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Progress in Vestibular Modeling PART I: RESPONSE OF SEMICIRCULAR CANALS TO CONSTANT ROTATION IN A LINEAR ACCELERATION FIELD ROBERT W. STEER, JR. Merrimack College SUMMARY The intensification in vestibular research that has been stimulated by the manned space flight program has brought to light several areas of conflict between experimental data and classical concepts of vestibular function. This paper presents the objectives, assumptions, analytic evaluations, and experimental data acquired during the investigations of two such topics which have been examined in some detail at the MIT Man-Vehicle Laboratory. The disparity between the experimentally evaluated time constants of objective and subjective responses to angular accelerations and the hydromechanical time constants of the semicircular canals is further accentuated by a rigorous analysis of the semicircular canals as a damped hydromechanical angular accelerometer. The dynamic response characteristics of the semicircular canals to angular acceleration are shown to be an order of magnitude faster than can be observed by nystagmus and subjective responses to vestibular stimulation. In addition, it is shown that "roller pump" action of the flexible canalicular duct can maintain an adequate pressure differential across the cupula to give it a constant deflection. This is physiologically equivalent to a constant angular acceleration stimulus. and offers a plausible explanation for the continuous nystagmus responses that are provoked by rota- tion at a constant angular velocity about an axis which is not colinear with an applied acceleration field. THE "RIGID TUBE" DYNAMIC CHAR- cular canals requires the solution of the classical ACTERISTICS OF THE SEMICIR- Navier-Stokes equations of fluid dynamics for CULAR CANALS an incompressible fluid subject to the boundary conditions of zero flow at the inner surface of A rigorous analytical evaluation of the the membranous canals. These equations, dynamic sensory capabilities of the semicir- in cylindrical coordinates, are [dvr , dvr vit,dvr vi . dfr~| ,, dp -d7 + V^ + --^-^ + V^\ = Fr~r \dZVr,IdVr Vr, Id~Vr 2dv* ,d*Vr] + M l"^"1 --- ; --- T + ~2Tn --- Â»TjT+TT \_dr- r dr H r2 dif> H dq> d2 ] [dv* . dv,i, v^,dv.i, vrVj, d H+1**:+-Jt~~+V- dp +_+++ 2 r fir r- 1 1 - 2 Idv, z , I + : + + Â£=0 (Id) dr r r dq> dz 353
354 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION where vn = component of velocity of fluid in the nth direction Fn â component of force on fluid in the nth direction â= pressure gradient in the nth direction on r, 4>, z = cylindrical coordinates p = density of the fluid These equations are solved utilizing the physical model of Van Egmond, Groen, and Jongkees (ref. 1) and the assumptions that the canalicular duct is a rigid torus of radii 0.015 cm and 0.3 cm filled with an incompressible fluid with a viscosity of 0.852 centipoise. Further, the cupula is considered to be a "flapper" valve with viscous drag and elastic restraint. Examination of equations (1) shows that the inertial acceleration forces and the pressure gradient forces on a particle of fluid are additive. Thus, it is possible to functionally separate the influence of the cupula and the canalicular duct on the performance of the semicircular canal. In figure 1 is presented a system block diagram which provides the necessary func- tional separation. The net "inertia-pressure feedback" force operates on the endolymph in the membranous duct and results in an average flow of endolymph. The inertia, drag, and elastic restrain characteristics of the cupula introduce a differential pressure feedback proportional to the average flow and flow rate of the endolymph. To determine the hydrodynamic drag charac- teristics of the canalicular duct, equations (1) can be solved for the average fluid flow which results from any transient angular accelera- tion. Since these equations are linear differen- tial equations with respect to time, the response to any angular acceleration can be found by use of the convolution integral and the response for any known input. A step input was used because of its relative simplicity. The average velocity of fluid through a cross section of the duct as a result of a step input of angular acceleration can be expressed as a weighted sum of exponential functions whose coefficients are determined by the radius of the duct, the viscosity of the fluid, and the zeros of the first-order Bessel function. â¬(t)= dt v(r, z, t)= (2) D\ where TJ = ; (3) The dynamic characteristics of the viscous drag of endolymph can therefore be represented as a parallel, weighted sum of the first-order lag networks as shown in figure 2. It is very significant to note that the first term accounts for 96 percent of the flow (Di = 0.957) and that the time constant of the flow is only 1/220 second. Further, all additional terms are so small in magnitude and have such short time constants that their contributions to the transfer function are negligible. The influence of cupula dynamics on the sen- sory capabilities of the semicircular canals can be quantified by evaluation of the influence of an ampullary pressure differential on the position of the cupula. Since a pressure difference across the ampulla results in a torque on the cupula, this functional dependence can be evaluated by a torque balance equation on the cupula. ,â 3I>% F* + 7 (FÂ» - Â¥Â»> Rigid torus Cupula e (eupula angle) ..-.. â v --? 3P dynamics dynamics 3Â« FIGURE I.âSchematic diagram for dynamics of the semicircular canal.
PROGRESS IN VESTIBULAR MODELING 355 v(s) FIGURE 2.â System block diagram for the average endolymph velocity (v) in the canalicular duct from an input F(s). From which obtains (Mp -M,)= JC'6C + DC0C + KB (4) where Mp = torque on cupula due to a pressure dif- ferential across the ampulla M/ = inertial reaction torque due to an input angular acceleration a Jc = inertia of the cupula and its surrounding endolymph Dc = viscous drag coefficient of the cupula K= stiffness of the cupula Utilizing the physical model of figure 3, the coefficients Jc and Dc can be approximated to be Jc = (5) Because of the lack of any of the elasticity properties of the cupula, its stiffness K can only be expressed in general terms. A general schematic diagram, which illustrates the interdependence of the cupula and the ducts in determining the cupula position which results from an angular acceleration is shown in figure 4. The overall transfer function, relating cupula position to applied angular acceleration, for the human semicircular canals is determined to be PULA SIDE MEMBRANOUS AMPULLA VESTIBULAR NEURONS AB 0.06 Cm. FRONT CUPULA ^ ,â ^ :RISTA ^VESTIBULAR NEURONS FIGURE 3. â A physical model for the cupula. 0.22 (7) By comparing the denominator to the original equation of Van Egmond, Groen, and Jongkees we find that Using 1 + AB 4.5X1Q-6 AB (8) (9) Therefore the calculated values of 7T/0 and are f=220 for AB == 10-4 cm
356 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION Jcs FIGURE 4. â Schematic model for cupula displacement 6 resulting from angular acceleration (a) inputs. The values of irjB and A/0 measured from ob- jective and subjective responses are approxi- mately 10 rad/sec and 1 rad2/sec2, respectively. Thus the calculated damping-to-inertia ratio for an "ideal" rigid torus-shaped acceleration sensor with the physical dimensions of the human semi- circular canals is at least an order of magnitude higher than the subjective responses indicate. Further, although the stiffness coefficient of the cupula is not known, a value of 10 < K < 100 dyne cm/rad is at least a realistic value for a gelatinous material such as we assume the cupula to be. In summary, the analyses of this section have shown that the effects of the viscous drag of the endolymph in the duct of the semicircular canals can be accurately represented by a first-order system with a time constant of about 0.05 second. They further show that the drag of the cupula on the wall of the membranous ampulla contributes some additional damping to the cupula-endolymph system. It has been shown that the fluid dynamic characteristics of the human semicircular canals have an order of magnitude higher frequency response than is observed from subjective and objective tests of the vestibular system. It appears that the observed high-frequency responses of the human semicircular canals are limited more by low carrier frequency of the vestibular neurons and that the experi- mentally measured values of the coefficients are more a measure of the response of the vestibular neurons, the "computation time" of the central nervous system, and neuromuscular delays than of the dynamic response charac- teristics of the semicircular canals. THE "ROLLER-PUMP" CHARACTERIS- TICS OF A FLEXIBLE TOROIDAL DUCT A flexible duct immersed in and containing an incompressible fluid will be distended by the influence of a linear acceleration if its density is different from the fluid, and a density dif- ference between the interior and exterior fluids will further accentuate this distention. As shown in figure 5, a flexible circular duct which is attached along its outer periphery to a rigid structure and is denser than the fluid surrounding it will have a constricted cross-sectional area where the acceleration field pushes it against
