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Journal of Experimental Biology 58,351-366 (1973)
Published by Company of Biologists 1973

The Mechanics of the Growing Semicircular Canal

J. H. TEN KATE ¹

¹ Department for Biophysics, Natuurkundig Laboratorium der Rijksuniversiteit Groningen, Netherlands; Biophysics, Applied Physics Department, Delft University of Technology, The Netherlands

1. The motion of the endolymph in the semicircular canal is described with the aid of a linear second-order system, comprising the applied angular acceleration and the linear displacement, the linear velocity and the linear acceleration of the endolymph.

2. A sensitivity factor G for angular velocity is derived and expressed in the dimensions of the semicircular canal.

3. The sensitivity factor G of the semicircular canal proves to be consistent with the equivalent sensitivity factor of a more sophisticated hydrodynamic model of these canals.

4. The sensitivity of the growing semicircular canal is defined to be G/h_c², independent of the pike's size. Threshold angular velocities for the vestibulo-ocular reflex of 27 pike between 4 and 50 cm bodylength are in agreement with this assumption.

5. At threshold stimulation with an angular velocity of 2°/sec the radius of curvature R_c of the cupula is calculated to be 220±48 cm.

6. At the threshold angular velocity = 2°/sec the deviation of sensory hairs 5 µm long is assessed to be between 0.06 Å and 1 Å.

7. Young's modulus of elasticity for the cupular substance is found to be between 0.35 x 10³ dyne/cm² and 1.85 x 10³ dyne/cm² (on the basis of a circular bending for the cupula).

8. Characteristics of the model of the growing semicircular canal are calculated for pike with body length between 5 and 100 cm.

9. Observed growth effects of the pike's vestibulo-ocular reflex arc are correlated to the growth effects calculated on basis of the model for the growing semicircular canal.

10. The pike possesses the same degree of vestibulo-ocular compensation in the high-frequency range (2 radians/sec < 7 radians/sec) of angular oscillations during its whole life (11 observations of pike of body length 4-56 cm).