartments, is to minimize the magnitude of soft tissue compartment vibrations. The mechanical properties of the soft tissue compartments depend in part on muscle activations and thus it was hypothesized that changes in the muscle activation pattern associated with different impact conditions would result in a change in the acceleration transmissibility to the soft tissue compartments. A pendulum apparatus was used to systematically administer impacts to the heel of shod male participants. Wall reaction forces, EMG of selected leg muscles, soft tissue compartment and shoe heel cup accelerations were quantified for two different impact conditions. The transmissibility of the impact acceleration to the soft tissue compartments was determined for each subject/soft tissue compartment/shoe combination. For this controlled impact situation it was shown that changes in the damping properties of the soft tissue compartments were related to changes in the EMG intensity and/or mean frequency of related muscles in response to a change in the impact interface conditions. These results provide support for the muscle tuning idea--that one reason for the changes in muscle activity in response to small changes in the impact conditions may be to minimize vibrations of the soft tissue compartments that are initiated at heel-strike.     

Muscle tuning during running: implications of an un-tuned landing

BACKGROUND: The impact force in heel-toe running is an input signal into the body that initiates vibrations of the soft tissue compartments of the leg. These vibrations are heavily damped and the paradigm of muscle tuning suggests the body adapts to different input signals to minimize these vibrations. The objectives of the present study were to investigate the implications of not tuning a muscle properly for a landing with a frequency close to the resonance frequency of a soft tissue compartment and to look at the effect of an unexpected surface change on the subsequent step of running. METHOD: Thirteen male runners were recruited and performed heel-toe running over two surface conditions. The peak accelerations and biodynamic responses of the soft tissue compartments of the leg along with the EMG activity of related muscles were determined for expected soft, unexpected hard and expected hard landings. RESULTS AND CONCLUSIONS: For the unexpected hard landing there was a change in the input frequency of the impact force, shifting it closer to the resonance frequency of the soft tissue compartments. For the unexpected landing there was no muscle adaptation, as subjects did not know the running surface was going to change. In support of the muscle-tuning concept an increase in the soft tissue acceleration did occur. This increase was greater when the proximity of the input signal frequency was closer to the resonance frequency of the soft tissue compartment. Following the unexpected change in the input signal a change in pre-contact muscle activity to minimize soft tissue compartment vibrations was not found. This suggests if muscle tuning does occur it is not a continuous feedback response that occurs with every small change in the landing surface properties. In previous studies with significant adaptation periods to new input signals significant correlations between the changes in the input signal frequency and the EMG intensity have been shown, however, changes in soft tissue accelerations have not been found. The results of the present study showed that changes in these soft tissue accelerations can occur in response to a resonance frequency input signal when a muscle reaction has not happened.     

Tissue vibration in prolonged running

The impact force in heel–toe running initiates vibrations of soft-tissue compartments of the leg that are heavily dampened by muscle activity. This study investigated if the damping and frequency of these soft-tissue vibrations are affected by fatigue, which was categorized by the time into an exhaustive exercise. The hypotheses were tested that (H1) the vibration intensity of the triceps surae increases with increasing fatigue and (H2) the vibration frequency of the triceps surae decreases with increasing fatigue. Tissue vibrations of the triceps surae were measured with tri-axial accelerometers in 10 subjects during a run towards exhaustion. The frequency content was quantified with power spectra and wavelet analysis. Maxima of local vibration intensities were compared between the non-fatigued and fatigued states of all subjects. In axial (i.e. parallel to the tibia) and medio-lateral direction, most local maxima increased with fatigue (supporting the first hypothesis). In anterior–posterior direction no systematic changes were found. Vibration frequency was minimally affected by fatigue and frequency changes did not occur systematically, which requires the rejection of the second hypothesis. Relative to heel-strike, the maximum vibration intensity occurred significantly later in the fatigued condition in all three directions. With fatigue, the soft tissue of the triceps surae oscillated for an extended duration at increased vibration magnitudes, possibly due to the effects of fatigue on type II muscle fibers. Thus, the protective mechanism of muscle tuning seems to be reduced in a fatigued muscle and the risk of potential harm to the tissue may increase.     