PROGRESS IN VESTIBULAR MODELING 357 FIGURE 5. â Illustration of the pumping action of the dis- tended duct when the linear acceleration field is rotated at a uniform angular velocity. its support, and it will be expanded where the acceleration pushes it away from its support. Further, as also illustrated in figure 5, if the linear acceleration vector a is slowly rotated at a constant angular velocity u>, the constriction will move along the outer periphery of the duct in phase with the rotation of the acceleration vector. The effect of the moving constriction is then to move or pump the fluid in the duct in the direction of the rotation. This pumping action works against the viscosity and inertia of the fluid, and at high angular rotation rates the fluid that is being pushed by the moving constriction cannot be displaced fast enough and thereby builds up a pressure gradient which expands the duct toward a uniform circular cross section. Thus, for high angular rotation rates of the linear acceleration vector, the mass of the fluid acts as a hydromechanical filter which reduces the duct constriction and along with it the pumping action of the flexible tube. For a flexible tube with an elastic flow restraint such as the cupula of the semicircular canals, the fluid is initially pumped against and displaces the elastic restraint which then produces a pressure differential across the tube. A static equilibrium state is then reached where the displaced elastic restraint provides sufficient pressure feedback to inhibit further flow. Thus, for a constant veloc- ity of rotation in a linear acceleration field, a constant cupula displacement can be maintained by this flexible roller pump action. By comparison of the cupula pressure differ- ential that is generated by a constant angular acceleration applied to a human semicircular canal, and the pressure differential across a re- striction in a flexible toroidal duct with dimen- sions similar to the human semicircular canals, the relationship between "roller-pump" displace- ment of the cupula and constant angular accelera- tion of the cupula can be established. This relationship between the rate of angular rotation, the magnitude of the duct restriction, and the equivalent constant angular acceleration that would produce the same steady-state cupular displacement in a l-g acceleration field is for the human semicircular canals where a = 0.015 cm K = 0.3cm p = 1 gm/cm3 /* = 0.0085 poise G = 980 cm/sec2 a, equiv 7 I o > rad/sec (11) To establish the applicability of the roller-pump principle to the semicircular canal, the relative magnitudes of the bias component of a slow phase nystagmus from rotation in a linear acceleration field and the steady-state nystagmus stimulated by constant angular acceleration can now be com- pared to determine how large a distention of the duct is necessary to produce a significant physio- logical response. From the data of Guedry (ref. 2), a 6Â°/sec bias component of vestibular nystagmus is noted for a 1 rad/sec rotation about a horizontal longitudinal axis. Several experiments have shown that such a 6Â°/sec slow-phase velocity would also result from a 0.6Â°/sec2 or 0.01 rad/sec2 constant angular acceleration. Solution of equation (11) for the value of AcIA when o>=l rad/sec Â«equiv = 0-01 rad/sec2
358 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION gives = 0.97 This is to say that a mere 3-percent constriction in duct area, or correspondingly, a 1.5-percent contraction of the radius of the membranous canalicular duct can produce sufficient roller- pump action to account for the observed bias component of nystagmus which results from con- stant rotation at 1 rad/sec in a l-g acceleration field. The question of whether or not a 3-percent con- striction in duct area is a realistic value remains a matter of conjecture. However, since it has been shown by Money et al. (ref. 3) that there is a density difference of the order of 0.1 percent between endolymph and perilymph (in pigeons) and that the duct is more dense than either fluid, by at least 1 percent, and since the duct tissue is only a few cell layers thick and thus quite flexible, it is at least plausible that the duct is sufficiently elastic to permit a 3-percent constric- tion in area in the presence of the l-g linear acceleration field. It is important to note that this roller-pump ac- tion does not require a continuous duct to produce the pressure difference which can force cupular displacement. A blocked duct will limit the amount of fluid that can be displaced and thereby reduce the cupula displacement, but it does not necessarily eliminate it. The rotation rates oj] and o>2 at which the roller- pump action diminishes are determined by the elasticity and strength of the fibrous attachments of the duct and are not readily calculable. How- ever, this cutoff frequency can be accounted for by adjoining to equation (10) a second-order lag term to provide for a diminished response at higher rates of rotation. From this we obtain a2pG (12) EXPERIMENTAL RESULTS To supplement the various experiments of Guedry, Benson, Bodin, Correia, Money, and others, and to investigate the variation of the bias and the amplitude of the sinusoidal component of vestibular nystagmus as a function of rotation rate, the MIT Instrumentation Laboratory pre- cision centrifuge with a rotating platform at a 32-foot radius was fitted with the Man-Vehicle Control Laboratory rotating chair simulator, and six experimental subjects were rotated at 5, 7.5, 10,20,30, and 40 rpm in a 0.3-g horizontal acceler- ation field. Nystagmus was measured with eyes open in the dark by use of a Biosystems. Inc., pulsed-infrared eye-movement monitor. The experimental setup is shown in figure 6. To minimize the influence of habituation and physical discomfort, the total rotation times were kept to a minimum. The subjects were brought up to the desired rotation rate relative to the boom while the boom was stopped. Nystagmus recordings were monitored until the acceleration transient subsided; then the centrifuge room lights were shut off to eliminate all possible light leaks in the rotating chair. The eye-movement monitors were calibrated, and the subjects were instructed to look straight ahead. The boom of the centrifuge was then brought up to speed (5.5 rpm) in about 5 seconds, held there for 2 minutes, then returned to zero. After the nystagmus from deceleration subsided, the eye-movement moni- tors were again calibrated to insure that no move- ment of the glasses had occurred during the run. Lights were then turned on, and the subject was accelerated to a different rotation rate. Three data runs were taken at each sitting, and a rest of at least 20 minutes was allowed between sittings. The rate and direction of rotation were randomly ordered for each subject. The slow-phase nystagmus velocities were calculated and plotted from the nystagmus re- cordings. The results showed a persistent si- (b) SinusoidaI aÂ»p. '/SEc 4 3 I 5 7.5 10 20 RPM 10 '/SEc 30 40 RPU FIGURE 6. â Bias (a) and sinusoidal amplitude (b) of slow- phase nystagmus from rotation in 0.3-gfield.
PROGRESS IN VESTIBULAR MODELING 359 nusoidal component at the period of rotation for all subjects at all rotation rates. For most sub- jects a clear bias component was observed for 5 and 7.5 rpm, and for some it still existed at 10 rpm. However, for 20, 30, and 40 rpm it was not observable in any of the subjects tested. The amplitude of the sinusoidal component increased with increasing rates of rotation. The ampli- tudes of the bias and the sinusoidal components of nystagmus are plotted as a function of rotation rate in figure 6 and their mean values and stand- ard deviation range for the six subjects tested are shown in figure 7. Magnitude of b 1 I e j I H j 5 7.5 10 30 RPM FIGURE 1.âAverage values of bias and sinusoidal amplitude (Â±lcr)for rotation in 0.3-gfield (six subjects). To compare these results with those of the horizontal rotation experiments, it is necessary, even though the assumption of linearity is tenuous, to normalize the results of the author's experiments with respect to a l-g gravity field. In figure 8 our normalized results are plotted along with those of Benson (ref. 4) and of Guedry (ref. 2). The model predicted bias component is also plotted in figure 8 for assumed upper break frequencies of o>i = o>2 = 7.5 rpm. The average bias components as measured by Guedry for 12 subjects at 10 rpm agree precisely with those found by the author. However, those found by Benson for eight subjects differ by about a factor of 2. It does appear that the predicted responses from the roller-pump model are borne out by the data in that at low and high rotation rates, the 30 '/SEc .-STEER O-GUEDRY o-BENSON ---MODEL PREDICTION I J 3 < 5 6 7 8 9 10 20 30 RPM Magnitude of sinusoidaI component VSEc â¢-STEER O-GUEDRY .-BENSON I I I 0 I Z 3 4 5 6 7 8 9 I0 20 30 10 RPM FIGURE 8. âSummary of available data of normalized bias and sinusoidal amplitude of human vestibular nystagmus from rotation in a 1-g field. bias component was not observable, and there was a general shape of measured response that did conform to the predicted second-order system. Further, the experimental data showed that the upper-break frequencies, which we were unable to calculate because of insufficient data, were in the range from 5 to 10 rpm. In summary, these experiments, which provide a slightly different vestibular stimulation than the "barbecue-spit" experiments of Guedry and of Benson or the "revolution-without-rotation" experiments of Money, further verify the hypothe- sis that rotation at a constant velocity in a linear acceleration field does provoke vestibular nys- tagmus. The results of the analysis show that a duct area constriction of only 3 percent provides sufficient roller-pump action to generate the ob- served bias component of nystagmus. And the upper cutoff frequencies o>\ and (o% were found experimentally to be in the range between 7.5 and 10 rpm.
