43.

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Page 140
2.2.6—
Example of Phase Space Sets Constructed from Direct Measurement:
Motion of the Surface of Hair Cells in the Ear
The hair cells in the inner ear convert sound into electrical signals. Each cell has a hair that is deflected by sound. The motion of this hair alters the shape of the cell and the electrical properties of the cell membrane. These changes produce an electrical signal in response to the sound.
Teich et al. used light reflected off the surface of an individual hair cell to measure the position and velocity of the cell surface. Their measurement technique, called heterodyne optical interferometry, makes it possible to measure the position of the cell surface to an accuracy of 10-13 meter, which is about 1/1000 the diameter of an atom. They used the change in frequency of the reflected light, called the Doppler shift, to measure the velocity of the surface of the cell.
They constructed phase space sets directly from the measured position and velocity of the surface of the hair cells. They analyzed the shape of these phase space sets and their fractal dimension. Each hair cell responds to sounds within a narrow range of frequencies around its natural frequency. They found that both the shape of the phase space set and its fractal dimension depended on the natural frequency of the cell and the frequency of the sound they used to stimulate the cell.
The hair can deflect more easily toward one direction than the opposite direction. They compared their experimental results to mathematical models where the mass or stiffness of the hair is greater in one direction than in the opposite direction. These models have provided information on the relationship between the motion of the hair and the electrical signals generated by these cells.

 
[Cover] [Abbreviated Contents] [Contents] [Index]


Fractals and Chaos Simplified for the Life Sciences
Fractals and Chaos Simplified for the Life Sciences
ISBN: 0195120248
EAN: 2147483647
Year: 2005
Pages: 261

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