Transfer Function of Labyrinthine Volleys Through the Vestibular Nuclei

139

Transfer Function of Labyrinthine Volleys Through the Vestibular Nuclei G . M E L V I L L JONES Canadian Defence Research Board, Aviation Medical Research Unit, Department of Physiology, McGiN University, Montreal, Quebec, Canada

In order to control the movement of a body in 3-dimensional space, it is necessary to know the separate components of movement in 3 translational and 3 rotational degrees of freedom. One of the basic means of obtaining such information derives from inertial forces generated by the body’s accelerations in those degrees of freedom. These forces, being dependent only upon acceleration relative to stellar, or inertial, space yield information about absolute movement. The principle has become familiar through the method of inertial guidance in man-made space vehicles. However, living systems evolved inertial guidance mechanisms long before Newton! The principle is used very early in the phylogenetic scale. Thus grains of starch in plant cells may transmit gravitational stimuli to the surrounding protoplasm, and Protozoan vacuoles may function in a similar way (Lowenstein, 1956a). Certainly, inertia-dependent statocysts are common in the Metazoa, and combined rotational and translational sensing endorgans are evident as early as the cyclostomes, where in Myxine two vertical ampullae share a single canal and a single undivided otolithbearing macula (Lowenstein, 1956b). In the fully developed vestibular system of vertebrates, all 6 degrees of freedom are represented in the mechanical endorgan. The endorgan in turn generates afferent neural signals bearing systematic relationships with both rotational and linear accelerative movements of the head. However, a key word here is ‘systematic’. The relation is seldom a direct one, and indeed the meaningful content of the neural signal may be quite different from that of acceleration; and yet it must always bear a systematic relation to the imposed acceleration since this is the basic adequate stimulus to the inertia-dependent sensory elements. This statement may appear at first sight to be paradoxical. Hopefully, its implications may be clarified by more detailed attention to the physical characteristics of the semicircular canals. PHYSICAL CHARACTERISTICS OF THE SEMICIRCULAR CANALS

The basic inertia-sensing properties of the semicircular canals have been appreciated for many years. For example, Breuer (1874) and later Stefani (1876) demonstrated the inertia-dependent movement of fluids in primitive models of the canals. Gaede (1922) appears to be the first to have recorded in the literature a proper physical References p p . IS4-IS6

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analysis of the fluid dynamics in a small closed circular tube. As so often happens, at about the same time several other authors arrived at similar analytical derivations of probable physical response characteristics (Masuda, 1922; Rohrer, 1922; Schmaltz, 1925, 1931 ; Rohrer and Masuda, 1926). Broadly, these authors attempted to calculate the likely relative movement of fluid in the endolymphatic canal as a result of angular acceleration of the head in a plane parallel to that canal. However, they were not in a position to appreciate the significance of forces introduced by deviation of the cupula in the ampulla, since at that time it was not certain whether such an organ existed. Steinhausen (1927-39) added the effects of a water-tight elastic cupular mechanism and derived a second order differential equation in an attempt to establish a quantitative relation between the angle of cupular deflection relative to its zero position and the angular acceleration of the head. The concept of a water-tight elastic cupula received support from the experimental work of Dohlman (1935). Various authors have developed the theme from this point to generate experimental investigations of the validity of Steinhausen’s conclusions. Thus, van Egmond et al. (1949) developed the method of cupulometry in an attempt to make rational measurements of clinical impairment in human subjects. At about the same time, Mayne (1950) using the relatively new methodology of systems analysis, inferred hydrodynamic response characteristics similar to those implicit in the differential equation formulated by Steinhausen. Later investigators have attempted to extend the observations of earlier workers using measurable manifestations of efferent reflex response to controlled rotational stimulation of the canals. Thus, Hallpike and Hood (1953), and subsequently Hixson and Niven (1961, 1962), used various measures of reflexly induced compensatory eye movement consequent to excitation of the vestibulo-ocular reflex arc. Others have used the information content of trains of unit action potentials in primary (Ross, 1936; Lowenstein and Sand, 1940; Groen et al., 1952; Rupert et al., 1962; Sala, 1965; Klinke, 1970; Goldberg and Fernkndez, 1971; Fernindez and Goldberg, 1971) and subsequent neural locations in the brain stem (Adrian, 1943; Gernandt, 1949; Duensing and Schaefer, 1958; Wilson et al., 1965; Shimazu and Precht, 1965; Wilson et al., 1968; Ryu et al., 1969; Melvill Jones and Milsum, 1970, 1971). The present article describes some results of a series of experiments in which the informational content of unit responses in the brain stem of cat vestibular nuclei has been examined as a function of various patterns of rotational stimulation of the endorgan. The endorgan response