360 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION REFERENCES 1. VAN EGMOND, A. A. J.: GROEN, J. J.; AND JONGKEES, L. B. W.: The Mechanics of the Semicircular Canal. J. Physiol., vol. 110, 1949, pp. 1-17. 2. GUEDRY, F. E.: Influence of Linear and Angular Accelera- tions on Nystagmus. Second Symposium on the Role of the Vestibular Organs in Space Exploration, NASA SP-115, 1966, pp. 185-196. 3. MONEY, K. E.; SOKOLOFF, M.: AND WEAVER, R. S.: Specific Gravity and Viscosity of Endolymph and Perilymph. Second Symposium on the Role of the Vestibular Organs in Space Exploration, NASA SP-115, 1966. pp. 91- 97. DISCUSSION Dietlein: The computers in black boxes involved in the spacecraft guidance and control are indeed complex and rather thought-provoking products of man's technical inge- nuity. I submit, however, that an even more challenging task and an acid test of scientific creative mettle is the model- ing of biological systems, particularly neurophysiological systems such as the multifaceted vestibular complex. Valentinuzzi: The good mathematical analysis performed by Dr. Steer concerning the hydrodynamics of the semicircular canal and, furthermore, the response of the semicircular canals to the changes of gravity direction are very useful and will help us. When I say help us, I am referring to experi- ments performed by Dr. Fernandez and myself, and we will be helped in the interpretation of two lines of work. In ex- periments with Coriolis acceleration applied in a continuous way, we have found that there is a contradiction between the prediction based on the classical equation and the experi- mental results; therefore, the correction introduced by Dr. Steer, I think, will improve the agreement we expect. On the other hand, Dr. Fernandez and I performed a series of experiments in cats last year in which we applied rotation about the cephalocaudal axis. This axis being horizontal, we tried to repeat in the cat what Benson, Bodin, and Guedry have done in the human being. In this case we have obtained a clear nystagmic response. Furthermore, the other type of experiments we have carried out consisted of rotating the cat about an axis which is perpendicular to the sagittal plane; that is, we have rotated the cat in the pitch plane in a con- tinuous way. In both cases the velocity was uniform. In the second case, when the cat was rotated in the pitch plane, the nystagmic response was clear and modulated in a si- nusoidal wave. From the point of view of the interpretation, we would say that the condition which Dr. Steer has con- sidered can give a reason for this kind of response. But we think that since there is the same modulation in both types of experiments, we cannot exclude the action of the otoliths, which are surely shifting on the macula in both kinds of rotations. Steer: I would attribute the sinusoidal component from my own limited experience to the otolith, no matter which axis you rotate about. But for the average value, I would at least conjecture that this type of roller-pump explanation is plausible. I noticed from Kellogg's counterrolling data pre- sented at last year's meeting that he showed a sinusoidal com- ponent which he attributed to the otolith function and the 4. BENSON, A. J.: Modification of Per- and Post-Rotational Responses by the Concomitant Linear Acceleration. Second Symposium on the Role of the Vestibular Organs in Space Exploration. NASA SP-115. 1966. pp. 199-211. bias component which he chose not to make any comments about because he did not have a theory for it. This would explain that. In a very brief mention in one of Dr. Guedry's papers, he commented that Hixson has observed, during head-over-heels rotation of the human at a constant angular velocity, that there is a bias component of nystagmus also. Any of these rotations where a canal is out of the plane of the applied linear acceleration should give rise to this roll-pumping action. Graybiel: In your experiments with plugged canals. Dr. Money, did you rotate your animals in the Earth-horizontal axis? Money: Dr. Correia and I have just finished an experiment wherein we spun cats about an Earth-horizontal axis before and after plugging all six canals. The results were unlike those obtained with counterrotation on three cats, and the nystagmus was eliminated by canal plugging. We have ro- tated about a dozen cats around the horizontal axis, and they have all retained constant velocity nystagmus in spite of their having all six canals plugged. The nystagmus is decreased from what it was before by something like one-third to one-half in the speed of the slow component and the frequency, but the nystagmus that is left is perfectly clear and obvious. It has a cyclical variation that is the same as in normal cats. Graybiel: I would like to recall at this point an experi- ment that Dr. Guedry performed using some of our subjects with bilateral loss of labyrinthine function. These subjects have been studied carefully over a long period of time. We assumed on the basis of functional tests that they had complete loss of canal function, with the exception of one ear in one subject. Irrigation with water at tempera- tures as low as 4Â° C for periods of a minute or more failed to evoke nystagmus with a single exception. Some manifested a slight amount of ocular counterrolling, and we thought this might be due to some residual otolith function. When Dr. Guedry rotated some of these subjects about an Earth-horizontal axis, nystagmus was evoked in some instances. And I am not over the shock of this yet. Lowenstein: 1 think this is a religious shock, sir. Graybiel: I think that one possible explanation is that the nystagmus may have had its origin in the otolith apparatus, and this cannot be ruled out. Guedry: I should like to clarify several points. During rotation at 60Â°/sec about an Earth-horizontal axis, some
PROGRESS IN VESTIBULAR MODELING 361 of these LâD subjects had nystagmus, but only one of 11 had a clear unidirectional nystagmus, and this for only one direction of rotation. In the other direction, nystagmus was present, but it was weak and of poor quality. Several of these L-D subjects had a fairly systematic direction-revers- ing nystagmus. Whether or not this reversing nystagmus came from residual otolith function, of course we do not know. The normal response during 60Â°/sec rotation about an Earth-horizontal axis is clear, prolonged, unidirectional nystagmus. When normal subjects are spun at a rate of 180Â°/sec about an Earth-horizontal axis, after about 40 seconds of such rotation they exhibit direction-reversing nystagmus and report subjective events like the responses of L-D subjects at 60Â°/sec. Anliker: I am fascinated by the presentation from Dr. Steer. I should like to add a few comments in support of the possibility that the semicircular canals could respond to circular translation. We think that the rotating pressure field which you have alluded to briefly is producing pressure waves in the semicircular canals. In reality, the canals do not constitute a rigid system and allow for the development of pressure waves in the membranous and in the bony canal. The rotating pressure field is so strong that we anticipate a sizable response of the cupula on the basis of our mathemati- cal and experimental model studies. Also, the waves induced by the rotating pressure field are much stronger than the roller-pump effects which you have mentioned, which would be due to the density difference between the membranous canal wall and the endolymph and perilymph. We only have a density difference of the order of 1 percent, and such a small volume taken up by the membranous wall itself, that 1 cannot see how you can get such a strong force that would produce a roller-pump effect, as you have convincingly demon- strated with mercury and water, where you have a density difference of 13 and not 1 percent. Steer: I formulated it in a way which is extremely simple to look at. This variation in cross-sectional area, An/A, that I have indicated in the block diagram could well be caused by a pressure gradient acting on the fluids, as well as it could be by a tiny density difference in the duct. I tried lo formu- late it in this general way. I looked at it and said, "Look, just a very small change in area makes a significant contribu- tion." It may well be that a fairly intensive circulating pres- sure wave could be responsible. However, I would add to your comment that it would have to be a flexible duct for the special waves to take effect. Anliker: Yes. Well, at least part of the duct has to be flexible, not all of it, but part of it. Steer: At least a portion of it has to be. Anliker: Yes; 1 fully agree with you. Graybiel: If you subject the horizontal semicircular canals to a very high angular acceleration or deceleration when the head is upright and the canals most responsive, and then you do not get a response but do in the Earth- horizontal axis, some way or other this does not add up. Anliker: We should emphasize that in our studies we have been looking at only the end organ, that is, the mechanical behavior of the semicircular canals plus maybe the otoliths, and not the sensory mechanisms, nor the neural conductors. nor the CNS, etc. We are focusing our attention on a small part of the problem. Maybe our conclusions will be compatible with what you find from neural responses and perception. Graybiel: Dr. Money, do you think it is reasonable to believe that, over a long period of years with all the fluid gone and a little bit of cupula left, the crista still might retain its function? Money: I have had experience with cats that have had their canals plugged for up to 4 years. As far as I can tell, the crista is still putting out its resting discharge after 4 years. The evidence for this is partly histological. The cristas still look normal after that length of time. Nothing seems to have shriveled up. The canal arm is plugged in one spot, but the crista apparently is histologically normal. The second bit of evidence for thinking that these cristas are still working is that, on some of these cats, after they have had all six canals plugged for a long time, I have done a labyrinthectomy on one side. Then you get the resting nystagmus of unilateral labyrinthectomy. In fact, I even did a second labyrinthectomy on one of these cats and got Bechterew's nystagmus when the second ear was done. So apparently these cristas in the plugged canals are still putting out their resting discharges. Graybiel: Was there endolymph fluid? Money: Yes. The membranous canal except near the plug was apparently normal and the canal was open. Graybiel: In that case your finding is a perfectly reasonable expectation. Money: Incidentally, the cats which I described as having this horizontal-axis, constant-velocity nystagmus with all six canals plugged, were entirely lacking in any response to angular acceleration about a vertical axis. We did quantitative tests at 10.0 and 20.0 rpm, and we also did some quick stops from 40.0 just to see if we could get anything out of them. There was nothing in response to vertical- axis acceleration. We found the specific gravity of endolymph in pigeons to be 1.0033 and of the perilymph to be 1.0022. More recently we have measured the specific gravity of sections of mem- branous canal including the endolymph inside and this was 1.03. So there is a 3-percent difference between membranous canal sections and perilymph. We have also measured the specific gravity of endolymph droplets including the cupula. We do not know the ratio of cupula to endolymph, but it is of the order of 25 percent. We could not demonstrate any difference between the specific gravity of the cupula plus endolymph globule and globules of pure endolymph. If there was a difference in the specific gravity of cupula and endolymph that was greater than one part in 2500, we think we would have picked it up; we did not see anything at that level. Anliker: May I add to my previous comment and stress the fact that we would also predict cupula deflection as a result of linear acceleration because of the nonsymmetry of the semicircular canals and the stiffness distribution, again on the basis of waves being generated. Steer: Based on the discussion we had the other day, I would disagree that the cupula is affected in this way because
362 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION you drew me the picture of an asymmetric structure and you are saying, "If I sum the pieces of the moments about the geometrical center, I have a much larger mass over here than over here. I have a net torque." Anliker: You are alluding to the hydrodynamic paradox. Of course if it would be perfectly rigid, you would not have a flow due to the inertial torque. Steer: If it were perfectly rigid, you would not, because the only thing that is important is the sum of torques about the center of mass. Anliker: But you do not have perfect rigidity and there- fore you have flexibility. Steer: If you have flexibility and a substantial mass in balance, it would be possible, but I still doubt it, the reason being that you need off-axial symmetry, off-axial asymmetry. The fact that you have a gradient field and a flexible duct will force some symmetry of the duct to begin with, if the duct is flexible. Anliker: I am referring to the canal itself plus the cupula. If you look at the cupular region, I think that you do not have the same stiffness as elsewhere. Steer: I think you have a much greater stiffness if you look at the cupular region, because it is much more firmly attached to the inner edge of the ampullary wall than any other part of the canal. Anliker: I think maybe we should continue this afterward and not put the patience of the audience to a test. Uillingliiiin: Did you measure the phase angle between the rotating linear acceleration vector and nystagmus; and if so, was it related to the rpm? Steer: Only in some cases. Unfortunately, with the chair rotating at one velocity and the arm rotating at another, it was not always possible to synchronize the phase because we did not have position pickup on the chair. At the lower rpm's we did, and the maximum nystagmus corresponded to the left side down, and the minimum of the nystagmus swing corresponded to right side down, as Dr. Guedry has found. At the higher rpm we did not check the phase. I thought of it too late to put a sensor on; the data had already been taken.
