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The Cochlea

The Cochlea

The cochlea is a coiled structure in the inner ear that contains hair cells—the sensory receptors of the auditory system. Sound waves are transmitted to the cochlea by small bones attached to the eardrum called the ossicles, which vibrate the oval window that leads to the inner ear. This causes fluid in the chambers of the cochlea to move, vibrating the basilar membrane.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Anatomy of the Ear

Anatomy of the Ear

Auditory sensation, commonly called hearing, involves the transformation of sonic waves into neural impulses facilitated by the structures of the auditory organ. The prominent, flesh-like structure on the side of the head, called the auricle, directs sound waves towards the auditory canal. The auricle is often mislabeled as the pinna, a term more aligned with mobile structures like a feline's external ear. The auditory canal penetrates the cranium via the external auditory meatus of the...

Hair Cells

Hair Cells

Hair cells are the sensory receptors of the auditory system—they transduce mechanical sound waves into electrical energy that the nervous system can understand. Hair cells are located in the organ of Corti within the cochlea of the inner ear, between the basilar and tectorial membranes. The actual sensory receptors are called inner hair cells. The outer hair cells serve other functions, such as sound amplification in the cochlea, and are not discussed in detail here.

Transfer Function to State Space

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

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Related Experiment Video

Updated: Jul 8, 2026

Cochlear Surface Preparation in the Adult Mouse

Cochlear Surface Preparation in the Adult Mouse

Published on: November 6, 2019

A state space model for cochlear mechanics.

Stephen J Elliott¹, Emery M Ku, Ben Lineton

¹Institute of Sound and Vibration Research, University of Southampton, Southampton, Hampshire SO17 1BJ, United Kingdom. sje@isvr.soton.ac.uk

The Journal of the Acoustical Society of America

|January 15, 2008

Summary

A new state space model simplifies cochlear stability analysis. This model reveals that spatial inhomogeneities can cause instability, potentially leading to spontaneous otoacoustic emissions.

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Area of Science:

Auditory Neuroscience
Bioengineering
Computational Biology

Background:

Determining cochlear model stability from frequency response alone is challenging.
Existing models may not fully capture the dynamic behavior of the active cochlea.

Purpose of the Study:

To develop a state space model for analyzing cochlear stability.
To investigate the impact of spatial inhomogeneities on cochlear stability.
To explore the link between cochlear instability and spontaneous otoacoustic emissions.

Main Methods:

A discretized state space model incorporating micromechanical elements and cochlear fluid coupling was developed.
Stability analysis was performed in the time domain for both linear and nonlinear models.
Simulations were conducted using the active micromechanical model of Neely and Kim.

Main Results:

The state space model allows for straightforward stability determination in the linear case.
Abrupt spatial inhomogeneities significantly destabilize the active cochlea, while smoother variations are less impactful.
Instabilities in nonlinear models can generate limit cycles, potentially explaining spontaneous otoacoustic emissions.

Conclusions:

The developed state space model is a valuable tool for studying cochlear instabilities.
Spatial inhomogeneities play a critical role in cochlear stability, with implications for auditory function.
The model provides a framework for understanding the generation of spontaneous otoacoustic emissions through limit cycles.