In order to appreciate the rationale for the methods of data analysis employed, it is first appropriate to examine the physical characteristics of the assumed endorgan response. Fig. 1 illustrates a simplified system comprising a thin circular tube containing a water-tight but freely moving piston, the movement of which faithfully follows fluid displacement round the circuit of the canal. To simulate the elastic characteristics of the cupular mechanism, the hypothetical piston is located between

TRANSFER F U N C T I O N OF L A B Y R I N T H I N E VOLLEYS

t(haad,canal) ln;,;tiaj moment

Viscous =be mommt

since p.9-Q

1

1

14 1

Elastic +kQ mmant

and p=Q-Q

I

canal ang. q = 6 +Pe+ke I accal.

Fig. I . Simple model of hydrodynamic components of the canal.

two springs in the circular tube of Fig. 1, in such a way that the spring mechanisms and their supports are supposed not to interfere with the fluid movement. Consider now the whole system commencing to rotate at time to in the direction indicated and at an angular acceleration q. In the figure, the arrow labelled to indicates the angular position at which the undeviated piston was located at the commencement of the acceleration. After a given time (t), the whole system has rotated to the position marked by the arrow labelled t (head, canal). However, owing to the inertia of the fluid (i.e., due to its mass), the fluid has been left behind relative to the tube so that the piston has only reached the position marked by the arrow labelled t (fluid). In doing so the movement of the piston has compressed the hypothetical spring as shown. Using this simple analogy of the real canal, we may now equate moments generated in opposite directions. Thus, since the fluid has moved through an angle p, then the fluid’s actual angular acceleration is given by p. Hence, a clockwise moment is established due to the inertial response of the fluid to its own angular acceleration. The value of this moment is given by Ip, where I = moment of inertia of the contained fluid. This moment is represented on the left-hand side of the equation in Fig. 1. However, as soon as fluid flow occurs as a result of this moment, there is an opposing viscous moment. Significantly, owing to the very small diameter, and hence Reynold’s number, of the fluid system, such flow as occurs must be strictly laminar. Under these specific conditions, the moment due to viscous forces must be strictly proportional to the rate of relative fluid flow. The viscous moment in the equation of Fig. 1 is therefore given as b@, where @ = the relative angular velocity of fluid flow and b = the viscous coefficient. Notice that the direction of this moment is opposite to the inertial moment. The viscous moment is represented in the first term on the right-hand side of the equation. Acting in the same direction as the viscous moment, there will also be an elastic moment, this time proportional to the relative displacement of fluid in the tube, and in the equation this is represented by kO, where 0 = the relative References p p . 154-156

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angular displacement of the fluid and k = spring constant. Since these are the only moments exerted on the fluid, we may write

18 = b e

+ kO

(1)