PART II: A MODEL FOR VESTIBULAR ADAPTATION TO HORIZONTAL ROTATION1 LAURENCE R. YOUNG AND CHARLES M. OMAN Massachusetts Institute of Technalogy SUMMARY Short-term adaptation effects are seen in subjective sensation of rotation and vestibular nystagmus. The mathematical model for semicircular canal function is improved by the addition of two adaptation terms (approximately 1/2-minute time constant for sensation and 2-minute time constant for nystagmus) to the overdamped second-order description. Adaptation is represented as a shift of reference level based on the recent history of cupula displacement. This model accounts for the differences in time constants among nystagmus and subjective cupulograms, secondary'nystagmus, and decreased sen- sitivity to prolonged acceleration. INTRODUCTION The lack of a suitable mathematical descriptor for adaptation and habituation has been a per- sistent difficulty with the simple, second-order torsion-pendulum mathematical model for semi- circular canal response (ref. 1). In particular, close examination of data for two types of rota- tion experiments indicates that both the nys- tagmus and the subjective response are funda- mentally different from that predicted purely on the basis of a second-order model, as shown in figure 1. 1. Experimentally, the sensation of rotation to sustained constant angular acceleration has been shown to decay (ref. 2), whereas the model pre- dicts a constant steady-state sensation of angular velocity and nystagmus. 2. The response to a sudden change (step) in angular velocity has been observed to overshoot, whereas the model predicts an exponential decay to the threshold level. Aschan and Bergstedt (ref. 3) noted that the nature of this overshoot, flnqular Acceleration Response Model T Trend of Experimental Results Time Response to Acceleration Step 1 This paper is based on research supported by National Aeronautics and Space Administration grants NGR 22- 009-156 and NSG-577/22-09-025. It contains excerpts from "On the Biocybernetics of the Vestibular System" by L. R. Young, presented at the Ford Institute Symposium on Biocybernetics of the Central Nervous System, Washing- ton, D. C., Feb. 1968, and also the S.M. thesis of Charles M. Oman, MIT, Department of Aeronautics and Astronautics, Sept. 1968. (Cupula Return Phase) Time Response to Velocity Step FIGURE I.âSecond-order "torsion pendulum" model. 363
364 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION or secondary nystagmus, depended on the length of the duration of the primary nystagmus. 3. There is ample evidence that the dynamics of the subjective velocity response are fundamen- tally different from those of the nystagmus: A consistent difference appears in the time con- stants conventionally determined for the second- order canal model, depending upon whether they are estimated from eye-movement recording or from measurements of subjective sensation of rotation (cupulograms). In particular, Groen (ref. 4) and others pointed out that the long-period time constant of the cupula return phase was estimated at approximately 10 seconds for the horizontal plane by subjective cupulometry, but was estimated at 16 to 20 seconds based on the nystagmus cupulogram. A fundamental assump- tion behind the second-order model is that both the subjective sensation of rotation and the angular velocity of slow-phase nystagmus are proportional to cupula displacement. Thus one would expect that they would follow a similar time course of decay until passing through their respective threshold levels, thus indicating the ratio of viscous damping to cupula spring constant. Apparently, this is not the case. As a result of these discrepancies, efforts have been underway at MIT to improve the mathe- matical model for the canals by including a mathematical descriptor for the effects of short- term adaptation. (Adaptation here refers to the short-term change in response resulting from a continuing stimulus, whereas habituation is taken to mean a decreased sensitivity to a re- peated stimulus pattern.) A MODEL FOR ADAPTATION A model was developed which cascaded an adaptation operator for nystagmus and for subjective response with second-order dynamics representing the physical behavior of the cupula itself, as shown in figure 2. This approach accounts for all the previously mentioned difficulties with the second-order formulation. The model was developed to fit average response data from a number of sources, .and allows a reinterpretation of the results from classical experiments on nystagmus and subjective response. I.nt C>- i0, I Com FIGURE 2. âModel for subjective sensation and slow-phase nystagmus velocity for rotation about a vertical axis. The fundamental assumption in the model is that adaptation has associated with it a short- term homeostatic mechanism which results in a shift in the zero sensation and nystag- mus-velocity-response reference levels. We hypothesize that the cupula-response signal undergoes more rapid adaptation in the sub- jective path than in the nystagmus path. It should be emphasized, however, that despite the success of the model in accounting for the differences between nystagmus and subjective response, tittle should be inferred directly from the mathematical adaptation operator about the underlying physical mechanism associated with this process. While the form of the model is based on what is known about the dynamic characteristics of the canals, the models are of the nonrational parameter type. The mathe- matics is not intended to reflect any exact physical mechanism in more than a general way. The approach is similar to that of a control engineer examining the dynamic characteristics of the sensors of a feedback system. The models are, however, valuable in that they provide a unifying mathematical format, which can be used to suggest new experiments and predict their results. In defining the parameters of the adaptation model, published experimental results on acceleration steps and impulses were examined. It is particularly instructive to study the data of Hulk and Jongkees (ref. 5) and the experi- mental results obtained by Guedry and Lauver (ref. 2) measuring the sensation of angular velocity in response to steps in angular accelera- tion. Whereas the nystagmus responses to steps of angular acceleration generally follow
PROGRESS IN VESTIBULAR MODELING 365 the second-order model, rising exponentially to a constant level, the subjective responses in fact begin to decline after 20 to 30 seconds of constant acceleration stimulation. These ob- servations, combined with the consistent dif- ferences between the frequency response phase lags of subjective and nystagmus measurements, lead to a preliminary model for subjective sensa- tion and nystagmus slow phase velocity. We assume that one of the significant aspects of short-term adaptation is a bidirectional phenomenon which in some way results in a shift- ing of the zero velocity reference level by some fraction of the time integral of the response itself. In particular, if R is the human response to the angular acceleration, either as subjective velocity or slow phase nystagmus velocity, and f (t) is the cupula position at the time t, then (1) T(, Jo where the second term on the right-hand side of equation (1) accounts for the shift in the re- sponse reference level by a fraction of the time integral of the response itself. The input-output transfer function of the adap- tation operator itself appears as R(*) â¬(>)' s + â Ta (2) in Laplace transform notation. The adaptation dynamics represented by the expression in equa- tion (2) exhibits a simple exponential decay with a time constant of ra in response to a step deflec- tion of the cupula. As a model of the dynamics of the physical end organ, we maintain the torsion pendulum form. Steer's rigorous fluid-dynamics analysis (ref. 6) has given support to the adequacy of the overdamped second-order transfer function. Our approach was to hypothesize two paths for the model output, one for the subjective response and one for the nystagmus slow phase velocity. Different adaptation time constants for each pathway were determined and placed in series with a second-order cupula transfer function resulting in the model shown in figure 2. The model was simulated on a GPS 290T hybrid computer. The responses were calculated for various kinds of inputs both with and without a threshold. For the subjective path, linear adaptation dy- namics of the form [s/(s + 0.033)] representing a 30-second time constant (TO) were included. To allow a fit to acceleration latency-time data, a threshold nonlinearity and a pure time delay of 0.3 second were also added. The dead zone of the nonlinearity is taken as 1.5Â°/sec. Note (fig. 2) that the threshold is interpreted in terms of subjective angular velocity rather than me- chanical displacement of the cupula. The cupula return phase time constant of the second-order physical dynamics was chosen to be 16 seconds. Figure 3 illustrates the response of the subjective path of this model to a step change in angular velocity such as that used in the cupulogram test. .The predicted cupula reponse is also shown. Note that the predicted subjective angular velocity decays more rapidly than the cupula return and over- shoots slightly. Also shown in figure 3 is the nystagmus response which exhibits the relatively weak 120-second time constant adaptation dynamics [s/(s +0.008)] in the oculomotor loop of the model. The nystagmus curve decays with prac- tically the same time constant as does the cupula deflection. When the model nystagmus data taken for several different velocity step magni- tudes are examined in terms of the duration of postrotation nystagmus or, equivalently, the time until the model curve passes below threshold, they indicate a long time constant of about 16 seconds. If the subjective angular velocity is 40 44 46 FIGURE 3. â Velocity-step response of MIT semicircular canal linearized model to lÂ°/sec step in horizontal plane.
366 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION similarly treated, however, and the time duration of subjective response is estimated as though the entire system were second order, the apparent time constant is approximately 10 seconds. These two values agree very closely with the observed objective and subjective time constants derived from cupulometry. Thus, the effect of the adaptation operator in the subjective loop is to shorten the apparent (second-order) time constant, and to explain the important discrep- ancy mentioned earlier. The linearized subjective response overshoots, as shown in figure 3. A large-enough accelera- tion impulse will cause the magnitude of the over- shoot to exceed threshold, and a "second effect" or subjective reversal of direction is predicted. This reversal has been noted on many occasions. The adaptation model also predicts an overshoot for nystagmus response to velocity steps, but its magnitude is not nearly so great as that of the subjective overshoot. "Nach-nach nystagmus" or "secondary nystag- mus" has been described by investigators (refs. 3 and 7). For example, Aschan and Bergstedt (ref. 3) noted that constant angular accelerations of 2Â°/sec2 for 25 seconds gave rise to "a secondary phase of nystagmus in a contrary direction with a delay of 20 to 30 seconds between the two phases," while larger accelerations of 3Â°/sec2 for 10 seconds and 4Â°/sec2 for 6 seconds produced no secondary nystagmus in the majority of subjects. Aschan and Bergstedt concluded that since the peak cupula deflection should be the same in all three cases on the basis of the model of Van Egmond et al., the strength of the second- ary nystagmus depends particularly on "the length of the duration of the primary nystagmus induced." As shown in figure 4, the results of the Aschan and Bergstedt experiments are predicted by the adaptation model. (Note that equal peak cupula deflections are predicted only with the time constants of the original Van Egmond model.) Apparently, then, second effect can also be attributed to the effects of adaptation. Since it was shown that the adaptation model produced generally correct responses to velocity steps, the time constants determined by the fit with experimental data were verified by matching the model response against data for AcceIeration |Q.5 | â \~j~\ StimuIus (s + 25Ks+.0625)(s + .008) \/ ' 1 ^ Nystagmus SIow Phase : VeIocity AnguIar 4 AcceIerat ion 3 StimuIus 2 Degrees /sec2 I0 20 30 4O 50 60 70 80 9O IOO I10 NondimensionaI CupuIa Position VeIocity of SIow Phose Nystagmus Time (Seconds) 25 Sec Detoy \ Secondary Nystagmus in 2Â°/sec2 Case OnIy FIGURE 4. â Model response for Aschan and Bergstedt experi- ment (ref. 3). higher order inputs. Guedry and Lauver's results were available to check the model for consideration of long-duration steps of angular acceleration. As seen in figure 5, the shape of the transient data agrees with the model for both nystagmus response and for subjective sensation. Note that, whereas adaptation effects are not readily noticeable in the nystagmus response to velocity steps, a definite decay is predicted in the acceleration step tests lasting more than about 30 seconds. This phenomenon is not predicted by the torsion pendulum model alone. I- In 20 30 4O SO SO TO r( Seconds) FIGURE 5. â Comparison of adaptation model for vestibular response with Guedry and Lauver experiments (ref, 2) for an angular acceleration step (l.SÂ°/sec2).