Quantification of the input signal for soft tissue vibration during running

Soft tissue compartment vibrations are initiated at heel-strike in heel-toe running. The concept of muscle tuning suggests that the body tries to minimize these vibrations with a muscle adaptation that changes the mechanical properties of the soft tissue compartment. A muscle tuning adaptation can be quantified by determining the biodynamic response, of the soft tissue compartment for different experimental conditions. To determine the biodynamic response a measure of both the input signal and the soft tissue compartment vibrations are required. The input signal for the vibrations is the rapid deceleration of the leg after initial ground contact. The aim of this study was to evaluate three non-invasive methods to quantify the input signal for the triceps surae soft tissue vibrations. Data from a force platform, a shoe mounted accelerometer and a video analysis of a reflective skin marker were used to quantify leg deceleration. Both the shoe mounted accelerometer and skin marker method provided a satisfactory evaluation of the input signal and could be used to determine the biodynamic response of the soft tissue compartment. The impact portion of the ground reaction force is primarily due to the deceleration of the leg at landing. However, due to the influence of the effective body mass on the impact magnitude, the force plate data was not appropriate for quantifying a muscle tuning response.     

Effect of rocker shoes and running speed on lower limb mechanics and soft tissue vibrations

Previous studies have shown a possible effect of running speed and the sole material of footwear on lower-limb mechanics and soft tissue vibrations, while little information has been offered concerning the influence of the shape of the footwear’s sole. The purpose of this study is to assess the effect of running speed and rocker shoes on muscular activity, ground reaction force, and soft tissue vibrations. Twenty participants performed heel-toe running with two shoes, differentiated only by their sole shape (i.e. rocker and non-rocker), at four running speeds. Ground reaction force and electromyograms of the gastrocnemius medialis and vastus lateralis were measured, and soft tissue accelerations of the same muscles were recorded with tri-axial accelerometers. A continuous wavelet transform was applied to the accelerometer’s signals to analyse them in the time-frequency domain. The rocker of the shoes did not change the muscular activations, ground reaction force, nor power of soft tissue vibrations. In opposite, increased running speed led to an augmentation of all of the measured parameters. Interestingly, running speed augmentation led to a greater increase in high frequencies component of soft tissue vibrations (25–50 Hz, 242%) than lower ones (8–25 Hz, 111%). Consequently, we indicated a 10% increase in the relative part of the high frequencies of the total power. In conclusion, although rocker shoes have shown an effect on lower-limb kinetics in some studies, no influence on soft tissue vibration is denoted. By contrast, soft tissue vibrations may be modulated by changing running speed.     

Vibration settling time of the gastrocnemius remains constant during an exhaustive run in rear foot strike runners

In this study, vibrations of human gastrocnemius during an exhaustive run protocol are considered for analysis. Previous studies have shown increased vibration intensity and damping coefficient within the soft tissue with fatigue. The question of this study was to investigate if the vibration settling time remains constant during a prolonged running. Eleven semi-professional middle/long distance runners ran to exhaustion on a treadmill with their preferred constant speed (4.29 ± 0.33 m/s) for 3873 ± 1147 m. Vibration of the gastrocnemius lateralis, electrical activity of the tibialis anterior and the gastrocnemius medialis along with ground reaction force (GRF) were recorded. The results demonstrated significant increase in impact peak and loading rate, and the frequency content of the impact, with no significant change in active peak of the vertical GRF. Fatigue resulted in increased vibration intensity, damping coefficient, and energy dissipation of vibration with no change in vibration settling time. Furthermore, peak acceleration significantly linearly (R = 0.59) increased as a function of running time. The mean frequency of muscle activity of the gastrocnemius medialis and the intensity of muscle activity in TA significantly decreased. The results suggest that constant vibration settling time might either be an objective for muscle tuning which is more pronounced in fatigued state or a passive by-product of muscle function in running. Further studies are needed to address this point.     

Soft tissue vibrations within one soft tissue compartment

The concept of muscle tuning suggests that vibrations of the soft tissue compartments of the leg initiated by impacts are minimized by muscular activity prior to heel-strike of heel-toe running. For the quantification of muscle tuning it has been assumed (1) that the soft tissue compartment acts as one lumped mass and (2) that vibration energy dissipation does occur within one muscle. The purpose of this study was to test these two assumptions. It was hypothesized that (H1) the movement of the soft tissue compartment is not homogeneous, (H2) the vibration frequencies for different muscles within one soft tissue compartment are different and (3) attenuation of vibration movement within one muscle does occur. Soft tissue vibrations were measured using accelerometers on four locations on the quadriceps soft tissue compartment during heel-toe running. There were differences in the peak soft tissue acceleration and time of peak acceleration between accelerometer locations. The dominant frequency was similar throughout the soft tissue compartment, however; there was an attenuation of high-frequency vibration energy between distal and proximal points overlying one muscle. This evidence suggests that accelerometer placement is important when quantifying the acceleration magnitude and timing of peak soft tissue compartment but not when estimating the resonant vibration characteristics of a soft tissue compartment. It also provides initial evidence to support the idea that vibration control through muscle tuning may be achieved through changes in energy dissipating properties within the soft tissue compartment.     

