## Institute for Sensory Research

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Cochlea Model

Computer Simulation of Zwislocki’s Model of the Cochlea - User's Guide
This program simulates the response of Zwislocki’s Model of the Cochlea to sinusoidal vibrations applied to the stapes. It is controlled by the Parameter Entry Window where values of network elements can be adjusted and computational options selected.

1. The default values of the network elements simulate a passive, but otherwise normal, human cochlea of 3.5 cm length. The values are “per section” quantities and are derived directly from “per cm” data on page 232 of “Auditory Sound Transmission.” The conversion factors are as follows:

For compliance elements: Model Coefficient = [3.5*Coefficient(per cm)]
For resistive and mass elements: Model Coefficient = [Coefficient(per cm)/3.5]
For all elements: Model Exponent = [100*Exponent(percent)]

The default values are set when the Parameter Entry Window is opened or when the Reset Defaults button is selected.

2. The following Cochlear Parameters can be adjusted:
1. The impedance of the helicotrema consists of a fluid resistance and a fluid mass. User selected values can be inserted.
2. The value of all resistive elements in the model can be user selected.
3. The value of mass and compliance elements of the network vary exponentially along the length of the cochlea and each takes the form:

element value = (mA/N)exp( αd/N ) [compliance elements]
element value = (mAN)exp( αd/N ) [resistance and mass elements]

where:
m = arbitrary multiplier
A/N or AN = element value at base of cochlea (d = 0)
(A is the Model Coefficient)
N = total number of sections
α = exponential constant
d = position along the cochlea

Both the coefficient, A, and the exponential constant, α, have been scaled to give “per section” values.
The variable, d, measures distance along the cochlea in “sections”
The coefficient, m, affects only the magnitude of an element value and not its exponent. It is useful for making quick, temporary, changes.
User selected values can be inserted for any or all of the three element parameters (m, A, α). (Note that since resistance values do not change with distance, there is no associated exponent.)
4. The magnitude and phase of the feedback variable are user selectable. The default values are zero, corresponding to the passive cochlea. (Warning: The program does not limit the values entered as feedback parameters. Certain selections will cause instability in output plots. The magnitude is usually smaller than 1 and the phase around -45°.)
5. The Inner Hair-cell multiplier values determine what fractions (0 to 1) of the radial component of the Reticular Lamina and Tectorial Membrane motions are used to create shear at the Inner Hair Cells. (See Notes 1,2)

3. The following Computational parameters can be adjusted:
1. The number of sections, and hence the resolution of the results, is user selectable. For reference, Section number, Distance, and Percentage distance from the base are related as follows:

2.  Section Number =
where N is the total number of sections.

3. A drop down menu allows selection of the motion to be generated:
1. Transverse Basilar Membrane displacement
2. Radial component of Tectorial Membrane displacement
3. Shear between Reticular Lamina and Tectorial Membrane at the Outer Hair Cells
4. Shear between Reticular Lamina and Tectorial Membrane at the Inner Hair Cells
4. For computations as a function of distance, up to four frequencies can be designated for simultaneous display.
5. For computations as a function of frequency, up to four cochlear locations can be designated for simultaneous display. The starting and ending frequencies as well as the number of data points used in the calculation can be selected.
6. A drop down menu allows selection of the output display format:
1. Graph with log magnitude axis
2. Graph with linear magnitude axis
3. Traveling Wave--A traveling wave animation is produced for the first valid frequency among the four selected for generation. The animation can also be produced for any of the four selected frequencies directly from the graphical display.
4. Text

4. When all parameters and options have been selected, clicking the Calculate button initiates the calculation and displays the results. In addition to the graph, the output panel contains a summary of all parameter values used to create the display. The display can be saved by dragging it to the Desktop (Macintosh Operating Systems) or using a right-click (Windows).

Notes:
1. The program assumes that the radial displacement of the Reticular Lamina is equal to the transverse displacement of the Basilar Membrane.

2. Shear is defined as positive when the steriocilia are bent toward the outer wall of the cochlear canal (Spiral Lamina) and the Outer Hair Cells are excited.