As indicated in Fig. 1 , we may rearrange this equation in the form

.. .. b k q=o+-&+-@ I I Thus a second order differential equation emerges in which the left-hand side gives the forcing function, namely, canal angular acceleration, and the right-hand side describes the response, 8, expressed here as the relative angle of fluid displacement in the canal. Of course, in the real canal, this would be equivalent to the angular deviation of the cupula in the ampulla, when a constant of proportionality, a, must be introduced to account for the proportionate relationship between cupular angle in the ampulla and the angle of relative fluid displacement round the canal circuit. Jones and Spells (1963), using the expression a = n2r2R/V found a mean value of a = 0.50 from measurements made on 44 different species. In this expression r = internal radius of the endolymphatic canal, R = radius of curvature of the canal and V = the volume of the ampulla. Equation (2) is essentially similar to that derived by Steinhausen and used in the formulation of the classical experimental study of van Egmond et al. (1949) referred to above. Providing this equation remains linear, it may conveniently be restated as a transfer function of the form proposed by Jones and Milsum (1965),

Owing to the heavy viscous damping term (b), the denominator may be restated in the form,

where

TIT2 = I/k and T1

+ Tz = b/k.

Since it can be shown that TI is probably more than two orders of magnitude greater than T2, we may write to a close approximation,

Ti = b/k. Substituting this value of T1 we may write

Tz

= I/b.

We now see the functional implication of this relationship is that two time-constants, TI and TZ emerge, having numerical values closely equal to identifiable ratios of coefficients in the equation. What does this imply in the context of the present theme? Probably the most useful, and functionally meaningful, way of illustrating the outcome of these observations

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143

..

(3

-1 -2

?fa

s

300

0.1 1 10 100 1000 Frequency ( Radlons per Sec 1

u 0

E-45

- 90

I

I

a1 1 Requency

I

I

100 1000 ( Radlans per Sec ) 10

Fig. 2. Frequency response of the model in Fig. 1 . Adapted from Jones and Milsum (1965).

is by means of a Bode plot of the form shown in Fig. 2. First, it is helpful to rewrite the transfer function of equation (4) in the form

From this we may draw a frequency response diagram as in Fig. 2. Here the upper curve is a conventional amplitude ratio plot in which the log of the gain (in this case, cupular angle/head angular velocity) is plotted as ordinate, against a logarithmic frequency scale plotted in radians per sec (rad/sec = 2nHz) as abscissa. Under this is plotted the conventional phase diagram in which the ordinate gives the phase of cupular response relative to that of stimulus head angular velocity. The plus sign indicates phase advancement of the response; the minus sign, phase lag. In a diagram such as this, the two time constants, TI and Tz, emerge as the reciprocal of the frequencies (in rad/sec) at which the asymptotic projections of the gain curve produce 'break-off' points indicated by the two vertical arrows. Thus choosing TI = 0.1 sec and TZ= 1/300 sec (Jones and Milsum, 1965), a curve emerges which is flat over a frequency range extending from about 0.1-5.0 Hz, as indicated between the two short vertical lines in the figure. Particularly noteworthy is the fact that over this range the response would be approximately in phase with the stimulus head angular velocity. However, with the extension of the frequency range below the 0.1 Hz level, both the amplitude and the phase begin to change rapidly with decreasing frequency. Similarly in the upper range of frequencies the response of the transfer function in equation (9,namely, the displacement of cupula per unit head angular velocity, decreases with increasing frequency; but here a phase lag would begin to develop. Refcrences p p . 154-1 56

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Thus, we may say from this relatively simple analysis that the hydrodynamic characteristics of the tube in Fig. I would be expected to perform one integration on the imposed angular acceleration, so that the relative fluid displacement would provide a measure of angular velocity at every instant, but only over a limited frequency range as indicated by the ‘flat’ region in Fig. 2. Specifically, the system in Fig. 1 would act as an angular speedometer, but only over the middle frequency range determined by the actual values of TI = b/k and Tz = I/b. Two additional features may be emphasized at this point. First, these conclusions only hold so long as the pattern of fluid flow in the tube is alwaysstrictlylaminar,i.e., obeys the Hagen-Poiseuille law of laminar flow in small tubes of circular cross section. Of particular relevance is the fact that this feature is ensured in the endolymphatic canal by its very small internal diameter, about 0.3 nim in man. Secondly, the speed registered is that of the head relative to inertial space. The vestibular system ‘sees’ the absolute velocity independently of all the other complex physiological variables such as neck and body rotation and limb movement. Critical dependewe oj’ canal response upon physical dimensions The critical dependence of the canal response upon its physical dimension may be further understood by examining the derivation of the coefficients in equation ( 5 ) . Van Egmond et af. (1949) give the coefficients I and b as,

