Amir Nankali

Targeted Energy Transfer for Suppressing Regenerative Instabilities in a 2-DOF Machine Tool Model

We study targeted energy transfer (TET) mechanisms by applying a nonlinear energy sink (NES) to suppress regenerative instabilities in a 2-DOF planar machine tool model. With the help of a numerical continuation tool, DDEBIFTOOL, we show that the tool instability is generated through a subcritical Hopf bifurcation in this simplified tool model. Studying modal energy exchanges reveals that only one of the DOFs is predominant, which may lead to the standard single-DOF machine tool model. Then, we apply an ungrounded NES to the 2-DOF tool model such that the NES interacts only with the dominant mode, which turns out to be more efficient than applying the NES to the other insignificant mode. Simple numerical simulations and bifurcation analysis demonstrate that the three typical TET mechanisms can be identified — That is, recurrent burstouts and suppression, and partial and complete suppression of tool instability.Copyright

On the stability and compressive nonlinearity of a physiologically based model of the cochlea

Hearing relies on a series of coupled electrical, acoustical (fluidic) and mechanical interactions inside the cochlea that enable sound processing. A positive feedback mechanism within the cochlea, called the cochlear amplifier, provides amplitude and frequency selectivity in the mammalian auditory system. The cochlear amplifier and stability are studied using a nonlinear, micromechanical model of the Organ of Corti (OoC) coupled to the electrical potentials in the cochlear ducts. It is observed that the mechano-electrical transduction (MET) sensitivity and somatic motility of the outer hair cell (OHC), control the cochlear stability. Increasing MET sensitivity beyond a critical value, while electromechanical coupling coefficient is within a specific range, causes instability. We show that instability in this model is generated through a supercritical Hopf bifurcation. A reduced order model of the system is approximated and it is shown that the tectorial membrane (TM) transverse mode effect on the dynamic...

Nonlinear dynamics of the organ of Corti, modeling both outer hair cell somatic motility and hair bundle motility

One of the principal questions in the cochlea biophysics is the determination of relative contributions of the two active processes, OHC somatic motility and HB motility, to the mechanics of the cochlea. Because of the difficulty of eliminating one mechanism without affecting the other, an unambiguous in vivo measurement differentiating their effects remains elusive. Theoretical models, therefore, have been used as one way to examine the contributions of the two active mechanisms to cochlear mechanics. In this paper, we use a physiologically based model of the mammalian organ of Corti to study the hearing active process and the relative contributions of these active forces. This local model integrates the electrical, acoustic, and mechanical elements of a cross section of the cochlea. The nonlinear dynamics of this model are studied with a special emphasis on the regions of stability and the amplification of the mechanical response arising from the active processes. [Work supported by NIH-NIDCD R01-04084 ...

The role of the tectorial membrane in cochlear mechanics

The tectorial membrane (TM) is strategically located in the mammalian cochlea, anchoring the apical pole of the outer hair cell stereocilia and hovering just above the sensory inner hair cell stereocilia. Genetic mutations of TM-specific proteins cause nonsyndromic deafness in humans while experiments in mutant mice clearly demonstrate the impact that manipulations of TM structural proteins have on hearing thresholds and cochlear sensitivity. This direct evidence shows the importance of this cochlear structure. Mathematical models (with Zwsilocki as an early proponent) have long incorporated the TM but have not included a complete electrical and fluidic coupling. We show that an electromechanical model of the active processes in the cochlea combined with a fluid-structure model that strongly couples the basilar membrane and the TM to the cochlear fluids is crucial in understanding the low and high frequency response in a base-to-apex model of the cochlea. Specifically, we show that the onset of nonlinearity at high frequencies is due to a radial resonance of the uncoupled TM and investigate the influence of fluid-loading on the TM and TM viscoelasticity on the low-pass behavior seen in the apex. A connection of this new wave bearing mechanism to otoacoustic emissions will be discussed.The tectorial membrane (TM) is strategically located in the mammalian cochlea, anchoring the apical pole of the outer hair cell stereocilia and hovering just above the sensory inner hair cell stereocilia. Genetic mutations of TM-specific proteins cause nonsyndromic deafness in humans while experiments in mutant mice clearly demonstrate the impact that manipulations of TM structural proteins have on hearing thresholds and cochlear sensitivity. This direct evidence shows the importance of this cochlear structure. Mathematical models (with Zwsilocki as an early proponent) have long incorporated the TM but have not included a complete electrical and fluidic coupling. We show that an electromechanical model of the active processes in the cochlea combined with a fluid-structure model that strongly couples the basilar membrane and the TM to the cochlear fluids is crucial in understanding the low and high frequency response in a base-to-apex model of the cochlea. Specifically, we show that the onset of nonlineari...

Frequency structure in intracochlear voltage supports the concept of tectorial membrane mechanical resonance

The mechanical and electrical responses of the mammalian cochlea to acoustic stimulus are nonlinear and tuned. This is reflective of the electromechanical response of the outer hair cells (OHC) which are responsible for mediating the active process necessary for normal hearing. In this paper, we use the experimental data in conjunction with simulations to study nonlinear amplification in the cochlea. The sound-evoked voltage inside the scala tympani was measured for a range of frequencies and pressure levels. The experimental data show a notch in the voltage response at frequencies below the characteristic frequency (CF). This notch is seen to locate the onset of nonlinear amplification (in the frequency domain). In order to interpret the experimental data, a comprehensive three-dimensional model of the cochlea is used. Our model predicts the notch in the extracellular voltage as well as the phase relations observed from the experiments. The notch frequency in the model corresponds to the tectorial membra...