PROGRESS IN VESTIBULAR MODELING 367 Acceleration steps have often been used in experiments to determine the latency time to sensation of rotation for constant angular acceleration. Latency times were calculated for the model subjective response. The model match with experimental data of Meiry (ref. 8) and of Clark and Stewart (ref. 9) is very good, except at low accelerations, as seen in figure 6. This may be attributable to the fact that for the low accelerations, the response is very near the limit of detection and the response times are unreliable indications. IUU - | i | i | i | i|i| 't 60 â - 40 â â 30 - - 20 â Â° "I deviation a Experimental data from Meiry, with one standard â "2 in yx x Data from Clark and Stewart - -2 6 â \ o â Model prediction \. x â a> >5 a . 3 â Â£2 x Vxsa â 5? .6 ^-DDOXQ[I _I .4 â â¢â ^__]__^ â 3 - "~" â¢^ .2 - - , 1 , 1 , ,il 1 i 1 i 1 , 1,1 ! i 1 , i I, 2 4 6 10 2 4 6 810 20 Angular Acceleration deg/sec2 40 70 FIGURE 6. âAdaptation model for subjective response latency to constant angular acceleration. Meiry data from refer- ence 8; Clark and Stewart data from reference 9. The frequency response of the linearized model for subjective response is shown in figure 7. The frequency response is very similar to that of the simple second-order model used to match subjective data over the midrange of frequencies, where all the test results lie. The frequency response for nystagmus velocity is shown in figure 8. As is the case for the subjective frequency response, the adaptation model predicts even greater phase lead and lower amplitude ratio for very low frequencies than does the second-order model. It should be noted that the time constants and thresholds specified for the model are the result of a fit of a particular set of average re- FREOUCNCt (Rodion* pw Secofid) FIGURE 7.â Frequency response of adaptation model for sub- jective sensation. Katz data from reference 10. sponse data. Data from individual subjects may deviate somewhat from the responses pre- dicted here. In this regard, however, it is interesting to note that, working independently, Jones and Malcolm ("Quantitative Study of Vestibular Adaptation in Humans," this sym- posium) of McGill University have measured nystagmus response for long-duration angular accelerations and also observed that their results were at variance with the second-order model. An adaptation operator for the nystagmus path- way was hypothesized, and an analog computer was used to match the model with the experi- mental data. The resulting model showed remarkably good fits for individual experimental data, as well as for average response. Sig- nificantly, while the assumptions made in the FREQUENCY ,n Aod,vn, 'S*c FIGURE 8. â Frequency response of compensatory eye move- ments for linearized model: eye velocity â input velocity* 10.5si -25)(s + 0.0625)(s Katz data from reference 10; Hixson and Niven data from reference II.
368 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION derivation of the adaptation operator were quite different in the McGill study, they lead to a dynamic expression for an adaptation operator identical in form with that of the MIT study. CONCLUSIONS Dynamic vestibular adaptation effects are evidenced in both the oculomotor and subjective responses. These effects can be incorporated into a control-theory model which accounts for the measured differences in nystagmus and subjective responses not predicted by the tor- sion-pendulum model: (1) cupulogram slopes, (2) secondary nystagmus, and (3) decaying re- sponse to sustained acceleration. Adaptation effects will only be readily observable in long- duration responses to sustained angular accel- eration. The adaptation operator cannot, however, be interpreted as a rational parameter model of a physiological process. Previous studies (ref. 4) have implied that adaptation might, in some way, be due to a change in the transmission gain of the neurological pathways. The implication of the adaptation operator developed here is some- what different in that one would not conclude that the transmission gain was changing, but rather that the zero-response reference level was being altered. This is not meant to imply that transmission gain changes do not take place, but only that the overall behavior of the system seems to involve a dynamic process which pro- duces a change in the reference level. The adaptation model can predict the general form of the average response of a normal, alert individual to angular accelerations in a horizontal plane, provided linear accelerations are not present. Possible effects of bias are not in- cluded. The model fails to predict the detailed time course of individual responses and does not account for the effects of habituation to repeated stimulus patterns. REFERENCES 1. VAN EGMOND, A. A. J.; GROEN, J. J.; AND JONGKEES, L. B. W.: The Mechanics of the Semicircular Canal. J. Physiol., vol. 110, 1949, pp. 1-17. 2. GUEDRY, F. E.; AND LAUVER, L. S.: Vestibular Reactions During Prolonged Constant Angular Acceleration. J. Appl. Physiol., vol. 16, 1961, pp. 215-220. 3. ASCHAN, G.; AND BERGSTEDT, M.: The Genesis of Sec- ondary Nystagmus Induced by Vestibular Stimuli. Acta Soc. Med. Upsaliensis, vol. 60, 1955, pp. 113-122. 4. GROEN, J. J.: The Semicircular Canal System of the Organs of Equilibrium. I. Phys. Med. Biol., vol. 1, 1956, pp. 103-117: II. Phys. Med. Biol.. vol. 1, 1956-57, pp. 225-242. 5. HULK, J.; AND JONGKEES, L. B. W.: The Turning Test With Small Regulable Stimuli. II. The Normal Cupulogram. J. Laryngol.. vol. 62, 1948, pp. 70â75. 6. STEER, R. W., JR.: The Influence of Angular and Linear Acceleration and Thermal Stimulation on the Human Semicircular Canal. Sc. D. thesis. Massachusetts Institute of Technology, 1967. 7. BARANY. R.: Physiologic und Pathologie des Bogengang- apparates beim Menschen (Funktionspriifung des Bogengangapparates). Klin. Studien, Deuticke (Wien, Leipzig), 1907. 8. MEIRY, J. L.: The Vestibular System and Human Dy- namic Space Orientation. Sc. D. thesis, Massachusetts Institute of Technology, 1965. 9.' CLARK. B.; AND STEWART, J. D.: Perception of Angular Acceleration About the Yaw Axis of a Flight Simulator. Aerospace Med.. vol. 33, 1962, pp. 1426-1432. 10. KATZ, G. B.: Perception of Rotation âNystagmus and Subjective Response at Low Frequency Stimulation. S.M. thesis, Massachusetts Institute of Technology, 1967. 11. HIXSON, W. C.: AND NlVEN. J. I.: Frequency Response of the Human Semicircular Canals. II. Nystagmus Phase Shift as a Measure of Nonlinearities. NSAMâ 830. NASA Order R-37. Naval School of Aviation Medicine, Pensacola, Fla., 1962.
