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Unification and extension of monolithic state space and iterative cochlear models
Michael J Rapson1, Jonathan C Tapson, David Karpul
1Department of Electrical Engineering, University of Cape Town, Private Bag, Rondebosch, 7701 Cape Town, South Africa. rpsmic001@gmail.com
The Journal of the Acoustical Society of America
|May 8, 2012
Summary
This study formalizes the relationship between two cochlear modeling approaches, enabling conversion between them. A new method for state space matrices improves numerical properties for advanced cochlear simulations.
Area of Science:
- Acoustics
- Computational Auditory Neuroscience
- Bioacoustics
Background:
- Traditional time-domain cochlear models often use the Allen and Sondhi method.
- The state space formalism, developed by Elliott et al., offers a versatile approach for simulating nonlinear cochlear models.
Purpose of the Study:
- To extend the state space formalism to two dimensions using the finite element method.
- To compare and formalize the relationship between the state space formalism and the earlier Allen and Sondhi approach.
- To present a novel method for deriving state space matrices with improved numerical properties.
Main Methods:
- Finite element method applied to a two-dimensional extension of the state space formalism.
- Comparative analysis of the state space formalism and the Allen and Sondhi method, referencing Diependaal et al.
- Development of a new method for deriving state space matrices.
Main Results:
- Established a formal relationship between the state space formalism and the Allen and Sondhi method, allowing model conversion.
- Demonstrated the effectiveness of the two-dimensional extension of the state space formalism.
- Presented a state space matrix derivation method with superior numerical properties.
- Numerical results confirmed the similarity between the two modeling approaches and supported claims regarding fluid dimension.
Conclusions:
- Understanding the relationship between these cochlear modeling techniques allows for leveraging the strengths of each.
- The proposed method for deriving state space matrices enhances computational efficiency and accuracy.
- The study provides a foundation for further advances in state space formalism for cochlear modeling, as discussed by Bertaccini and Sisto.
Related Concept Videos
01:13The 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.
01:27State 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.
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01:16Anatomy 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...
01:21State Space to Transfer Function
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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01:15Auditory Pathway
Auditory pathways constitute the complex neural circuits responsible for transmitting and interpreting auditory information from the peripheral auditory system to the brain. Sound waves are initially captured by the outer ear, funneled through the ear canal, and reach the tympanic membrane (eardrum). These vibrations are transmitted via the middle ear's ossicles to the inner ear's cochlea.
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01:22Hair 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.