Oaes Assignment Discovery

I've seen two of the six-episode "Elements" subsections so far, both made in the 2000s: Elements Chemistry and Elements Biology.

They're an excellent way to get a brief summary of the subject's basics. I've tried out some other short series for this purpose, but those are often bloated, boring, and, what's worse, - uninformative, leaving you frustrated and unenlightened.

Assignment Discovery is different. Take Chemistry: they give you 6 episodes. They spend the first 10-15 minutes of the episode giving you a very clear, graphically great, illuminating primer on an aspect of chemistry: the periodic table, acids and bases, hydrocarbons. They play some suitable music - bouncy but unobtrusive - in the background, and the narrators - one male, one female - switch between segments. You don't actually see them, which is a refreshing change from annoying, in-your-face narrators with their lame-looking enthusiasm. AD is made in a way that's perfect for people with concentration problems - it relaxes you into learning.

The rest of each episode will proceed in a completely different vein, and a more BBC-ish style, leisurely telling you about how the subject is topical to our lives, usually - to modern technology. You can watch that part, or you can immediately skip to the next episode and get the next condensed-info 15-minute segment from its beginning. That's what I did. Consequently, you can catch up on chemistry in a little over an hour, maybe a little longer if you're gonna take notes and/or pause to look the issue up on the Web. I had to do a couple of such searches, but mostly the presentation of the material was extremely comprehensible.

All of the results presented here depended strictly on the hydrodynamic character of cochlear dynamics, in particular, the instantaneous character of fluid coupling between BM and stapes. This model conceives OAEs not as due to some kind of waves back-propagating from irregularity sites on the cochlear partition but rather as residual oscillations of the BM, possibly caused by such irregularities but often imputable to other factors too, and instantly transmitted to the stapes by fluid coupling [Eq. (1)].

To clarify the rationale underlying our approach, we analyze comparatively the BM integrodifferential motion equation [Eq. (A3)] and the hyperbolic differential equation that governs sound, light, and surface wave propagation (ignoring dissipative effects). As is well known, Eq. (3) admits two independent types of solutions. For example, if the local phase velocity v(x) is a smooth function of its argument, approximate solutions to Eq. (3) for a given frequency ω are representing forward and backward propagating waves, respectively (Carrier and Pearson 1997). In the case of Eq. (3), a local force input (think of pinching the string of a guitar) generates both forward and reverse wave components that propagate with amplitude scaling as the square root of v(x). Therefore, the two components proceed towards the ends of the integration domain, where reflection can occur. Dispersive waves, such as earthquake, Shroedinger, and surface waves, albeit governed by different equations, exhibit similar long-range propagation properties for each of their frequency components.

Our model disclosed a different behavior. Here, the BM oscillation profile elicited by a sinusoidally varying force directly applied to the BM (Fig. 6, solid lines) is very similar to a scaled version of the TW profile generated by a tone that drives the stapes at the same frequency (Fig. 6, dotted lines). In particular, both profiles affect, with appreciable amplitude, the same limited region of the cochlear partition, i.e. a neighborhood of the CF site. The most relevant difference is that the amplitude profile of the TW elicited by the local stimulus presents a more or less pronounced notch near the stimulus site (Fig. 6, top, arrow), while the phase profile (Fig. 6, bottom) presents a distortion basal to the CF site. By analogy with the relationship between phase sign and wave propagation direction in transmission lines, the phase distortion in Figure 6 might be interpreted as a back-traveling wave. However, its effects remain confined to the neighborhood of the CF site, as wave amplitude decreases rapidly toward the base of the cochlea.

Since the effect of a discontinuity of the cochlear partition parameters is equivalent to a local perturbation of the type described above, the result illustrated in Figure 6 indicates that internal TW reflections could hardly be invoked to explain the generation of OAEs. Instead, according to Eq. (2), OAEs arise from the cumulative hydrodynamic effect of BM residual oscillations.

In the transmission line view, the delays between input and output in the ear canal are interpreted as travel time of back-propagating waves. Instead, the delays observed in our simulations resulted simply from the delayed expression of BM oscillations due to the interplay of BM elasticity and the kinetic energy of the hydrodynamic field.

Hydrodynamics appeared to be responsible for a number of other interesting phenomena that we discuss later.

Spontaneous BM oscillations

How is it that a local amplification fall generates spontaneous BM oscillations, which would be expected only from a local amplification excess? As shown in Figure 4c, because of the nature of fluid coupling, a locally decreased BM acceleration (a labeled downward arrow) rebounds laterally as positive hydrodynamic forces (f labeled upward arrows) acting on adjacent BM segments. With CA gain very close to criticality, not only a slight gain increment but also a decrement may make dissipation and injection of power unbalanced, locally increasing amplification at the discontinuity and engendering spontaneous BM oscillations at that site. Both maximum hearing sensitivity, corresponding to threshold level minima in psychoacoustic measurements, and self-sustained BM oscillations, corresponding to spontaneous OAEs, are then expected to occur at CFs corresponding to local maxima or minima of the first space derivative of an irregular CA gain profile. To further clarify this crucial point, we consider in detail energy dissipation and the interplay between mechanical and hydrodynamic forces in the cochlea.