Signal flow inside the tunnel of Corti

All With the advent of Optical Coherence Tomography (OCT), a variation of the standard laser-interferometer technique, vibrations of various points inside the cochlea can be measured separately and concurrently. In this work we measured vibrations of the basilar membrane (BM) and the Reticular Lamina (RL) in the cochlea of the guinea pig. Stimulus tones had frequencies in the range from 10 to 25 kHz, they were generated and measured with a spacing of 250 Hz. By smoothing and interpolation the spacing was reduced to 50 Hz. We confirmed earlier findings in that in viable animals the responses at the RL are generally larger than those of the BM, and have smaller phase delays. Moreover, these differences are little dependent of the level of stimulation. Our main hypothesis is: stimulation of the stapes primarily excites the structures in the upper (RL) part of the Organ of Corti (OoC) channel. Subsequently, movements of the RL cause movements of the fluid in the OoC channel, which in turn moves the BM. Computation of the sound field generated by the RL yielded results that agree very well with the data. These results thus confirm the hypothesis.All With the advent of Optical Coherence Tomography (OCT), a variation of the standard laser-interferometer technique, vibrations of various points inside the cochlea can be measured separately and concurrently. In this work we measured vibrations of the basilar membrane (BM) and the Reticular Lamina (RL) in the cochlea of the guinea pig. Stimulus tones had frequencies in the range from 10 to 25 kHz, they were generated and measured with a spacing of 250 Hz. By smoothing and interpolation the spacing was reduced to 50 Hz. We confirmed earlier findings in that in viable animals the responses at the RL are generally larger than those of the BM, and have smaller phase delays. Moreover, these differences are little dependent of the level of stimulation. Our main hypothesis is: stimulation of the stapes primarily excites the structures in the upper (RL) part of the Organ of Corti (OoC) channel. Subsequently, movements of the RL cause movements of the fluid in the OoC channel, which in turn moves the BM. Comput...

Simulating the Chan-Hudspeth experiment on an active excised cochlear segment

Hearing relies on a series of coupled electrical, acoustical, and mechanical interactions inside the cochlea that enable sound processing. The local structural and electrical properties of the organ of Corti (OoC) and basilar membrane give rise to the global, coupled behavior of the cochlea. However, it is difficult to determine the root causes of important behavior, such as the mediator of active processes, in the fully coupled in vivo setting. An alternative experimental approach is to use an excised segment of the cochlea under controlled electrical and mechanical conditions. Using the excised cochlear segment experiment conducted by Chan and Hudspeth [Nat. Neurosci. 8, 149-155 (2005); Biophys. J. 89, 4382-4395 (2005)] as the model problem, a quasilinear computational model for studying the active in vitro response of the OoC to acoustical stimulation was developed. The model of the electrical, mechanical, and acoustical conditions of the experimental configuration is able to replicate some of the experiment results, such as the shape of the frequency response of the sensory epithelium and the variation of the resonance frequency with the added fluid mass. As in the experiment, the model predicts a phase accumulation along the segment. However, it was found that the contribution of this phase accumulation to the dynamics is insignificant. Taking advantage of the relative simplicity of the fluid loading, the three-dimensional fluid dynamics was reduced into an added mass loading on the OoC thereby reducing the overall complexity of the model.

Simulating cochlear nonlinearity in an excised, active in vitro segment

Hearing relies on a series of coupled acoustical, electrical, and mechanical interactions in the auditory periphery. There exists a distinct nonlinear amplification process inside the cochlea that enables sound processing of a broad range of frequencies and intensities. The precise operating principles of the active mechanics underlying nonlinear cochlear amplifier remains an open question in biophysics. Using the experimental protocol devised by Chan & Hudspeth of an excised cochlear segment as a model problem, we develop a computational model for studying the active in vitro response of the organ of Corti (OoC) to acoustical stimulation. Both experiment and theory show that there exists a traveling wave even for a very small, 700 mm cochlear segment. However, we show that the contribution of the traveling wave on the partition dynamics is insignificant in this preparation as the phase accumulation is less than one-tenth of a cycle. This finding enables us to reduce the macroscopic fluid dynamics of the ...

Light-induced basilar membrane vibrations in the sensitive cochlea

The exceptional sensitivity of mammalian hearing organ is attributed to an outer hair cell-mediated active process, where forces produced by sensory cells boost sound-induced vibrations, making soft sounds audible. This process is thought to be local, with each section of the hearing organ capable of amplifying sound-evoked movement, and nearly instantaneous, since amplification can work for sounds at frequencies up to 100 kHz in some species. To test these precepts, we developed a method for focally stimulating the living hearing organ with light. Light pulses caused intense and highly damped mechanical responses followed by traveling waves that developed with considerable delay. The delayed response was identical to movements evoked by click-like sounds. A physiologically based mathematical model shows that such waves engage the active process, enhancing hearing sensitivity. The experiments and the theoretical analysis show that the active process is neither local nor instantaneous, but requires mechanical waves traveling from the cochlear base toward its apex.

Calculation of energy exchange between the outer hair cell and structural components of the organ of Corti, using the in vivo measurement data

The mammalian cochlea amplifies the sound born vibration of the microstructures of the OoC through a frequency and level dependent active process. The somatic motility of the mechanosensory outer hair cells (OHCs) is hypothesized as the key element of the cochlea active mechanism. During the sound stimulation, the OHCs respond to the membrane potential fluctuation through a fast alteration of their length. This cellular length change applies an active harmonic force to both sides of the OHC (reticular lamina (RL) on the apical part and basilar membrane (BM) on the basal part), and boosts the OoC motion. In this paper, we use the in vivo experimental data on the OHC extracellular receptor potential together with the displacement of the OoC structural components to estimate energy exchange between the modes. It is found that when the OHC transmembrane potential leads the BM displacement by a phase between 0 and 180 degree, with an optimal value of 90 degree, the electrical power is transmitted into the BM m...