Muscle activity reduces soft-tissue resonance at heel-strike during walking

Muscle activity has previously been suggested to minimize soft-tissue resonance which occurs at heel-strike during walking and running. If this concept were true then the greatest vibration damping would occur when the input force was closest to the resonant frequency of the soft-tissues at heel-strike. However, this idea has not been tested. The purpose of this study was to test whether muscle activity in the lower extremity is used to damp soft-tissue resonance which occurs at heel-strike during walking. Hard and soft shoe conditions were tested in a randomized block design. Ground reaction forces, soft-tissue accelerations and myoelectric activity were measured during walking for 40 subjects. Soft-tissue mass was estimated from anthropologic measurements, allowing inertial forces in the soft-tissues to be calculated. The force transfer from the ground to the tissues was compared with changes in the muscle activity. The soft condition resulted in relative frequencies (input/tissue) to be closer to resonance for the main soft-tissue groups. However, no increase in force transmission was observed. Therefore, the vibration damping in the tissues must have increased. This increase concurred with increases in the muscle activity for the biceps femoris and lateral gastrocnemius. The evidence supports the proposal that muscle activity damps soft-tissue resonance at heel-strike. Muscles generate forces which act across the joints and, therefore, shoe design may be used to modify muscle activity and thus joint loading during walking and running.     

Dynamic mechanical characteristics of intact and structurally modified bovine pericardial tissues

Bovine pericardium (BP) is a source of natural biomaterials with a wide range of clinical applications. In the present work we studied the dynamic mechanical behavior of BP in native form and under specific enzymatic degradation with chondroitinase ABC extracted a 17% of the total glycosaminoglycans (GAGs). The GAGs content of native BP was composed mainly from hyaluronan, chondroitine sulfate and dermatan sulfate. Dynamic tensile mechanical testing of BP in the frequency range 0.1-20 Hz demonstrated its viscoelastic nature. The storage modulus was equal to 6.5 (native) and 5.5 (degraded) MPa initially, increased in the region nearby 1 Hz by about 15%. This was related with physical resonance mechanisms activated in this frequency region. The high modulus (modulus of the high linear phase of stress-strain) was equal to 14 (native) and 10 (degraded) MPa, dropped at high frequencies to 7 and 5 Mpa, respectively. The damping, expressed by the hysteresis, was equal to 20% of the loading energy, changed exponentially with the frequency to 30% at 20 Hz. It seemed that of the elastic mechanical parameters, the storage modulus and the high modulus were even slightly dropped as a result of degradation. As a final conclusion, there was evident that GAGs may play a non-negligible role in the dynamic mechanical behavior of BP and, probably in other soft tissue biomechanics. It is suggested that the GAGs content may be considered during the design and chemical modification of biomaterials based on BP and other soft tissues.     

Assessment of tibial stiffness by vibration testing in situ--II. Influence of soft tissues, joints and fibula

The influence of soft tissues and joints on the vibration of the human tibia was examined by modal analysis on amputated lower limbs, where the soft tissues and the fibula were dissected gradually. Measurements were made in two different set ups, IFR and BRA, which were both designed to monitor fracture healing. In IFR, vibrations are generated by hammer impact on a relaxed hanging lower leg, with the knee flexed. Resonant frequencies are determined by a computer Fourier transform procedure. In BRA, a steady state vibration is induced in a lower leg, supported near the ankle and the tibial tuberosity, using an electromagnetic shaker. Resonant frequencies are determined from the maxima in vibration amplitudes. In both set ups the soft tissues have a similar influence on the vibration of the tibia: the skin hardly influences the determined modal parameter. The mass of the muscles influences both the resonant frequency and the damping. The fibula has a stiffening effect on the tibia. The influence of the joints is small in the IFR-set up: the tibia vibrates in conditions close to those for the free-free vibration. In the BRA-set up, the supports determine the boundary conditions.     