On undamping

Two main types of viscous drag hinder the motion of the cochlear partition: One opposes BM displacement relative to its resting position (positional viscosity; Fig. 2a, third panel), the other opposes relative displacements of adjacent organ of Corti segments (shearing viscosity; fourth panel). In a cochlea model with zero shearing viscosity, even the slightest overcompensation of positional viscosity would drive the system into instability, priming spontaneous BM oscillations. In our model, compensation of positional viscosity alone was insufficient to achieve large amplification levels because of the residual dissipation caused by shearing viscosity. As fluid coupling forced the BM to oscillate with a negative-definite phase gradient all along its length, thus preventing shearing forces from vanishing locally, the maintenance of subcritical dissipation conditions was consequently favored. In summary, shearing viscosity contributed everywhere to the energy balance of cochlear dynamics, providing distributed sinking for possible excess power locally delivered by the CA. We then conclude that the distributed (nonlocal) balance between energy injected by the OHCs and energy dissipated by viscous losses (Fig. 7) can be kept within stability boundaries even at high amplification levels, up to 60 dB gain, as found experimentally in the active cochlea (Robles and Ruggero 2001; Shera et al. 2002). Note that, because of the nonlocal character of energy balance, the power dissipation profile (Fig. 7, solid line) crosses the zero axis close to the CF site, meaning that energy delivered basal to the peak of the TW (dotted line) is absorbed apical to the peak, i.e., where shearing viscosity is mostly effective.

On the mechanism underlying stimulus frequency emissions

When the effect of a local decrease of the OHC feedback force at BM site x0, in a cochlea model otherwise characterized by a regular CA gain, is treated as a first-order perturbation term, the motion equation modifies as if the BM sensed an additional local force at x0 of strength proportional to the BM velocity at x0 (see Appendix). At high amplification, the BM response to a force like this is a sort of phase-distorted TW whose amplitude and phase depend on the velocity at x0 of the main (unperturbed) TW elicited by stapedial input. Because of phase distortion, the hydrodynamic feedback to the stapes produced by such a perturbation term is small, but non-negligible (about 2 dB). Consequently, vestibular pressure is perturbed by an additional contribution whose phase depends on the position of the main TW with respect to x0. The interference of this contribution with the main TW ultimately imposes on the ear canal pressure the frequency-dependent amplitude modulation typical of stimulus-frequency OAEs (Fig. 5). The effect is maximum for the largest amplification levels, i.e., for input at the threshold of hearing, and when the peak of the main TW passes across x0. It is then clear that the modulation is related to the wavelength of the TW around the peak region (peak wavelength).

In our model, the modulation cycle caused by local damage at the 1.2 kHz CF site was about 50 Hz because in the frequency range of 1–2 kHz this corresponds to the TW peak wavelength measured in frequency units. Discrepancies between model results and experimental data showing a modulation cycle of about 100 Hz (Shera and Zweig 1993; Zweig and Shera 1995) are probably attributable to underestimation of the BM shearing viscosity coefficient s(x) (see Appendix), since the peak wavelength increases with s(x). Nonetheless, the qualitative features of this phenomenon are reproduced well in our simulations. If the local CA gain damage is not too small, spontaneous BM oscillations also appear at x0, resulting in spontaneous OAEs at the CF of the damaged site. Note, however, that all such phenomena are relevant if the CA gain is larger than ~40–50 dB, as the number of modulations in the interference pattern depends on the number of oscillations enveloped by the TW peak (which increases with increasing amplification level).

On the time course of TWs and spindles

The BM response to a tone of given frequency, i.e., a TW, has a characteristic oscillatory waveform related to the cyclic exchange of BM elastic potential energy and kinetic energy of the surrounding fluid. Since this exchange is local (see Fig. 1A in Nobili et al. 1998), no total energy propagation takes place along the BM.

Dissipation phenomena resulting from cochlear partition viscosities determine the time course of the TW at the offset of an eliciting tone. During this decay process, energy exchange continues to take place over the limited BM region where the oscillation amplitude is appreciable. In the case of a highly amplified cochlea near threshold, the spatial extent of this region is extremely limited (Ren 2002).

In our model, the BM response to a click has a spindle waveshape. This depends on the fact that a click can be Fourier synthesized from a continuum of pure tones of suitable phases and amplitudes. Consequently, in the linear approximation, i.e., both in the passive cochlea and in the active cochlea near threshold, the BM response is a superposition of TWs, each one evolving independent of the others. When a click is presented to the stapes, each TW component of the global BM response is elicited with a different delay, proportional to the TW period. Therefore, basal BM regions begin to oscillate earlier than more apical regions, imparting the characteristic spindle waveshape to the BM oscillation pattern and also giving the impression that the forming spindle extends progressively toward the apex of the cochlea. At stimulus offset, in the linear regime, the shape of the spindle is determined by the distribution of decay times of the underlying TW components, which are shorter at higher frequencies. This gives the impression of forward propagation for the extinguishing wave packet, however, no effective energy propagation occurs.

In the nonlinear regime, the time course of the spindle is also influenced by tone-to-tone suppression. This is the main cause for the arising and persistence of residual BM oscillations, which may yield OAEs under the conditions analyzed in this article. Furthermore, the asymmetry of tone-to-tone suppression accentuates the apparent forward propagation of the spindle, as its components of lower frequency suppress more those of higher frequency than vice versa.

0 Replies to “Oaes Assignment Discovery”

Lascia un Commento

L'indirizzo email non verrà pubblicato. I campi obbligatori sono contrassegnati *