Power Dissipation in the Cochlea Can Enhance Frequency Selectivity

The cochlear cavity is filled with viscous fluids, and it is partitioned by a viscoelastic structure called the organ of Corti complex. Acoustic energy propagates toward the apex of the cochlea through vibrations of the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred (e.g., the basilar membrane) to a few micrometers (e.g., the stereocilia bundle). Vibrations of microstructures in viscous fluid are subjected to energy dissipation. Because the viscous dissipation is considered to be detrimental to the function of hearing—sound amplification and frequency tuning—the cochlea uses cellular actuators to overcome the dissipation. Compared to extensive investigations on the cellular actuators, the dissipating mechanisms have not been given appropriate attention, and there is little consensus on damping models. For example, many theoretical studies use an inviscid fluid approximation and lump the viscous effect to viscous damping components. Others neglect viscous dissipation in the organ of Corti but consider fluid viscosity. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti microstructural mechanics, and electrophysiology of the outer hair cells. The model is validated by comparing with existing measurements, such as the viscoelastic response of the tectorial membrane, and the cochlear input impedance. Using the model, we investigated how dissipation components in the cochlea affect its function. We found that the majority of acoustic energy dissipation of the cochlea occurs within the organ of Corti complex, not in the scalar fluids. Our model suggests that an appropriate dissipation can enhance the tuning quality by reducing the spread of energy provided by the outer hair cells’ somatic motility.     

A problem in the mathematical biophysics of blood circulation: I

The standard approximation method used in mathematical biophysics is applied to the problem of flow of an incompressible viscous fluid in an elastic distensible tube. It is found that the wall of the tube may perform damped transversal harmonic oscillations due to that flow. The phenomenon is independent of the viscosity, the latter contributing only a damping factor. While, due to rather rough approximations, the practical applicability of the equation derived is rather limited, it is suggested that they may give a clue to the understanding of vibrations of the walls of blood vessels which long ago have been suggested as the possible source of some hemic murmurs.     

High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models

High-frequency vibrations e.g., induced by legs impacting with the ground during terrestrial locomotion can provoke damage within tendons even leading to ruptures. So far, macroscopic Hill-type muscle models do not account for the observed high-frequency damping at low-amplitudes. Therefore, former studies proposed that protective damping might be explained by modelling the contractile machinery of the muscles in more detail, i.e., taking the microscopic processes of the actin–myosin coupling into account. In contrast, this study formulates an alternative hypothesis: low but significant damping of the passive material in series to the contractile machinery—e.g., tendons, aponeuroses, titin—may well suffice to damp these hazardous vibrations. Thereto, we measured the contraction dynamics of a piglet muscle–tendon complex (MTC) in three contraction modes at varying loads and muscle–tendon lengths. We simulated all three respective load situations on a computer: a Hill-type muscle model including a contractile element (CE) and each an elastic element in parallel (PEE) and in series (SEE) to the CE pulled on a loading mass. By comparing the model to the measured output of the MTC, we extracted a consistent set of muscle parameters. We varied the model by introducing either linear damping in parallel or in series to the CE leading to accordant re-formulations of the contraction dynamics of the CE. The comparison of the three cases (no additional damping, parallel damping, serial damping) revealed that serial damping at a physiological magnitude suffices to explain damping of high-frequency vibrations of low amplitudes. The simulation demonstrates that any undamped serial structure within the MTC enforces SEE-load eigenoscillations. Consequently, damping must be spread all over the MTC, i.e., rather has to be de-localised than localised within just the active muscle material. Additionally, due to suppressed eigenoscillations Hill-type muscle models taking into account serial damping are numerically more efficient when used in macroscopic biomechanical neuro-musculo-skeletal models.     

Viscous damping of Alfvén surface waves in the solar atmosphere

The dispersion relation for the propagation of viscous Alfvén surface waves along viscous plasmaplasma interface has been derived. Two modes of Alfvén surface waves are found to propagate with their characteristics depend on the interface parameters like magnetic field, density ratio, viscosity, etc. The viscous damping of Alfvén surface waves has been studied in the astrophysical point of view. The damping length of Alfvén surface waves due to viscosity in the solar atmosphere has been estimated.     