I

=

2n2erzR3

(6)

and b

= 87~2qR3

(7)

= nr2,uR

(8)

Whilst Jones and Spells (1963) give

k where

R

r

= radius of curvature of endolymphatic canal =

internal radius of the thin endolymphatic tube

p

= fluid density

q

=

fluid viscosity = the pressure exerted by the cupula per unit angular deflection of ,LA fluid round the circuit. There are certain reservations attached to some of these relations, but it is not appropriate to enter into these details in this article. They are considered at greater length in another article (Melvill Jones, 1972). In that article and from the work of Jones and Spells (1 963), the results of dimensional analysis predict that if the canal is to continue to measure head angular velocity during head movements, then these dimensions, particularly r and R, should increase with animal size according to the slower head movements to be expected from larger animals. However such increase would only be very gradual indeed, roughly 10 log cycles increase in weight being required for one log cycle increase in canal radius of curvature. Moreover, it was

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predicted that r2, and R and RZ/r2 should all vary in proportion to one another, maintaining the ratio rz/R constant. Now it can be seen from equations (6) and (7) that the value of TZ(= I/b) is proportional to rz. Moreover, the longer time-constant, TI (= b/k), is proportional to R2/r2. Thus, from the previous paragraph it emerges that if the above criteria are maintained, then the two break frequencies in Fig. 2 (1/T1 and 1/Tz rad/sec) would move proportionately up and down the frequency scale (abscissa) according to animal size. In effect, therefore, the frequency range of angular velocity transduction would be increased or decreased to match the likely frequency content of natural head movement. As Jones and Spells (1963) showed, for this to occur it is only necessary that the two variable r2 and R, and hence also Rz/rz, should vary according to a power relationship to body mass, such that r2, R and R2/r2 K (body mass)" The prediction was that n should be close to 0.1. In view of these analytical conclusions, it was particularly intriguing to find from a survey of canal dimensions in 93 specimens from 87 different species ranging from mouse to horse (about 0.04 kg to 450 kg), that this general relation was rather closely maintained, since a statistically reliable value of n = 0.095 f 0.05 emerged from these data. The detailed dimensional analysis of cat canals made by Fernhndez and Valentinuzzi (1968) conforms closely with this general conclusion. NEURAL RESPONSE

These two analytical approaches suggest rather strongly that evolution has favoured very particular physical characteristics for the semicircular canal such that, over the range of natural head movement, the hydrodynamics of the system should perform one accurate integration on the angular acceleration of the head relative to inertial space. It therefore becomes of special interest to investigate the extent to which this conclusion is realized in the information content of the afferent neural signal received by the brain. A series of experiments was therefore performed with this end in view (Milsum and Melvill Jones, 1969; Melvill Jones and Milsum, 1969, 1970, 1971). Fig. 3 illustrates diagramatically the system of experimental equipment employed in these experiments. Decerebrate cats were located in a stereotaxic device mounted on a multi-degree of freedom platform capable of being fixed coaxially to a horizontal velocity-servo-controlled turntable. The platform could be suspended either from 4 parallel springs or 4 parallel inextensible wires, permitting multi-degree of freedom of movement. The usual procedure was to advance an extra-cellular steel microelectrode through the floor of the fourth ventricle at approximately the anteroposterior level of the medial vestibular nucleus, whilst maintaining gentle multidegree freedom of movement. Relevant units were then subjected to sequential movement excitation in the separate rotational and translational degrees of freedom. Only units responding specifically to rotational movement in the plane of one pair of canals were retained for measurement of their response to angular movements. Cells selected References p p . 154-156