Theory of acoustic mode vibrations of DNA fibers

A previous model for acoustic mode vibrations of a DNA molecule in water is extended to the case of an array of many DNA molecules, as occurs in the fibers studied in most experimental work on DNA. The acoustic modes of this system are found to consist of coupled modes of water sound vibrations and DNA acoustic modes. This model is used to study the electrostatic coupling of acoustic vibrations to the relaxational modes of the orientational degrees of freedom of the water molecules. It is found that the long-range or macroscopic electric field generated by the acoustic mode vibrations of the water-DNA system gives too small a damping and frequency shift of the acoustic modes to account for the observations on DNA fibers. Therefore, the observed damping and frequency shifts are most likely due to either friction between the surrounding water and the vibrating DNA, or coupling to the water orientation degrees of freedom resulting from the short range (i.e., screened) Coulomb interaction. The latter explanation (which is most likely the correct one) implies that the relaxation time of the hydration shell water is longer than the observed relaxation time by a factor of the static dielectric constant of the hydration water.     

Frequency tuning in animal locomotion

In locomotion that involves repetitive motion of propulsive structures (arms, legs, fins, wings) there are resonant frequencies f(*) at which the energy consumption is a minimum. As animals need to change their speed, they can maintain this energy minimum by tuning their body resonances. We discuss the physical principles of frequency tuning, and how it relates to forces, damping, and oscillation amplitude. The resonant frequency of pendulum-type oscillators (e.g. swinging arms and legs) may be changed by varying the mass moment of inertia, or the vertical acceleration of the pendulum pivot. The frequency of elastic vibrations (e.g. the bell of a jellyfish) can be tuned with a non-linear modulus of elasticity: soft for low deflection amplitudes (low resonant frequency), and stiff for large displacements (high resonant frequency). Tuning of elastic oscillations can also be achieved by changing the effective length or cross-sectional area of the elastic members, or by allowing springs in parallel or in series to become active. We propose that swimming and flying animals generate oscillating propulsive forces from precisely placed shed vortices and that these tuned motions can only occur when vortex shedding and the simple harmonic motion of the elastic elements of the propulsive structures are in resonance.     

Parameter Identification in a Generalized Time-Harmonic Rayleigh Damping Model for Elastography

The identifiability of the two damping components of a Generalized Rayleigh Damping model is investigated through analysis of the continuum equilibrium equations as well as a simple spring-mass system. Generalized Rayleigh Damping provides a more diversified attenuation model than pure Viscoelasticity, with two parameters to describe attenuation effects and account for the complex damping behavior found in biological tissue. For heterogeneous Rayleigh Damped materials, there is no equivalent Viscoelastic system to describe the observed motions. For homogeneous systems, the inverse problem to determine the two Rayleigh Damping components is seen to be uniquely posed, in the sense that the inverse matrix for parameter identification is full rank, with certain conditions: when either multi-frequency data is available or when both shear and dilatational wave propagation is taken into account. For the multi-frequency case, the frequency dependency of the elastic parameters adds a level of complexity to the reconstruction problem that must be addressed for reasonable solutions. For the dilatational wave case, the accuracy of compressional wave measurement in fluid saturated soft tissues becomes an issue for qualitative parameter identification. These issues can be addressed with reasonable assumptions on the negligible damping levels of dilatational waves in soft tissue. In general, the parameters of a Generalized Rayleigh Damping model are identifiable for the elastography inverse problem, although with more complex conditions than the simpler Viscoelastic damping model. The value of this approach is the additional structural information provided by the Generalized Rayleigh Damping model, which can be linked to tissue composition as well as rheological interpretations.     

A piecewise mass-spring-damper model of the human breast

Previous models to predict breast movement whilst performing physical activities have, erroneously, assumed uniform elasticity within the breast. Consequently, the predicted displacements have not yet been satisfactorily validated. In this study, real time motion capture of the natural vibrations of a breast that followed, after raising and allowing it to fall freely, revealed an obvious difference in the vibration characteristics above and below the static equilibrium position. This implied that the elastic and viscous damping properties of a breast could vary under extension or compression. Therefore, a new piecewise mass-spring-damper model of a breast was developed with theoretical equations to derive values for its spring constants and damping coefficients from free-falling breast experiments. The effective breast mass was estimated from the breast volume extracted from a 3D body scanned image. The derived spring constant (k_a = 73.5 N m⁻¹) above the static equilibrium position was significantly smaller than that below it (k_b = 658 N m⁻¹), whereas the respective damping coefficients were similar (c_a = 1.83 N s m⁻¹, c_b = 2.07 N s m⁻¹). These values were used to predict the nipple displacement during bare-breasted running for validation. The predicted and experimental results had a 2.6% or less root-mean-square-error of the theoretical and experimental amplitudes, so the piecewise mass-spring-damper model and equations were considered to have been successfully validated. This provides a theoretical basis for further research into the dynamic, nonlinear viscoelastic properties of different breasts and the prediction of external forces for the necessary breast support during different sports activities.     