The effects of selective matrix degradation on the short-term compressive properties of adult human articular cartilage.

The effects of proteoglycan and collagen digestion on the transient response of human articular cartilage when tested in unconfined compression were determined. Small cylindrical specimens of cartilage, isolated from the femoral head of the hip joint and from the femoral condyles of the knee joint, were subjected to a suddenly applied compressive load using a test apparatus designed to yield a transient oscillatory response. From this response values of the elastic stiffness and the viscous damping coefficient were determined. Cathepsin D and cathepsin B1 were used to digest the proteoglycan in some specimens, while in other specimens leukocyte elastase was used to attack the non-helical terminal regions of the Type II tropocollagen molecules and possibly the Type IX collagen molecule and thereby disturb the integrity of the collagen mesh. The results showed that proteoglycan digestion alone reduced the viscous damping coefficient but it did not significantly alter the elastic stiffness as determined from the oscillatory response. In contrast, the action of elastase reduced both the damping coefficient and the elastic stiffness of the cartilage. The results demonstrated the role of proteoglycans in regulating fluid transport in cartilage and hence controlling the time-dependent viscous properties. The elastic stiffness was shown to be dependent on the integrity of the collagen fibre network and not on the proteoglycans.     

Viscous properties of human muscle during contraction.

The purpose of this study was to determine viscous properties of human muscle during plantarflexion efforts. Experiments were performed on 17 subjects with an ankle ergometer allowing sinusoidal oscillations during isometric contractions and isokinetic movements. Sinusoidal oscillations led to the expression of (i) Bode diagrams of the musculo-articular system allowing the determination of a damping coefficient (Bbode); and (ii) a viscous coefficient (Bsin) using an adaptation of Hill's equation to sinusoidal oscillations. Isokinetic movements led to torque-velocity relationships. They showed a fall in torque associated to an increase in angular velocity what was quantified by calculating a damping coefficient (Biso). Both experiments gave consistent results indicating that Bbode was the lowest viscous parameter. This difference is discussed in terms of (i) "analog" viscosity originating from muscle cross-bridges; and (ii) real mechanical damping of passive structures.     

Soft-tissue vibrations in the quadriceps measured with skin mounted transducers

The purpose of this study was to develop a method to characterize the frequency and damping of vibrations in the soft tissues of the leg. Vibrations were measured from a surface-mounted accelerometer attached to the skin overlying the quadriceps muscles. The free vibrations in this soft tissue were recorded after impact whilst the muscle was performing isometric contractions at 0, 50, and 100% maximum voluntary force and with the knee held at 20, 40, and 60 degrees angles of flexion. The acceleration signals indicated that the soft tissue oscillated as under-damped vibrations. The frequency and damping coefficients for these vibrations were estimated from a model of sinusoidal oscillations with an exponential decay. This technique resolved the vibration coefficients to 2 and 7% of the mean values for frequency and damping, respectively.     

Natural frequencies and damping ratios of Norway spruce (<Emphasis Type="Italic">Picea abies</Emphasis> (L.) Karst) growing on subalpine forested slopes

We investigated the natural frequencies and damping ratios of 24 Norway spruce trees (Picea abies (L.) Karst) growing on subalpine forested slopes using swaying experiments. Trees were winched to the release position using a manually operated cable winch. Before release, the stem base rotation was approximately 2 degrees. All trees were tested in both fall-line and cross-slope direction if possible to reveal the difference between the two perpendicular directions. A new method based upon the Hilbert transformation for evaluating the damping ratio for trees was used. It enabled us to investigate the damping ratio for all excited modes of vibration in the tree structure during the swaying experiments and to study if velocity proportional damping (viscous damping) is a reasonable assumption when predicting the tree response to different external actions using mechanical models. No difference in first natural frequency and damping ratio was found between the fall-line and cross-slope direction for all tested trees. The first natural frequencies correlated best with the diameter at breast height and squared total tree height DBH/H ². For the damping ratio, no significant correlation with different tree characteristics could be found. A non-velocity proportional damping ratio was observed for two trees. This indicates that using a viscous damping for all frequencies is an appropriate simplification when modelling the wind-tree interaction.     