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G. M E L V I L L J O N E S

Fig. 3. The multi-degreeof freedom stimulus system. From Melvill Jones and Milsum (1970).

were therefore specifically sensitive to rotational stimulation in the plane of one pair of canals. With these canals oriented in the plane of turntable rotation, the neural responses to sinusoidal and transient rotational stimuli were examined systematically. Fig. 4 illustrates a sample of spike responses to sinusoidal rotational stimulation within the frequency range presumed to be associated with angular velocity transduction in the canal of the cat. Evidently, at least when the cell was firing actively, the spike frequency was modulated approximately in phase with the stimulus record, which in all records was derived from a tachometer registering turntable angular velocity.

--_----

--

-

-

-

-_

__

--

Fig. 4. Extract from an original train of action potentials (upper trace) related to the sinusoidal angular velocity of rotational stimulation (lower trace). Period, 4.0 sec; Amplitude, 32"/sec. From Milsum and Melvill Jones (1969).

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Fig. 5 . Averaged stimulus angular velocity and neural response (action potential frequency) from two canal-dependent units in the medial vestibular nuclei of decerebrate cats during sinusoidal rotation in the plane of the lateral canals. (a) Period, 1.4sec; (b) Period, 4.0 sec. From Melvill Jones and Milsum (1970).

Computer analysis of records such as these can be made to yield averaged responses in the form shown in Fig. 5. In both halves of this figure, the upper trace gives averaged turntable angular velocity during a typical cycle of the sinusoidal stimulus and the dotted trace gives the computer-averaged spike frequency associated with every point in the stimulus cycle. Again, it seems that the spike frequency tends to be modulated in an approximately sinusoidal fashion in phase with the sinusoidal stimulus angular velocity. In a detailed investigation, Melvill Jones and Milsum (1970) concluded that this general relation was representative of the information content of the neural signal received in the brain stem during sinusoidal rotational

a

C

b

d

Fig. 6. Averaged stimulus response ielationships obtained from one unit assessed to be located in the left medial vestibular nucleus. (a) Period, 4 sec; (b) Period, 64 sec; (c) Triangular velocity ramps of period 128 sec; (d) Square wave changes in angular velocity of period 64 sec. From Melvill Jones (1 968). References p p . 154-156

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stimuli in the frequency range about 0.25-1.0 Hz; a conclusion which is closely in line with the predictions made on the analytical and dimensional bases discussed above. Low frequency and transient responses If the neural signal were to maintain a faithful representation of the endorgan mechanical response, then it would be expected from the transfer function of equation (5) that at low frequencies the response, rather than being tied to the stimulus angular velocity, would progressively phase advance with respect to it as the frequency of stimulus decreased. Fig. 6a,b shows two responses recorded at frequencies of 1/4 and 1/64 Hz respectively. Marked phase advancement is evident in this second (low frequency) response.

1 0

Stimulus lraquancy ( w ) radlsoc

4

20

Stlmulu5 f r Q q u Q n C y (W) r O d / S Q C

A

Fig. 7. Bode plot of normalised gain and phase from twelve single units retained sufficiently long to examine their frequency response over a wide frequency range of sinusoidal rotational stimulation. Normalisation of gain based on the mean gain in the frequency range 0.25 Hz-1.0 Hz. The intermittent lines give the response of equation (5), with TI = 2.0 and 6.0 sec. Individual cells are represented by separate symbols. From Melvill Jones and Milsum (1971).

