MECHANICS AND NEURAL RESPONSE OF RECEPTOR SYSTEMS 



405 



respectively to the viscosity and elasticity 

 of the system, and f(t) is proportional to the 

 instantaneous normal component of the 

 force acting to deflect the otolith from its 

 equilibrium position relative to the macula. 

 This force may arise in various ways, e.g., 

 one may reach into the labyrinth and pull 

 away an otolith from its macula, either di- 

 rectly or (in the case of the sacculus) by 

 the centrifugal force generated in a rota- 

 tion; or, one may accelerate the macula, by 

 accelerating the entire cranium, in which case 

 the inertial force of the otolith causes the 

 same drawing away action. In all these 

 cases, once f(i) is specified, equation (3) is 

 readily integrable to give v(t) as a function 

 of the parameters 2X and k^. From a suit- 

 able analysis of experiments in which f{t) 

 was known and v(t) was observed, 2X and 

 K^ may be calculated, and from them v(t) 

 for any f(t) . So far, however, such experi- 

 ments have not been done, and the justi- 

 fication of equation (3) is largely on struc- 

 tural grounds. 



In the case of the canals, elementary 

 mechanical considerations lead to an equa- 

 tion like (3), the assumption being that the 

 cupula deflects as a damped vibrator, and 

 that the change in afferent fiber frequency 

 is proportional to the deflection. The forc- 

 ing function f(t) now represents the sum of 

 the torques brought about by the motion 

 imposed on the cranium. As an illustra- 

 tion we may consider the stimulation of a 

 vertical canal by rotation about a distant 

 axis in its plane — a situation not unlike 

 that in pitching and rolling. The motion 

 imposed on the walls of the canal can be 

 resolved into (two) translations and a 

 rotation, and the effects may be considered 

 separately. That a pure Iranslalional ac- 

 celeration can twist the cupula out of its 

 resting position is theoretically certain, for 

 not only will it generally give rise to an iner- 

 tial torque, but also it will generate an anti- 

 parallel pressure gradient in the endolymph 

 (and therefore a torque, unless the angular 



and endolymphatic densities are identical).^ 

 This is an important objection to the as- 

 sumption of many writers (see 21) that the 

 canals are not involved in detecting linear 

 accelerations. A pure rotation gives rise 

 to two inertial torques on the cupula, and — 

 by virtue of the friction between canal walls 

 and endolymph — to an endolymph thrust 

 equivalent to a torque. The experiments of 

 Lowenstein and Sand (16), in which v{t) 

 was observed and the known f{t) were the 

 torques of pure rotations, are described 

 quite well by equation (3). This circum- 

 stance therefore permits a calculation of 2X 

 and K^, and from them a prediction of 

 v{t) in the course of oscillating rotation, 

 i.e., ship-like motion (23). 



Crude as the analytic studies to date have 

 been, they have nonetheless provided cer- 

 tain important results: they have ruled out 

 persistent endolymph flow as the explana- 

 tion of persistent neural responses such as 

 nystagmus (33), and have shown (38, 39) 

 that such phenomena are fully explained 

 by the high 2A/^- ratio for cupular deflection. 

 The numerical evaluation of 2X and k^ 

 has further suggested (23) that the fre- 

 quency of the oscillations imposed by ships 

 may be a frequency which renders the cupu- 

 lar deflections just 90° out of phase with the 

 imposed displacement, and therefore pre- 

 sumably with instantaneous receptors like 

 the eye. Whether this maximal asyn- 

 chrony is an etiologic factor in motion 

 sickness is still for future experimentation to 

 decide. Perhaps the most useful contribu- 

 tion which the analytic model of labyrinthine 

 receptors makes to the study of motion 

 sickness, however, is the suggestion of a 

 quantitative measure of the stimulating 

 effectiveness of an imposed disturbance. 

 We shall describe this measure briefly now, 



^ Sjoberg (34) has studied this effect both theo- 

 retically and in models. More recently, Morgan, 

 Summers, and Reimann (20), have given an inter- 

 esting derivation of the expressions for the gradient 

 in the case of half-canals (actually, the so-called 

 "semi-circular" canals are hydraulically complete 

 canals, i.e., the liquid column forms a ring). 