PART III: A QUANTITATIVE STUDY OF VESTIBULAR ADAPTATION IN HUMANS RICHARD MALCOLM Canadian Forces Institute of Aviation Medicine SUMMARY A mathematical model for short-term adaptation to vestibular stimuli is presented in which the physiological response is driven by a signal proportional to the difference between the peripheral end-organ response 0r and a central reference level R in such a way that dR/dt i* (6C â R). From this relation a transfer function is derived relating slow-phase angular velocity of resulting nystagmus to the angular velocity of head rotation. The resulting model has been tested by comparing its responses to controlled step and ramp angular velocity stimuli with those of human subjects. A close match was obtained in all cases, which strongly supports the view that a significant adaptive effect is at play. The main time constant of the adaptive term was 82 seconds (S.E. 6.5) and the mean cupular restora- tion time constant Tc was 21 seconds (S.E. 1.5). It is suggested that previous values quoted for TV represent underestimates of the true value owing to superposition of the adaptive term here described. The adaptive term accounts well for the phenomenon of secondary nystagmus, especially during either strong stimuli or prolonged rotations. Some implications of the findings in relation to clinical and aviation medicine are discussed. INTRODUCTION Secondary nystagmus, or post-postrotatory nystagmus as it is sometimes called, has often been described in the literature (ref. 1). It is typically seen after a step change in angular velocity when, after cessation of the primary nystagmic response, a secondary nystagmus develops in the opposite direction from the primary one. The secondary response, although of lower amplitude than the primary one, usually extends over a relatively prolonged period, amounting in the experiments here described to 2 to 3 minutes. It is considered that this pro- longed action of the secondary response prob- ably represents an important source of misleading sensory information responsible for the genera- tion of illusions of movement during flight. This paper describes theoretical considera- tions and experimental results which strongly suggest that the secondary response is chiefly due to a quantitatively definable adaptive process which operates whenever a signal is generated in the semicircular canals. THEORETICAL CONSIDERATIONS The mechanical portion of the semicircular canals can be described as a second-order linear system, comparable to a torsion pendulum with heavy viscous damping (ref. 2). Thus, during angular acceleration, the inertia of the endo- lymphatic fluid contained in a semicircular canal generates relative fluid flow which is opposed by heavy viscous damping in the thin circular tube and a weak elastic restoring force due to cupular deflection. Assuming parabolic fluid flow, the response of this system, namely the angle of cupular deflection, can be related to the angular velocity of stimulus in the plane of the canal by the following transfer function (ref. 3): ( ks (7-,s+l)(7Vs + (1) where 6C = angle of deflection of cupula &H = angular velocity of head TI o polar moment of inertia of endolymph 369
370 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION J -T- viscous torque per unit relative angular velocity of fluid flow B Tc Â° B -5- moment of cupular restoration force per unit angle of fluid displacement in the canal K k=a JIK, where a is the proportionality constant relating cupular angle to angle of fluid displacement. In this experiment 7",- is the time constant of approach to steady endolymph flow on sudden application of a steady angular acceleration and, as indicated in the above reference, is too short to be significant during the patterns of movement employed in these experiments. Equation (1) may therefore be simplified for the present purposes to 0r 6H , , (S) ks or &â¢(*) = Tcs+l (2) in which TV is the time constant of exponential cupular return due to the interaction of elastic and viscous forces after sudden change in stimu- lus angular velocity. With this system a step change in angular velocity input will lead to an initial response (cupular deflection) followed by an exponential return to zero response with a time constant Tc o 16 seconds estimated by cupulometric nystagmography (refs. 4 and 5). The form of this basic response is illustrated in figure IA. If the oculomotor response were proportional to the vestibular input as suggested by results of Hallpike and Hood (ref. 6), this curve should also represent the time course of the slow-phase eye angular velocity during nystagmus. However, figure 2 exemplifies the time course of the slow-phase eye velocity ac- tually observed in a human subject during the present experiments. The primary response did not simply decay to zero as would be expected from equation (2); it reversed after 34 seconds to yield a prolonged period of secondary nystagmus. It is suggested in this paper that this form of secondary nystagmus is the result of a superim- posed adaptive process. This hypothesis rests on two assumptions. First, signals generated in the canals, proportional to the deflection of FIGURE I.âForm of time dependence of response to step change in head angular velocity. A: Cupular deflection 6C from resting position. B: The shifting reference level R nliifh tends to minimize 6C â R (dashed lines). C: Slow-phase eye angular velocity â¢'.',,, i the cupula, are compared to a shifting reference level central to the mechanical components of the canal. This reference level R changes such that it always tends to minimize the difference between 6C and R. Figure IB illustrates this point. R continually drifts toward the in- stantaneous value of the canal signal 6C, attempt- ing to minimize 6C â R. In particular, the rate of change of R is assumed to be proportional to the value of the difference 6C â R. Hence (3) where 6 is the constant of proportionality. In Laplace notation 60C - 0o 's + b-Tas+l (4)
PROGRESS IN VESTIBULAR MODELING 371 where Ta= 1/6 and is the adaptive time constant. Substituting for 6c from equation (2) (Tcs+l)(Tas+l) (5) The second assumption is that the slow phase angular velocity of resulting nystagmus is pro- portional to 6C-R- The dotted vertical lines in figure IB indicate 6C â R, while figure 1C shows 6C â R as a function of time. If 0eye represents the slow-phase eye angular velocity relative to the skull during nystagmus, then (8e- (6) The parameter m is included since there is no a priori reason why 6C and R are viewed with the same gains. If m is not unity, the model behaves as though it had a directional pre- ponderance. Substituting from equations (2) and (5) for Be and R, the vestibularly driven eye angular velocity (6eye) becomes mks 6H (7) where p is the constant of proportionality. This transfer function formally describes the relation between head angular velocity as input (stimulus) and resulting slow-phase eye angular velocity as output (response), and defines the variables concerned in a manner permitting experimental verification of the hypothesis from which it is derived. It may be noted here that in practice none of the subjects tested exhibited a significant directional preponderance (response uniformly biased in one direction), and accordingly the parameter m was held at unity throughout. EXPERIMENTAL METHODS After a number of preliminary experiments to determine suitable stimulus profiles, eight human subjects (three male, five female) ranging from age 18 to 39, and free from overt vestibular or oculomotor pathology, were exposed to two sets of stimuli. The first was a ramp velocity generated by an angular acceleration lasting 120 seconds and having an amplitude of 4.5Â°/sec2. This stimulus was chosen since, after approximately 60 seconds, the cupula should have reached a constant angle of deflection, and any changes in the response after this time should be attributable to adaptation. The second stimulus was a step change in angular velocity of 270Â°/sec requiring 10 seconds for completion. This stimulus was large enough to produce a clear secondary re- sponse without generating maximum eye veloc- ities so high as to be limited by eye dynamics. In practice, the ramp velocity was achieved by first taking the subject slowly to the appropriate angular velocity in one direction and leaving him in this steady state for 3 minutes to permit complete cupular restoration. For the ramp velocity profiles, the table was driven to follow the required acceleration through zero velocity to an angular velocity in the opposite direction equal to that of the initial steady condition. This procedure was adopted to minimize the maximum absolute angular velocity attained by the turn- table. The step change in velocity was achieved by taking the subject from a constant velocity to zero velocity. The subjects were rotated while sitting on a servo-controlled rotating chair with their heads fixed to the chair by a dental bite. Their arousal was maintained by having them compete for a monetary reward by working out factorial 10 mentally. The instantaneous eye position was recorded by means of dc electro-oculography (EOG) and static calibration was done at 10 degrees and 20 degrees left and right before and after each experiment. Before experimental runs, all subjects were dark adapted for at least 40 minutes in red light, previously shown to yield EOG gains indistin- guishable from complete darkness after this time (Gonshor and Malcolm, in preparation). All calibrations were performed in red light and all experiments in total darkness. The eyes- closed condition was adopted on account of difficulties with lacrimation, blinking, and ex- traneous facial EMG activity introduced with eyes open during these high-level stimuli. From the resulting nystagmographic records, beat-by-beat slow-phase angular velocity was
372 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION 100 01 V -o I 0 c - 50 -\ t-Vo (,& ,'co ISO I 200 ( o nd s FIGURE 2. âThe response of one subject to a sudden change in angular velocity. The slow-phase angular velocity of the nystagmus is plotted beat by beat against the time after the onset of the stimulus. The eye movement after reversal of direction at 34 seconds is secondary nystagmus. plotted (ordinate) against time elapsed after commencing the rotational stimulus (abscissa) as in figures 2 and 3. Early results were labori- ously measured by hand. But the majority of original records were analyzed by means of a tangent analyzer, similar in principal to that described by Benson and Stuart (ref. 7), but generating a direct writeout in graphical form on an XâY plotter, as in figures 2 and 3. The accuracy of eye angular velocity measurement was of the same order of magnitude as the size of the dots in these figures. To match the results obtained in this way with the mathematical model, the transfer func- tion defined in equation (7) was programed onto an EAI TR-20 analog computer whose output was displayed on an oscilloscope. The computer could be made to run at 500 times real time, causing the response to any chosen input wave- form to appear on the oscilloscope as a complete and continuous curve. The values of the parameters in the equation could be manually adjusted, producing an immediate change in the output curve viewed on the oscilloscope. The graphs of the eye velocity versus time (such as shown in figs. 2 and 3) were photo- graphed, and projected by means of an ordinary 35-mm slide projector onto the face of the oscil- loscope. The computer was adjusted so that the output time base corresponded to the time divisions of the graph, and the predicted curve was then matched by eye with the observed responses of the subjects. The superposition thus obtained was photographed for subsequent reference through semisilvered mirrors, the results appearing as in figures 4 and 5. The matching procedure leading to the values of Tc and TH in table 1 used the following criteria
PROGRESS IN VESTIBULAR MODELING 373 44 01 C â¢ â¢ â¢â¢â¢ ' *. .. â¢ â¢ â¢â¢â¢ .'â¢ â¢ â¢,' \ . ' â¢ "Â» â¢ â¢ t *â¢ \ , SO I 100 FIGURE 3. â The response of one subject to a velocity ramp. The slow-phase angular velocity of the nystagmus function of the time after onset of the stimulus. seconds I'.N plotted as a for obtaining the best fit between the model and the observations: 1. The parameters TV and Ta were adjusted so that the model should fit with similar accuracy, the data from both stimuli for a given subject. 2. Parameters Tc and Ta obtained from the visual fit of a given set of data should be reason- ably reproducible (see table 1). RESULTS Figures 1 and 6 illustrate the forms of response to be expected from the model defined in equa- tion (7) for a condition approximating TV. = 47V. In all curves (thick lines) the ordinate indicates response; and the abscissa, time elapsed after commencing the rotational stimulus. The thin line in figure 6A gives the imposed stimulus angular velocity which was a ramp followed by steady angular velocity. The curves in figures IA and 6A represent the change of cupular angle (6C) with respect to time. As previously mentioned in the theoretical con- siderations, a stepwise stimulus generates an initial response followed by an exponential decay. The response to a ramp stimulus rises with the same exponential time course as in figure IA to achieve an asymptotic level which is held steady until cessation of the acceleration (fig. 6A). On assuming steady angular velocity of stimulus (6n) the response decays to zero. In the fi-curves the hypothetical reference levels R are shown with their time course de- fined by equations (3) and (4). The vertical dashed lines between 0r and R give the value 6e â R which determines the instantaneous slope of the reference curve R. In the C-curves the final oculomotor responses, manifest as the slow-phase angular velocity of
374 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION FIGURE 4. â The photographs show the superposition of the experimental data (dots), and the output of the analog computer (solid lines). The upper response is from a sudden change in angular velocity, while the lower one is from a velocity ramp. The ordinates give slow-phase angular velocity of the nystagmus, while the abscissae give the time in seconds after the onset of the stimuli.
