1. Effect of asymmetrical organ of Corti mechanics on the onset-delay of the cochlea Wenxiao Zhou1, and Jong-Hoon Nam1, Department of Mechanical Engineering, 2Department of Biomedical Engineering, University of Rochester
Introduction
Sounds propagate at the speed of 340 m/s in the air and 1500 m/s in water in the form of compressive waves. In the mammalian cochlea, sounds propagation is two to three orders of magnitude slower in the form of transverse vibrations of the cochlear partition. According to the classical ‘slow traveling wave’ theory, it takes in the order of milliseconds before any vibrations at the stapes (the basal sound port of the cochlea) arrive at a location in the cochlear partition. However, recent evidence shows that throughout the basal end of chinchilla cochlea, the signal-fronts of intense clicks and high-frequency tones arrive at the cochlear partition with ~4 µs latency, too quickly for “slow” traveling waves to provide. In contrast, all measured onset latencies in the apical region are much longer, consistent with slow-wave propagation.
We propose that the fast response in the base of the cochlea originates from two asymmetries: the organ of Corti (OC) mechanics, and the sound port geometry. To prove that, a computational model of the cochlea that features a fully deformable OC mechanics was used. The experimentally observed onset delay patterns were reproduced only when those two asymmetrical conditions were incorporated.
2 The model: A multi-physics model to investigate the cochlear mechano-transduction
(A) Cochlear fluid dynamics: The cochlear cavity was represented by a fluid-filled rectangular chamber divided into the top and the bottom fluid spaces separated by the elastic OC complex. (B) OC micro-mechanics: The 3-D finite element model of the OC incorporated realistic geometrical and mechanical characteristics of the gerbil cochlea. The OC micro-structures repeat with a longitudinal grid size of 10 μm. (C) Outer hair cell mechano-transduction and electro-mechanics: Two active forces were incorporated with the outer hair cells—the force originating from mechano-transduction in the hair bundle (fMET) and the electromotive force of the cell membrane (fOHC). (D) Interactions between the three dynamic systems. As far as possible, the physical and physiological parameters were from the gerbil cochlea.
4 Asymmetrical boundary conditions due to sound ports
First column: sketches of model with different locations and sizes of the footplate (red) and round window (RW, green). Second column: click responses at 5 different locations. Third column: Rise time and onset delay to the click.(A) Sound ports in their conventional places. (B) Stapes and RW form a 4-mm vestibule. (C) Entire upper and lower boundaries are sound ports. (D-F) The BM vibration along time at five longitudinal locations for corresponding sound port configurations in the first column. Asterisk symbols in panels D-H indicate the time when 20% of first response peak is reached at x=5 mm. (G) 20% rising times to clicks. (H) Onset latency.
6 When active, slow waves dominates despite asymmetrical sound ports
Response to pure tones. (A-C) The BM vibrations of active cochlea to a 10 kHz stimulation for three SP configurations. (D-F) Passive responses. (G) Top plot: Normalized snapshots of BM vibrations of the SP[0,4] model for three different stimulating frequencies that make peaks near x = 2, 6, and 10 mm. Active responses are shown in solid lines, passive responses in dashed lines. Bottom plot: phases calculated from the respective individual waveforms shown in these snapshots. (H) Phase delays as functions of the SP[0,4] configuration, for active (black line) and passive (light blue lines) model modes. Frequency-domain, linearized simulations
1 Motivation: Little onset delay in the base of the cochlea contradicts to the classical theory
(A) A schematic drawing of the mammalian cochlear fluid space. In the base (left in the drawing), there exists a large vestibule to accommodate the ‘sound ports’. Middle to apical turns are a narrow tube. (B) Most theoretical models use either constant or gradually varying cross section that looks like a tube. (C) Measured cross-sectional (CS) scala areas of chinchilla and gerbil cochlea (data from Kim, Yoon, Steele & Puria, 2008). (D) Measured neural and mechanical onset delay (Temchin, Recio-Spinoso, Cai & Ruggero, 2012). The classical slow traveling wave theory is not consistent with the negligible onset delay in the basal turn of the cochlea. We hypothesize that the zero onset delay is caused by asymmetrical mechanics in the basal turn of the cochlea.
5 Asymmetrical organ of Corti mechanics
The fully deformable OC model interacts with the fluid space with the top (TM) and the bottom (BM) surfaces, and the two surfaces do not necessarily vibrate in phase. These two interacting surfaces break the symmetry of the cochlear fluid mechanics. (A, B) Fluid pressures in the cochlear fluid space when 10 kHz stimulation was applied through the stapes. Color scale indicates the pressure in mPa per μm/s stapes velocity. The scale bar in panel B indicate 1 mm in the x-axis and 0.1 mm in the y-axis. The active (A) and passive (B) response are shown. (C, D) The zero onset delay disappears either when active, or when the OC mechanics become symmetrical.
3 Compliance to the classical model: traveling waves
Spatial vibration patterns when stimulated at different frequencies. (A) BM traveling waves. (B) TM traveling waves. (C) Comparison of the TM and the BM traveling waves when active (top) and passive (bottom). (D) Low frequency case.
Summary
Our computational analyses explain why some experimental observations regarding the onset latency are inconsistent with the classical slow traveling wave theory. When two realistic mechanical conditions were incorporated, the zero-onset latency in the basal turn of the cochlea was reproduced. They are the longitudinally located sound ports, and the fully deformable OC. These two conditions break the symmetry of cochlear mechanics (anti-symmetrical fluid pressure). The no-onset delay was a consequence of standing waves that become more apparent when the active feedback from the outer hair cells are reduced (when passive).
This study was supported by NIH NIDCD R01 DC