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Fig. 7 gives the Bode plot of accumulated data reported by Melvill Jones and Milsum (1971) and examines this feature in terms of the curves in Fig. 2. The results only examine response characteristics across the low frequency half of the curves in Fig. 2. Bearing in mind that the two sets of data in the upper and lower curves are essentially tied to one another, it is remarkable to see how closely the data points obtained conform with the predictions of the simple linear transfer function for the mechanical response of the canal, as shown in equation (5). Not only does the gain, expressed here as the ratio of change in firing frequency per unit change in angular velocity, decrease rapidly with decreasing stimulus frequency (note the logarithmic ordinate) but also an appropriate phase advancement occurs over the two decades of frequency employed. The same transfer function predicts specific patterns of response to transient or step changes in both angular velocity and angular acceleration of stimulus. The systematic nature of the neural responses to such stimuli can be seen in Fig. 6d and c respectively. A sudden change in stimulus angular velocity (Fig. 6d) leads to a correspondingly sudden change in firing frequency followed by an exponential decay towards the steady state value. A sudden change in angular acceleration (Fig. 6c) shows the predicted exponential rise to a plateau level which in the absence of nonlinearity would be maintained indefinitely. Thus, at least from the records discussed here, it seems that the neural signal received in the brain stem does indeed tend to follow the hydrodynamical response of the endorgan with generally good fidelity, even during movements extending well beyond the natural evolutionary experience.

Non-linearities

If the neural response to rotational canal stimulation were to follow accurately the simple transfer function of equation (3,linearity would have to obtain throughout. However, various forms of non-linearity have been described in the literature and it is therefore important to examine their influence on the system's response. For example, Melvill Jones and Milsum (l970), investigating the dependence of neural gain (change of firing frequency per unit change in angular velocity) upon stimulus amplitude (angular velocity) at a given sinusoidal frequency, found a power relationship such that Gain cc (angular velocity)-0.28

Stimulus Amplitude

(*I

sec )

Fig. 8. Dependence of gain upon stimulus amplitude. Individual cells are represented by separate symbols. From Melvill Jones and Milsum (1970). References p p . 154-156

150

a

G. MELVILL JONES

b

Fig. 9. Transition from all-round firing to threshold cut-off in a single unit, to illustrate the asymmetric pattern of firing associated with the cut-off pattern. From Milsum and Melvill Jones (1969).

Fig. 8 illustrates the normalized data from 5 units and indicates a rather consistent relationship in which the slope of -0.28 is clearly statistically significant. An intriguing point is that such a small index would lead to but a small divergence from linearity over a considerable range of stimulus magnitudes. Fig. 9 illustrates a further form of non-linearity (Milsum and Melvill Jones, 1969) such that there appears to be a tendency for units exhibiting ‘threshold cut-off’ to respond with a more rapidly changing leading, than trailing, edge in their response waveform. Interestingly, this finding was statistically significant in units cut off at one point in their cycle by their threshold of firing, but not evident, even in the same unit, when firing was maintained throughout the cycle due to either a high spontaneous firing frequency or because of a relatively low stimulus amplitude or both. Possibly this phenomenon is one manifestation of the ‘kinetic’ response patterns seen by Shimazu and Precht (1965). In any case, presumably both these phenomena would contribute to the changes in upper frequency response characteristics reported by Goldberg and Fernkndez (1971). Examining neural unit responses in primary afferent fibres of the monkey, they have shown a marked tendency for phase advancement and gain increase of the response to occur as the frequency of sinusoidal stimulation increases above about 1.0 Hz. Moreover, their results conform well with those of Benson (1970) who investigated the gain of vestibulo-ocular response in man at high frequencies. It seems therefore that the upper frequency range of Fig. 2 may not be as representative of the real system’s response as is the middle frequency range. In the lower frequency range, an adaptive term becomes significant. Although some units, both in the primary (Goldberg and Fernhndez, 1971) and subsequent (Shimazu and Precht, 1965; Melvill Jones and Milsum, 1971) neural pathways appear to be essentially non-adapting, others show consistent adaptation. A relatively nonadaptive pattern is seen in the response to a step change of angular acceleration in Fig. 6c, whilst a relatively adaptive response is seen in the corresponding record at the top right hand corner of Fig. 10 obtained from another cell. Moreover an adaptive term has been shown to account for the systematic response of subjective sensation (Oman, 1968; Young, 1969) and compensatory nystagmus (Oman, 1968; Malcolm and Melvill Jones, 1970) during low frequency rotational

