Foundations of the Wentzel-Kramers-Brillouin approximation for models of cochlear mechanics in 1- and 2-D.

The Wentzel-Kramers-Brillouin (WKB) approximation is frequently used to explore the mechanics of the cochlea. As opposed to numerical strategies, the WKB approximation facilitates analysis of model results through interpretable closed-form equations and can be implemented with relative ease. As a result, it has maintained relevance in the study of cochlear mechanics for half of a century. Over this time, it has been employed to study a variety of phenomena, including the limits of frequency tuning, active displacement amplification within the organ of Corti, feedforward mechanisms in the cochlea, and otoacoustic emissions. Despite this ubiquity, it is challenging to find rigorous exposition of the WKB approximation's formulation, derivation, and implementation in cochlear mechanics literature. In this tutorial, the foundations of the WKB approximation are discussed in application to models of one- and two-dimensional cochlear macromechanics. This includes mathematical background, rigorous derivation and details of its implementation in software.

Regional differences in cochlear nonlinearity across the basal organ of Corti of gerbil: Regional differences in cochlear nonlinearity.

Auditory sensation is based in nanoscale vibration of the sensory tissue of the cochlea, the organ of Corti complex (OCC). Motion within the OCC is now observable due to optical coherence tomography. In a previous study (Cooper et al., 2018), the region that includes the electro-motile outer hair cells (OHC) and Deiters cells (DC) was observed to move with larger amplitude than the basilar membrane (BM) and surrounding regions and was termed the "hotspot." In addition to this quantitative distinction, the hotspot moved qualitatively differently than the BM, in that its motion scaled nonlinearly with stimulus level at all frequencies, evincing sub-BF activity. Sub-BF activity enhances non-BF motion; thus the frequency tuning of the OHC/DC region was reduced relative to the BM. In this work we further explore the motion of the gerbil basal OCC and find that regions that lack significant sub-BF activity include the BM, the medial and lateral OCC, and the reticular lamina (RL) region. The observation that the RL region does not move actively sub-BF (already observed in Cho and Puria 2022), suggests that hair cell stereocilia are not exposed to sub-BF activity in the cochlear base. The observation that the lateral and RL regions move approximately linearly sub-BF indicates that linear forces dominate non-linear OHC-based forces on these components at sub-BF frequencies. A complex difference analysis was performed to reveal the internal motion of the OHC/DC region and showed that amplitude structure and phase shifts in the directly measured OHC/DC motion emerge due to the internal OHC/DC motion destructively interfering with BM motion.

Compressed sensing on displacement signals measured with optical coherence tomography.

Optical coherence tomography (OCT) is capable of angstrom-scale vibrometry of particular interest to researchers of auditory mechanics. We develop a method for compressed sensing vibrometry using OCT that significantly reduces acquisition time for dense motion maps. Our method, based on total generalized variation with uniform subsampling, can reduce the number of samples needed to measure motion maps by a factor of ten with less than 5% normalized mean square error when tested on a diverse set of in vivo measurements from the gerbil cochlea. This opens up the possibility for more complex in vivo experiments for cochlear mechanics.

A frame and a hotspot in cochlear mechanics.

Auditory sensation is based in nanoscale vibration of the sensory tissue of the cochlea, the organ of Corti complex (OCC). Motion within the OCC is now observable due to optical coherence tomography. In the cochlear base, in response to sound stimulation, the region that includes the electro-motile outer hair cells (OHC) was observed to move with larger amplitude than the basilar membrane (BM) and surrounding regions. The intense motion is based in active cell mechanics, and the region was termed the "hotspot" (Cooper et al., 2018, Nature comm). In addition to this quantitative distinction, the hotspot moved qualitatively differently than the BM, in that its motion scaled nonlinearly with stimulus level at all frequencies, evincing sub-BF activity. Sub-BF activity enhances non-BF motion; thus the frequency tuning of the hotspot was reduced relative to the BM. Regions that did not exhibit sub-BF activity are here defined as the OCC "frame". By this definition the frame includes the BM, the medial and lateral OCC, and most significantly, the reticular lamina (RL). The frame concept groups the majority OCC as a structure that is largely shielded from sub-BF activity. This shielding, and how it is achieved, are key to the active frequency tuning of the cochlea. The observation that the RL does not move actively sub-BF indicates that hair cell stereocilia are not exposed to sub-BF activity. A complex difference analysis reveals the motion of the hotspot relative to the frame.

A high-efficiency model indicating the role of inhibition in the resilience of neuronal networks to damage resulting from traumatic injury.

Recent investigations of traumatic brain injuries have shown that these injuries can result in conformational changes at the level of individual neurons in the cerebral cortex. Focal axonal swelling is one consequence of such injuries and leads to a variable width along the cell axon. Simulations of the electrical properties of axons impacted in such a way show that this damage may have a nonlinear deleterious effect on spike-encoded signal transmission. The computational cost of these simulations complicates the investigation of the effects of such damage at a network level. We have developed an efficient algorithm that faithfully reproduces the spike train filtering properties seen in physical simulations. We use this algorithm to explore the impact of focal axonal swelling on small networks of integrate and fire neurons. We explore also the effects of architecture modifications to networks impacted in this manner. In all tested networks, our results indicate that the addition of presynaptic inhibitory neurons either increases or leaves unchanged the fidelity, in terms of bandwidth, of the network's processing properties with respect to this damage.

Reconstruction of transverse-longitudinal vibrations in the organ of Corti complex via optical coherence tomography.

Optical coherence tomography (OCT) is a common modality for measuring vibrations within the organ of Corti complex (OCC) in vivo. OCT's uniaxial nature leads to limitations that complicate the interpretation of data from cochlear mechanics experiments. The relationship between the optical axis (axis of motion measurement) and anatomically relevant axes in the cochlea varies across experiments, and generally is not known. This leads to characteristically different motion measurements taken from the same structure at different orientations. We present a method that can reconstruct two-dimensional (2-D) motion of intra-OCC structures in the cochlea's longitudinal-transverse plane. The method requires only a single, unmodified OCT system, and does not require any prior knowledge of precise structural locations or measurement angles. It uses the cochlea's traveling wave to register points between measurements taken at multiple viewing angles. We use this method to reconstruct 2-D motion at the outer hair cell/Deiters cell junction in the gerbil base, and show that reconstructed transverse motion resembles directly measured transverse motion, thus validating the method. The technique clarifies the interpretation of OCT measurements, enhancing their utility in probing the micromechanics of the cochlea.

Using volumetric optical coherence tomography to achieve spatially resolved organ of Corti vibration measurements.

Optical coherence tomography (OCT) has become a powerful tool for measuring vibrations within the organ of Corti complex (OCC) in cochlear mechanics experiments. However, the one-dimensional nature of OCT measurements, combined with experimental and anatomical constraints, make these data ambiguous: Both the relative positions of measured structures and their orientation relative to the direction of measured vibrations are not known a priori. We present a method by which these measurement features can be determined via the use of a volumetric OCT scan to determine the relationship between the imaging/measurement axes and the canonical anatomical axes. We provide evidence that the method is functional by replicating previously measured radial vibration patterns of the basilar membrane (BM). We used the method to compare outer hair cell and BM vibration phase in the same anatomical cross section (but different optical cross sections), and found that outer hair cell region vibrations lead those of the BM across the entire measured frequency range. In contrast, a phase lead is only present at low frequencies in measurements taken within a single optical cross section. Relative phase is critical to the workings of the cochlea, and these results emphasize the importance of anatomically oriented measurement and analysis.