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.     

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.     

Lung tissue resistance during contractile stimulation: structural damping decomposition.

Research in the mechanics of soft tissue, and lung tissue in particular, has emphasized that dissipative processes depend predominantly on the viscous stress. A corollary is that dissipative losses may be expressed as a tissue viscous resistance, (Rti). An alternative approach is offered by the structural damping hypothesis, which holds that dissipative processes within soft tissue depend directly more on the elastic stress than on the viscous stress. This implies that dissipative and elastic processes within lung tissues are coupled at a fundamental level. We induced alterations of Rti by exposing canines to aerosols of the constrictors prostaglandin F2 alpha, histamine, and methacholine and by changing volume history. Using the structural damping paradigm, we could separate those alterations in Rti into the product of two distinct contributions: change in the coefficient of coupling of dissipation to elastance (eta) and change in the elastance itself (Edyn). Response of Edyn accounted for most of the response of resistance associated with contractile stimulation; it accounted for almost all the response associated with differences in volume history. The eta changed appreciably with constriction but accounted for little of the response of Rti with volume history. According to the structural damping hypothesis, induced changes in eta with constriction must reflect changes in the kinetics of the stress-bearing process, i.e., differences in cross-bridge kinetics within the target contractile cell and/or differences in the influence of the target cell on other stress-bearing systems. We conclude that, regardless of underlying processes, the structural damping analysis demonstrates a fundamental phenomenological simplification: when Edyn responds, Rti is obligated to respond to a similar degree.     

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.     

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.     

Radiofrequency and microwave interactions between biomolecular systems

The knowledge of mechanisms underlying interactions between biological systems, be they biomacromolecules or living cells, is crucial for understanding physiology, as well as for possible prevention, diagnostics and therapy of pathological states. Apart from known chemical and direct contact electrical signaling pathways, electromagnetic phenomena were proposed by some authors to mediate non-chemical interactions on both intracellular and intercellular levels. Here, we discuss perspectives in the research of nanoscale electromagnetic interactions between biosystems on radiofrequency and microwave wavelengths. Based on our analysis, the main perspectives are in (i) the micro and nanoscale characterization of both passive and active radiofrequency properties of biomacromolecules and cells, (ii) experimental determination of viscous damping of biomacromolecule structural vibrations and (iii) detailed analysis of energetic circumstances of electromagnetic interactions between oscillating polar biomacromolecules. Current cutting-edge nanotechnology and computational techniques start to enable such studies so we can expect new interesting insights into electromagnetic aspects of molecular biophysics of cell signaling.     

Lorentz approach to static magnetic field effects on bound-ion dynamics and binding kinetics: Thermal noise considerations

The present study characterizes an ion-binding site, a molecular cleft in a signalling molecule such as calmodulin or troponin C, as a damped linear isotropic oscillator potential for small displacements about the origin. Quantitative assessments of the effects of thermal noise and exogenous static magnetic fields are made through a statistical mechanical treatment of the Lorentz-Langevin equation for an ion bound in a molecular cleft. Thermal noise causes a bound ion to be ejected from the site after a bound lifetime dependent upon the thermal noise spectral density. It is shown that the Lorentz-Langevin model requires values of the viscous damping parameter many orders of magnitude below those for bulk water in order to characterize the binding site and to obtain realistic lifetimes for a bound ion. The model predicts that milliTesla-range magnetic fields are required for static field effects on dissociation kinetics. The Lorentz equation also yields a classic coherent solution describing precession of the boundion oscillator orientation at the Larmor frequency. The bound-ion dynamics described by this coherent solution are sensitive to micro Tesla-range static magnetic fields in the presence of thermal noise. Numerical integration of the contribution of thermal noise forces to these dynamics is in good agreement with the results of statistical mechanical analysis, also producing realistic bound lifetimes for only very low viscous damping values. The mechanisms by which modulation of precessional motion might enable a signalling molecule such as calmodulin to detect an exogenous magnetic field are presently unclear. © 1996 Wiley-Liss, Inc.     