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stimulation of man. The latter authors, for example, showed that a transfer function of the form

stimulated the observed nystagmoid response of human subjects very closely, where y = angular velocity of slow phase eye movement relative to the head T3 = an adaptive time constant e = a proportionality constant I, k, q and TI are as in equation (5). The similarity of equations (9) and (5) becomes evident when it is appreciated that compensatory slow phase eye angular velocity (y) is functionally related to cupular angle (O), and that at low frequencies the influence of the short (inertia/viscous) time constant (Tz) becomes negligible. Malcolm and Melvill Jones (1970) found the adaptive time constant (T3) to be 82 sec (S.E. f 6.5) in man, and this is the same order of magnitude as the estimates of Oman (1968) and Goldberg and Fernindez (1971). In the present context an important conclusion is that the great length of this adaptive time constant excludes its significant influence upon the system’s response in the middle and upper frequency ranges of Fig. 2. It is, of course, well known that habituation can in the long term substantially influence the transfer of information from sensory endorgan to efferent response. Indeed it has very recently been shown that, with an appropriate long term experimental procedure, it is even possible to effect retained reversal of the adult human vestibulo-ocular reflex (Gonshor, 1971 ; Gonshor and Melvill Jones, 1971). But it is not yet possible to predict with assurance how effects such as these may modify the transfer function of labyrinthine volley through the vestibular nuclei.

Interactions bet ween rotational and linear accelerative stimuli An additional complication associated with real natural movement stems from interactions between linear and accelerative stimuli. Fig. 10 illustrates one aspect of this feature. The upper 3 computer-averaged records from this single cell show that its response derived essentially from mechanical stimulation of the semicircular canal. Thus, decreasing frequency of sinusoidal stimulation produced the substantial phase advancement to be expected from the transfer function of equation (5). Moreover, transient accelerative stimuli produced the response characteristic of exponential rise to a plateau as discussed above. Furthermore, the unit was non-responsive to linear accelerative stimuli imposed in straight lines by means of the parallel swing suspension of Fig. 3. However, when the whole parallel swing system was moved in such a way that its centre of gravity described a circular path without there being rotational movement of the platform (sometimes referred to as counter rotational stimulation), the spontaneous activity of this cell (lower left-hand record of Fig. 10) was systematically increased (lower middle record of Fig. 10) during movement of the platform round References pp. 154-156

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siiiusoidal r o t a t i o n a t 1/4 cps 119 cycles)

Lpoiit arieous freq 7 se(

AP

l/64 cps j3 cycles)

parallel swing anticlock (50 cycles)

t otat lorial acceleration period 128 sec (4 cycles)

parallel swing clockwise (50cyclesi

Fig. 10. Series of averaged responses to rotational stimulation (upper series) and counter rotating stimuli (lower series), to illustrate interaction between rotational and linear accelerative stimulations. From Melvill Jones (1968).

a circle in the same direction as that of excitatory endolymphatic fluid flow. In contrast to this, during counter rotation in the opposite direction, the maintained firing frequency of this cell was suppressed well below that during counter rotation in the excitatory direction (lower right-hand record of Fig. lo), and even below that associated with ‘spontaneous’ neural activity shown in the lower left figure. This counter rotating movement imposes a rotating, radially oriented, linear acceleration vector without introducing real rotation of the animal. Thus, it is quite possible to complicate the pattern of response in a specifically semicircular canaldependent unit by imposing changes of direction in a linear acceleration vector. This feature has been systematically explored by Benson et al. (1970) who concluded that possibly the interference was due to alteration of the mechanical response in the endorgan, although neural interaction between canal and otolithic afferent signals could not be excluded. DISCUSSION