PROGRESS IN VESTIBULAR MODELING 375 FIGURE 5. â The entire curve, from which the points and dotted curve were taken for figure 7. The dots represent the experimental points while the solid line represents the computed response. resulting ocular nystagmus and defined by equa- tion (7), are plotted. The deviations of C-curves from /4-curves are easily seen. Not only is con- siderable secondary nystagmus evident, but the whole shape of the response is changed in a sys- tematic way. It is particularly important to ap- preciate that if curve 1C is plotted on log-linear graph paper, only the portion above zero is nor- mally visible and gives the impression of a decay which is considerably more rapid than the basic exponential decline in figure 1A. This matter will be referred to again in the discussion. Figure 2 illustrates the plot of resulting slow phase eye angular velocity (ordinate) against time, obtained from one subject by the analytical process described above. Each spot gives the velocity during one nystagmic beat. All nystag- mic beats from one experimental run are in- cluded. In practice, the step change of angular velocity occupied approximately 10 seconds, which accounts for the initial rising response. The subsequent primary response decayed smoothly through zero into a prolonged secondary phase of reversed nystagmus. The values of points on the zero ordinate were obtained from clearly defined horizontal lines on the original eye-movement record, interspersed with well- marked saccades, and could be easily measured. It is incidentally noteworthy that the curve passes smoothly, rather than discontinuously, through this zero, the theoretical implications of which will be discussed below. Figure 3 is a similar plot obtained from the same subject as in figure 2, exposed to the
376 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION TABLE 1.âExperimental Values for the Canal Cu.pu.lar Restoration Time Constant Tc and the Adaptation Time Constant Ta for Each of the Subjects Tested Subject TV, sec Ta, sec A B' A B1 JR 17.5 15.5 18 23 21 26 30 15.3 14 15.2 23 20.5 20.5 29.5 32 14 63 82 105 66 125 78 58.5 81 66 81 93.5 66 150 64 53 83 DC. VS JO CN LS DP AF ... . Mean2 S D- 21 5.9 1.5 82 25.8 6.5 S.E.2 ' Col. B values were obtained 10 days after those in col. A. 2 Mean, S.D., and S.E. values are calculated from the com- bined data in cols. A and B. FIGURE 6. âform of time dependence of response to ramp velocity of the head (6H). A, B, and C as in figure I. stimulus depicted in figure 6/4 and described nu- merically under "Experimental Methods." This was the only record in which "lumping" of data points tended to occur on the zero ordinate. The similarities between the plots in figures 2 and 1C, and 3 and 6C are striking and form the basis of the numerical analysis. Figure 4 (top and bottom) illustrates examples of the actual fits obtained on the oscilloscope face as described under "Experimental Methods" for the two plots shown in figures 2 and 3, respec- tively. The values of the time constant of cupular restoration Tc and the adaptive time constant Ta calculated from the relevant potentiometer settings on the analog model of equation (7) are given in table 1 for all subjects and all experi- ments. The two columns under each parameter heading give duplicate values obtained from curve fittings on a single set of data plots per- formed with a 10-day interval between the fitting procedures, a period sufficiently long to forget prior knowledge of results. The duplicate sets of results for each time constant indicate reason- able reproducibility. The standard deviation and standard error values are calculated from the combined results from first and second fittings. Mean values for cupular time constant and adaptive time constant were TV = 21 seconds (S.E. 1.5) and Ta = 82 seconds (S.E. 6.5), respectively. DISCUSSION Results such as those exemplified in figures 2 and 3 demonstrate dramatically how wide the divergence of physiological response to rotational stimulation of the canals can be from that pre- dicted by the simple torsion pendulum model usually considered a fair approximation of the cupular-canal-endolymph system. The fact that the recorded divergence of these objective results could in all subjects and all experiments be adequately accounted for by the adaptive model here proposed, strongly suggests that such an adaptive function, or one closely resembling it, is in fact constantly active in all circumstances. It appears that a similar phenomenon may account for subjective effects as well (Young and Oman, personal communication).
PROGRESS IN VESTIBULAR MODELING 377 The findings raise the question, What func- tional role could be served by the adaptive effect here described? In attempting to answer this question, it is important to appreciate first that the long time constant attaching to the adaptive phenomenon appropriately precludes it from interfering significantly with the active vestibular sensory message during the relatively short, sharp head movements of everyday life. On the other hand, long time constant adaptation would be highly effective in tending to maintain, over long periods, the steady state, or dc, balance of the differential inputs impinging on the central nervous system (CNS) from the two sides of the head. The physiological implications of this become apparent when it is appreciated that the average neural discharge from each ampulla has a resting value which is increased by rotation in one direction and decreased by rotation in the other direction (refs. 8 to 11). As pointed out by Melvill Jones in 1965 (ref. 12), this evi- dence, coupled with results of unilateral canal plugging experiments (refs. 13 and 14), indicates that the CNS acts differentially upon the signals from pairs of canals. Let the resting discharge rates from a pair of opposite canals be A and 6, respectively. It may then be postulated that reflex response to canal stimulation will be in proportion to the differential term AâB, which, for dc balance, may or may not be zero in the stationary condition. But during skull rotation, since each canal is a mirror image of its contra- lateral counterpart, the change in firing rates will be from A to (A + M) and B to (fi-Afi). The CNS would then "see" these two inputs differentially and compare the new result with the resting condition (i.e., (A + bAâ Zf + AB) to (A â B)). In this notation the relevant change amounts to A/i + AZ?. But presumably such a change would be indistinguishable to the CNS from a change in the value Aâ B due to natural biological drift or some pathological cause. However, if the reference level R proposed above always shifted toward the difference A â B, an effective dc balance would be maintained in- definitely. The process could be akin to auto- matic maintenance of the dc balance in a dif- ferential amplifier. The value of such a feature in the canal vestibular system is further em- phasized by the fact that the sensory signal is essentially one of angular velocity; and hence a maintained signal, even though very small, would in time indicate a large change in angular position. In the present context, the significance of this latter observation is highlighted by the fact that, in curves such as that in figure 2, the areas under the primary and secondary responses are of similar magnitude. Since the basic plot is here one of angular velocity, this implies that the total angle (integral of angular velocity with respect to time) of primary response is roughly equaled by the opposite secondary one. Since one's sense of attitude in space is determined by the impression of angular displacement at any given time, the rather surprising conclusion may be drawn that the secondary response, if sufficiently above "threshold," can exert an influence of the same order of magnitude as the primary one. It is of interest to note the rather long value of 21 seconds obtained for the mean value of the cupular restoration time constant (Tc). This value is considerably greater than those quoted under theoretical considerations. The difference can readily be accounted for by the fact that the earlier values were essentially obtained from data points restricted to the primary response, largely on account of the fact that results were usually plotted on log-linear graph paper. Since from the torsion pendulum model the response to a step change in stimulus angular velocity should be an exponential decay, it has been customary to approximate the plotted response with a straight line, the slope of which then gives the required time constant. Such a plot for one of the present subjects is given as the straight line in figure 7. From the slope of this line a value of 11.5 seconds emerges for the cupular restoring time constant. But adopting the best fit to the whole set of data, as depicted in figure 5 (which represents the same data as in fig. 7 but with primary response dis- played downward in this case), a value of 31 seconds emerges for TF for this individual, which is more than double the value estimated in the customary manner. The intermittent line in figure 7 represents the fitted line of figure 5 superimposed on the log-linear plot of data. It
378 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION may be noted that the separation of the two lines in figure 7 corresponds to the small deviation of points from the upward sweep of the continuous line in figure 5. This is perhaps an extreme example, but it suffices to indicate an inherent error in assessing definitive parameters of the canal system using the method illustrated in figure 7. The present considerations suggest that the tendency in the past has been to underestimate the canal time constant as a result of the adaptive effect here described modifying the end-organ response before generation of the functional physiological one. Some single-cell recordings from primary vestibular neurons of the rayfish have shown a similar pattern of behavior (ref. 11). Firing frequency, after changing in response to a change in angular velocity, tended to overshoot the rest- 00 I L T, i 3t see T- : S3 â¢â¢, FIGURE 7. â The log of the slow-phase angular velocity of nystagmus plotted as a function of time from the results in figure 5. If adaptation did not occur, the points should lie along a straight line, giving a mistaken value for Tc of 11.5 seconds from these results. The dotted line shows the computer fit based on Tc equal to 31 seconds. The semilog scale exaggerates the error between the- points and the dotted line in figure 5. ing frequency and only slowly return. This leads one to speculate as to the possible site of this adaptive process. Possibly the shift in reference level represents a shift in ions which occurs within the hair cells of the crista, so as to compensate the generator potential, following cupula deflection. Perhaps, as has been sug- gested by Lowenstein (personal communication), it may represent a depletion of the synaptic transmitter of the hair cells. Alternatively the adaptation may manifest as central feedback to the periphery via the efferent pathways (ref. 15), resulting in a sensitivity or gain change of the transducer. And, finally, a number of central mechanisms might combine to bring about the effect. It should be emphasized that the mathematical model is incapable of discriminat- ing between such processes and cannot therefore shed any light on their source. It could be that some or all of the above are acting simultaneously. As mentioned earlier, figure 2 shows that the response tends to cross the zero axis with little or no discontinuity. This poses the problem as to whether or not a threshold exists. Figure 8A shows diagrammatically what one would expect to find if a threshold to cupula deflection existed. During the time when the cupula was passing through its subthreshold region of deflection, one should get no nystagmus, and this causes a discontinuous curve as shown in figure 8A. However, if the problem was one of resolving the angle of cupula deflection, then the eye velocity during nystagmus would lie between the two lines shown in figure KB. The similarity between figure 2 and figure 8B leads to the conclusion that resolution of one angular acceleration from another is really the problem, and that if a thresh- old does exist, it is probably very small. It should be pointed out, however, that a form of threshold would exist if there was stiction be- tween the cupula and the walls of the membra- nous ampulla. This would be seen only when the subject was rotated from a resting position, and would disappear once he was moved. Should this be the case, the threshold for perception of a change in angular acceleration for a subject who has been at constant angular acceleration should be greater than for a subject who has just previ- ously been exposed to a change in acceleration.