Resonant ac-dc magnetic fields: calculated response

An elementary model consisting of one charged particle in a viscous medium exposed to weak ac-dc low-frequency magnetic fields is analyzed to identify and explain the fundamental characteristics of the physical mechanisms that result in a resonance response, which is similar to the familiar cyclotron resonance. The model predicts both frequency and amplitude windows, which are explained in terms of synchronization of the particle with electric fields. Although extrapolation of model results to biological systems is limited by the elementary nature of the model, the model results indicate that observed resonant responses by others of biological systems to ac-dc magnetic fields are probably not due to resonant response of ions in solution, since the model predicts that no resonant response is possible unless the viscous damping is very low, many orders of magnitude lower than the viscous damping of ions in solution.     

Acoustical response of hair receptors in insects

Summary A detailed mechanical model is developed to account for the behaviour of hair-like acoustical sensory receptors in insects. For the small hair diameters commonly found, it is concluded that the force acting on the moving hair is caused almost entirely by the viscosity of the air, as analyzed long ago by Stokes. The result of this viscous force is to provide a bending moment about the base of the hair that is proportional to the acoustic particle velocity but that lags behind it by about 135°. In addition the viscous force increases the moment of inertia of the hair by a large and frequency dependent addition, and provides a viscous damping term of sufficient magnitude to reduce the Q value to near unity.The measurements of Tautz (1977) on the thoracic hairs of the caterpillarBarathra brassicae are discussed in detail in terms of the model. Many of these observations are well accounted for, though a few discrepancies remain.This work is part of a programme in biological acoustics supported by the Australian Research Grants Committee.     

Vibration of DNA polymer in viscous solvent

The problem of viscous damping of vibrating DNA polymer in solution is solved in the low-amplitude limit for all acoustic branches of the spectrum. The acoustic spectrum covers the microwave region of frequencies. Analytic solutions are obtained for a model describing the DNA polymer as a smooth circular cylinder. Numerical solutions are presented for a model describing the DNA polymer as a twisted cylinder of elliptical cross section. The amount of mass loading is determined for both models and the damped spectrum for the mass-loaded oscillator is calculated. The viscous damping is found to be a strong function of frequency, singular at very low frequencies for all modes except the torsional mode of the circular cylinder. All acoustic modes are overdamped, implying that the observation of well-defined resonances in DNA requires either highly structured water on the molecular level or very dry material.     

Self-oscillations of biological microbodies

Theoretical analysis of natural oscillation spectra of different kind of cells is presented. The study of received dispersive equation shows that the character of the cell natural movement depends on its size and the viscosity of internal and external liquids. If the depth of viscous wave penetration is small in comparison with the cell radius, the natural movements are weak damping oscillations. If the depth viscous wave penetration is comparable to the cell size, we have a relaxation process of cell form restoration.     

Postural differences in shoulder dynamics during pushing and pulling

Assessments of shoulder dynamics (e.g. the inertial, viscous, and stiffness properties of the joint) can provide important insights into the stability of the joint at rest and during volitional contraction. The purpose of this study was to investigate how arm posture influences shoulder dynamics while generating pushing or pulling torques in the horizontal plane. Sixteen healthy participants were examined in seven postures encompassing a large workspace of the shoulder. At each posture, the participant’s shoulder was rapidly perturbed while measuring the resultant change in shoulder torque about the glenohumeral axis. Participants were examined both at rest and while producing horizontal flexion and extension torques scaled to 15% of a maximum voluntary contraction. Shoulder stiffness, viscosity, and damping ratio were estimated using impedance-based matching, and changes in these outcome measures with torque level, elevation angle, and plane of elevation angle were explored with a linear mixed effects model. Shoulder stiffness was found to decrease with increasing elevation angles (p < 0.001) without subsequent changes in viscosity, leading to a greater damping ratios at higher elevation angles (p < 0.001). Shoulder stiffness, viscosity, and damping ratio (all p < 0.05) were all found to significantly increase as the plane of elevation of the arm was increased. The relationship between the viscosity, stiffness and the damping ratio of the shoulder is one that the central nervous system must regulate in order to maintain stability, protect against injury, and control the shoulder joint as the inertial and muscle contributions change across different arm postures.