The combined outcome of these analytical, anatomical and neurophysiological studies leads the author to the general conclusion that evolutionary pressures have strongly favoured a canal ‘design’ such that its hydrodynaniical response to rotation accurately registers instantaneous head angular velocity during much natural head movement, i.e., in the middle frequency range of Fig. 2. Not only do the directly observed patterns of neural signals dispatched from the brain stem of cats favour this view : but associated analytical and anatomical studies indicate that, with very specifically appropriate changes of canal dimensions with animal size, head angular velocityco ntinues to be the relevant informational content of the canal signal generated by natural head movements over a wide range of animal species of varying size.

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Of course, the neurophysiological findings from a single series of experiments must always be treated with caution until further results become available in the literature. But the recent comprehensive inwstigation of response in primary afferent neurones of the squirrel monkey by Goldberg and Fernandez (1971) and FernBndez and Goldberg (1971), and the earlier investigation of cat brain stem units by Shimazu and Precht (1 965) together with the results summarised above (Melvill Jones and Milsum, 1970, 1971) substantially support the view that many neurones carry informational content broadly described by the transfer function of equation ( 5 ) , a t least in the middle frequency range of Fig. 2. This general conclusion in turn leads one to enquire into the potential functional advantage of accurate rate-dependent feedback from head rotation. In this connection, it is noteworthy that the dynamic response of the purely visual tracking system associated with optokinetic following of a moving visible object when the head is still, is rather poor (Young, 1962; Young and Stark, 1963); particularly so when the target movement is relatively random in nature (Michael and Melvill Jones, 1966). However, it seems that the rate-dependent vestibular signal from the canals is entirely appropriate for establishing neuromuscular damping of such head movement relative to space, through vestibulo-collic stabilising reflexes (Outerbridge, 1969; Outerbridge and Melvill Jones, 1971) which have recently been shown to exhibit extremely rapid neural response characteristics (Wilson and Yoshida, 1969a,b). In addition, such residual head movement relative to space as remains after vestibulo-collic reflex stabilisation of the head, would seem to be most appropriately compensated by a velocity driven vestibulo-ocular reflex system (Melvill Jones, 1971). An additional important feature to which attention has been drawn by Roberts (1967) is the close functional link established between canal afferents and motor responses in the limbs. Thus, nose-down rotation of the head of the cat activates forelimb extensors, so that velocity-modulated canal afferents would automatically induce an appropriate damping term in these, and presumably other, postural muscles as a consequence of unintended changes in body attitude. One might well ask how such automatic stabilising responses would be suppressed in order to permit intended voluntary changes in attitude. Perhaps the remarkable observations of Klinke (1970) will go far towards answering this question. Apparently the attempt of a paralysed fish to follow a rotating visual target substantially modified the primary afferent vestibular signal in such a way that voluntary angular movements would be associated with automatic nulling of the induced vestibular response, presumably through the efferent innervation of the vestibular organ (Gacek, 1960). SUMMARY

Simple analysis of canal hydrodynamics yields a second order linear differential equation which is restated as a transfer function. An experimental study of action potential frequencies induced in central vestibular units by rotational stimulation of the canals yields a similar transfer function. It is inferred that the nervous system transfers the canal response signal to the References p p . 154-156

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brain stem with generally good fidelity. In particular it is shown that, over a middle range of frequencies, probably corresponding to those encountered in natural life, the informational content of this signal essentially corresponds to that of head angular velocity. Adjustment of canal frequency response according to animal size is apparently brought about by precise, but very small, changes in canal dimension from one species to another. Attention is drawn to various non-linearities i n the whole system. These include a form of dynamic asymmetry in the neural signal, a power relation between input and output amplitudes, neural adaptation to prolonged unidirectional stimuli and habituation to repeated stimuli which conflict with other sensory information. The potential influence of these non-linearities calls for caution in the utilisation of a simple transfer function to predict the overall physiological response to canal stimulation.

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