PROGRESS IN VESTIBULAR MODELING 379 THRESHOLD A RESOLUTION B FIGURE 8.â A: The form of the response to a step change in head velocity expected (slow-phase angular velocity of nystagmus versus time) if a threshold to cupula deviation existed. B: The form of the response to a step change in head angular velocity to be expected if only finite resolution of i niniliii deflection existed. The response should tend to lie within the two lines, which represent the resolution limits. This point is of particular importance to pilots, since the thresholds found for humans during controlled experiments on smoothly moving platforms may be quite large compared to what the pilot can sense in a constantly moving aircraft. There are additional implications in the applied context of aviation. First, the unnaturally large and/or prolonged rotational stimuli commonly experienced in flight maneuvers probably gen- erate, at least temporarily, residual unidirectional effects in the vestibular system (ref. 16). Hence an adaptive capability may represent an impor- tant functional asset which is normally active in offsetting such an effect. Possibly failure to do so may be associated with generation of the biased impressions of attitude often referred to as "the leans." On the other hand, such "leans" may be due to the secondary effects which this paper attributes to adaptation. The methods here described provide the basis for tests by which adaptive capability might be as- sessed before selection for flying duties. Second, alteration of adaptive capability by the flight environment may be important to achieving proficiency as a pilot and is now amenable to testing. Third, as inferred in a general context above, the functional significance of the second- ary response may in some circumstances be approximately equal to the primary one. Pre- sumably in violent rotational maneuvers, such as repeated rolls and aerodynamic spinning, the adaptive term stands to introduce adverse effects which would not be accounted for by previously described physiological phenomena (ref. 17). Fourth, it is clearly important to incorporate the adaptive function in any model aimed at permit- ting calculation of the overall vestibular response to movement (ref. 18). From the clinical standpoint, the results indi- cate a certain lability in the conventional cupulo- metric turning test. It seems from the present work that the response to the test is composed of two main components, that due to cupular restoration and that due to subsequent adapta- tion. Possibly the effect of the adaptive mech- anism could mask a pathological cupular com- ponent, and vice versa. Second, it could be that pathological involvement of the adaptive mechanism might itself prove to comprise a significant clinical entity. Finally, it is of interest to speculate on the extent to which the present results reflect biological adaptive functions in other sensory channels. Possibly the adaptive principle and analytical methods here described could be employed to examine this question on a quanti- tative basis. REFERENCES 1. GRAYBIEL, A.; AND HUPP, D. E.: The Oculo-gvral Illusion. A Form of Apparent Motion Which May Be Observed Following Stimulation of the Semicircular Canals. J. Aviat. Med., vol. 17,1946, pp. 3-27. 2. VAN EGMOND, A. A. J.; GROEN, J. J.; AND JONGKEES, L. B. W.: The Mechanics of the Semi-circular Canal. J. Physiol., vol. 110, 1949, pp. 1-17. 3. JONES, G. MELVILL; AND MILSUM, J. H.: Spatial and Dynamic Aspects of Visual Fixation. IEEE Trans. Bio-Med. Eng. BME-12, 1965. pp. 54-62. 4. GKOEN, J.: Problems of the Semi-circular Canal From a Mechanico-physiological Point of View. Acta- Otolaryngol., suppl. 163,1960, pp. 59-67. 5. MELVILL JONES, G.; BARRY, W.; AND KOWALSKY. N.: Dynamics of the Semicircular Canals Compared in Yaw, Pitch and Roll. Aerospace Med., vol. 35, 1964, pp. 984-989.
380 THE ROLE OF THE VESTIBULAR ORGANS IN SPACE EXPLORATION 6. HALLPIKE. C. S.; AND HOOD, J. D.: The Speed of the Slow Component of Ocular Nystagmus Induced by Angular Acceleration of the Head; Its Experimental Determination and Application to the Physical Theory of the Cupular Mechanism. Proc. Roy. Soc. B, vol. 141,1953, pp. 216-230. 7. BENSON. A. J.; AND STUART. H. F.: A Trace Reader for the Direct Measurement of the Slope of Graphical Records. J. Physiol., vol. 189,1P, 1967. 8. LOWENSTEIN, O.; AND SAND, A.: The Individual and Integral Activity of the Semi-circular Canals of the Elasmobranch Labyrinth. J. Physiol.. vol. 99, 1940, pp. 89-101. 9. ADRIAN, E. D.: Discharges From the Vestibular Receptors in the Cat. J. Physiol., vol. 101, 1943, pp. 389-407. 10. GERNANDT, B. E.: Response of Mammalian Vestibular Neurons to Horizontal Rotation and Caloric Stimulation. J. Neurophysiol., vol. 12, 1949. pp. 173-184. 11. GROEN, J. J.: LOWENSTEIN, O.; AND VENDRIK, A. J. H.: The Mechanical Analysis of the Responses From the End-Organs of the Horizontal Semi-circular Canal in the Isolated Elasmobranch Labyrinth. J. Physiol., vol. 117,1952, pp. 329-346. DISCUSSION Lowenstein: This is what one frequently sees when one deals with single-fiber units after step-function stimuli. They return like this and then dip under the reference level, and gradually return to it. This may be in conflict with the mechanical model of the cupula endolymph system, but do not forget that, in the hair cell, ihe hair processes are en- sheathed in the cupula. Up at the top of the cell your mechanical model may be valid, but down in the synaptic region there is a clfemical transmission process which may already introduce the first distortion. Guedry: It seems to me that part of these effects may be explained by events within the end organ, but it does not seem reasonable to explain on this basis certain rather definite discrepancies between the subjective and the nystagmus responses. I can add a little to some of the data that have been reported today. We have done, over the past few years, experiments in which we have maintained a ramp velocity change for 16 seconds, but this was a 40-rpm change in angular velocity, which is a strong stimulus. The average time for the cessation of the primary subjective reaction occurred while primary nystagmus was in progress with a slow velocity of roughly 30 deg/sec. Then after a minute with secondary nystagmus still in progress, we introduced a triangular velocity waveform. The subjective response in most subjects seems to be based on the secondary level of nystagmus, which seems to fit fairly well with the model 12. MELVILL JONES, G.: The Vestibular Contribution to Sta- bilization of the Retinal Image. The Role of the Vestibular Organs in the Exploration of Space, NASA SP-77.1965, pp. 163-171. 13. MONEY, K. E.; AND SCOTT. J. W.: Functions of Separate Sensory Receptors of Non-auditory Labyrinth of the Cat. Am. J. Physiol., vol. 202, 1962, pp. 1211-1220. 14. ZUCKERMAN, H.: The Physiological Adaptation to Uni- lateral Semi-circular Canal Inactivation. McGill Med. J., vol. 36.1967. pp. 8-13. 15. GACEK. R. R.: Efferent Component of the Vestibular Nerve. Neural Mechanisms of the Auditory and Vestibular Systems, G. L. Rasmussen and W. F. Windle, eds., Charles C Thomas, 1960, pp. 276-284. 16. CAPORALE, R.; AND CAMARDA, V.: La Funzionalita Vestibolare di Acuni Pilotidi Pattuglia Acrobatica. Rjv. Med. Aeron., vol. 21,1958, pp. 13-36. 17. MELVILL JONES, G.: Vestibulo-ocular Disorganization in the Aerodynamic Spin. Aerospace Med., vol. 36. 1965, pp. 976-983. 18. YOUNG, L. R.: A Control Model of the Vestibular System. International Federation of Automatic Control, Sym- posium on Technical and Biological Problems in Cybernetics, Yerivan, Armenia, U.S.S.R., Sept. 1968. that was presented here by Malcolm. In other words, a triangular waveform can be introduced which will increase and then decrease the secondary nystagmus response. The sensation of rotation follows a similar pattern, first increas- ing and then decreasing, and the point in time when nystag- mus crosses over the (extrapolated) secondary baseline is a close approximation to the average point in time when subjects signal a stop. In most cases nystagmus overshoots the (extrapolated) secondary baseline, and during the over- shoot period, many subjects signal rotation in the opposite direction even though nystagmus continues in the secondary direction. So we have during this interval a dissociation of directions of sensation and nystagmus. Malcolm: I find this very interesting. Dr. Guedry. and it certainly bears further looking into. It also serves to illus- trate a rather important point, namely, that the process we are examining here is most probably not a simple one such as the model just described, but rather a network of series and parallel loops, each one similar to the one shown in the model. Mathematically, one could not make this distinction, however, and so the very complicated real situation can be nicely approximated by a very simple model, merely by playing with the algebra. The value in doing this lies in the fact that it can imply the kind of processes going on, as well as providing a means of predicting the responses to a complicated stimulus pattern.