Reduced elbow extension torque during vibrations

Impact sports and vibration platforms trigger vibrations within soft tissues and the skeleton. Although the long-term effects of vibrations on the body have been studied extensively, the acute effects of vibrations are little understood. This study determined the influence of acute vibrations at different frequencies and elbow angles on maximal isometric elbow extension torque and muscle activity. Vibrations were generated by a pneumatic vibrator attached to the lever of a dynamometer, and were applied on the forearm of 15 healthy female subjects. The subjects were instructed to push maximally against the lever at three different elbow angles, while extension torque and muscle activity were quantified and compared between vibration and non-vibration (control) conditions. A change in vibration frequency had no significant effects on torque and muscle activity although vibrations in general decreased the maximal extension torque relative to the control by 1.8% (±5.7%, p>0.05), 7.4% (±7.9%, p<0.01), and 5.0% (±8.2%, p<0.01) at elbow angles of 60°, 90°, and 120°, respectively. Electromyographic activity increased significantly between ～30% and 40% in both triceps and biceps with vibrations. It is speculated that a similar increase in muscle activity between agonist and antagonist, in combination with an unequal increase in muscle moment arms about the elbow joint, limit the maximal extension torque during exposure to vibrations. This study showed that maximal extension torque decreased during vibration exposure while muscle activity increased and suggests that vibrations may be counterproductive during activities requiring maximal strength but potentially beneficial for strength training.     

Dynamic nonlinearity of lung tissue: frequency dependence and harmonic distortion

Harmonic distortion (HD) is a simple approach to analyze lung tissue nonlinear phenomena. This study aimed to characterize frequency-dependent behavior of HD at several amplitudes in lung tissue strips from healthy rats and its influence on the parameters of linear analysis. Lung strips (n = 17) were subjected to sinusoidal deformation at three different strain amplitudes (Δε) and fixed operational stress (12 hPa) among various frequencies, between 0.03 and 3 Hz. Input HD was <2% in all cases. The main findings in our study can be summarized as follows: 1) harmonic distortion of stress (HD) showed a positive frequency and amplitude dependence following a power law with frequency; 2) HD correlated significantly with the frequency response of dynamic elastance, seeming to converge to a limited range at an extrapolated point where HD=0; 3) the relationship between tissue damping (G) and HD(ω=1) (the harmonic distortion at ω=1 rad/s) was linear and accounted for a large part of the interindividual variability of G; 4) hysteresivity depended linearly on κ (the power law exponent of HD with ω); and 5) the error of the constant phase model could be corrected by taking into account the frequency dependence of harmonic distortion. We concluded that tissue elasticity and tissue damping are coupled at the level of the stress-bearing element and to the mechanisms underlying dynamic nonlinearity of lung tissue.     

Vibration transmission to lower extremity soft tissues during whole-body vibration

In order to evaluate potential risks of whole-body vibration (WBV) training, it is important to understand the transfer of vibrations from the WBV platform to the muscles. Therefore, the purpose of this study was to quantify the transmissibility of vibrations from the WBV platform to the triceps surae and quadriceps soft tissue compartments.     

Task-specific recruitment of motor units for vibration damping

Vibrations occur within the soft tissues of the lower extremities due to the heel-strike impact during walking. Increases in muscle activity in the lower extremities result in increased damping to reduce this vibration. The myoelectric intensity spectra were compared using principal component analysis from the tibialis anterior and lateral gastrocnemius of 40 subjects walking with different shoe conditions. The soft insert condition resulted in a significant, simultaneous increase in muscle activity with a shift to higher myoelectric frequencies in the period 0-60 ms after heel-strike which is the period when the greater vibration damping occurred. These increases in myoelectric frequency match the spectral patterns which indicate increases in recruitment of faster motor units. It is concluded that fast motor units are recruited during the task of damping the soft-tissue resonance that occurs following heel-strike.