Biological Cybernetics O Springer-Verlag 1989

Transcription

1 Biol. Cybern. 60, (1989) Biological Cybernetics O Springer-Verlag 1989 A Model of Otolith Stimulation M. J. Dai 1"2, I. S. Curthoys a, and G. M. Halmagyi 1 1 Eye and Ear Unit, The Department of Neurology, Royal Prince Alfred Hospital, 2 The Centre for Biomedical Engineering, The University of New South Wales, and 3 The Department of Psychology, The University of Sydney, Sydney N.S.W. 2006, Australia Abstract. A new model of otolithic stimulation by linear acceleration is presented and compared to previous models, based upon anatomical evidence and on the ability of normal subjects to sense the direction of a linear acceleration vector acting in the coronal plane (roll-tilt perception). There are two basic methods of generating roll-tilt stimuli: 1) tilt-chairs either inside or outside a centrifuge and 2) fixed-chair centrifuges. The present model is based on consideration of the probable otoconial displacement produced by these two different methods of stimulation and the model incorporates a major role for the elastic restoring force of the otolith membrane. When this force is taken into account, and most previous models have ignored it, the model predicts that different patterns of otoconial displacement will be produced in tilt-chair and in fixed-chair centrifuge experiments. The different roll-tilt perception produced by these two methods may be caused by the different otoconial displacement patterns. It is suggested that the elastic restoring force of the otoconial membrane may contribute to space motion sickness. 1 Introduction The present model of otolith function has been developed from previous experimental data on the ability of normal subjects to perceive the direction of a linear acceleration vector in the coronal plane, an ability we refer to as roll-tilt perception (Noble 1949; Graybiel 1952; Colenbrander 1964; Schrne 1964; Correia et al. 1968; Dai et al. 1988). The otoliths consist of sensory receptor cells projecting into a gelatinous mass superimposed upon which is a layer of calcium carbonate crystals - the otoconia (Igarashi 1966). Because of the density difference between the otoconia and the receptor cell region (the macula), a linear acceleration stimulus results in a shearing force acting on the receptor cells. The magnitude and direction of the shearing force depends upon the magnitude and direction of the linear acceleration stimulus relative to the macula. In each inner ear the two otolithic receptor regions in the utricle and the saccule are approximately orthogonal to one another, allowing almost any direction of linear acceleration stimulus to be transduced. Recent understanding of normal otolith function derives from studies of the physiological effects of a tilt stimulus on the otoliths studied by recording responses of single primary afferent neurons from the utricle and the saccule (e. g. Fernfindez and Goldberg 1976). Complementing this physiological data there is a large body of data on the perception of linear acceleration stimulation under a variety of conditions (see Howard 1982). There have been a number of attempts to account for the perception of body posture and the effects of linear acceleration on visual perception in terms of peripheral otolith function (see Young 1984) and it seems that perceptual judgements may reflect, in a very direct fashion, the physiological operation of the peripheral otolith receptor mechanisms. In a series of experiments using a fixed-chair human centrifuge, we measured the errors in roll-tilt perception produced by a resultant vector acting in the coronal plane (Dai et al. 1988). From a study of these errors, and from comparing them with the errors obtained by others in tilt-chair experiments we have been led to put forward a new model of otolith function based on a presumed different pattern of otoconial displacement produced by different methods of roll-tilt stimulation. This model is drawn from anatomical considerations, explains observations in different force environments and has important implications for otolith function in microgravity. To understand the model and its background it is necessary to define some terms. In the erect human subject at rest, the gravitoinertial vector (R) is directed along the body longi-

2 186 tudinal (Z) axis. The magnitude of the vector R is 1 g and the angle between the vector and the body Z-axis is zero degrees. Any change in the angle between R and the Z-axis is in our terms a "tilt stimulus". A tilt stimulus about the inter-aural axis or Y-axis, in the sagittal or XZ plane, is called a pitch-tilt stimulus; a tilt stimulus about the naso-occipital or X-axis, in the coronal or YZ plane, is called a roll-tilt stimulus. The angle between R and the Z-axis in the XZ plane is called "angle fl"; the angle between R and the Z-axis in the YZ plane is called "angle 0"; when R is directed along the Z-axis, both 0 and fl are zero. In this article we consider the effects of roll-tilt stimulation, i.e. changes in angle 0 on roll-tilt perception. A tilt stimulus may be produced either by tilting the body Z-axis with respect to the vector R or conversely by tilting the vector R with respect to the body Z-axis. It is simple to increase 0 by tilting the body with respect to R by putting the subject on a tilt-chair: while 0 increases, R remains constant at 1 g and is aligned with the gravitational vertical (Fig. 1). Increasing 0 by tilting R with respect to the body Z-axis, while keeping the Z-axis fixed with respect to the gravitational vertical, is more difficult to achieve and requires a fixed-chair human centrifuge, i.e. one in which the subject sits with his Z-axis always aligned with the gravitational vertical (Fig. 1). Increasing 0 by tilting R with respect to the body Z-axis, on a fixed-chair centrifuge, is not equivalent to increasing 0 by tilting the body Z-axis with respect to the R on a tilt-chair, because on a fixed-chair centrifuge the magnitude of the component of R acting in the Z-axis (F,) is, by definition, fixed at 1 g, whereas on a tilt-chair the magnitude of is a function of 0, the roll-tilt stimulus angle, so that increasing 0 on a tilt-chair decreases F~. In a variant of the tilt-chair paradigm both the body Z-axis and R are tilted away from gravitational vertical, but by different amounts. In this situation the subject is tilted on a chair inside the freely-swinging cabin of a gondola-centrifuge; the angle of the tilt-chair with respect to the long axis of the gondola (i.e. with respect to the direction of the resultant vector R) can be adjusted independently of the magnitude of R which depends only on the radius and the angular velocity of the centrifuge (Fig. 1). The roll-tilt stimulus produced by a tilt-chair inside a gondola centrifuge is essentially the same as the stimulus produced by a tilt-chair on the ground (i.e. in a 1 g force environment). In a tilt-chair inside the gondola centrifuge just like in a tilt-chair outside a gondola (but unlike a fixed-chair centrifuge), is a function of 0, so that in both cases increasing the rolltilt angle (0) decreases F~. There is however a difference between the roll-tilt stimulus produced on a tilt-chair inside a gondola and the roll-tilt stimulus produced on a tilt-chair outside a gondola: outside a gondola R always equals 1 g so that is less than 1 g, inside a gondola R is always greater than 1 g so that can take any value between + R and - R. Previous research has shown that when R is greater than 1 g a perceptual elevation of the stimulus may occur (the "elevator effect") (Cohen 1973). Consequently roll-tilt perception in a gondola centrifuge may be influenced by an elevator effect (Cohen 1973) induced by greater than 1 g. Table 1 presents values of forces associated with these different stimulation methods. There are also important differences between the roll-tilt stimulus produced on a fixed-chair centrifuge and the roll-tilt stimulus produced on a gondolacentrifuge. On a fixed-chair centrifuge the horizontal semicircular canals will be stimulated during angular acceleration, whereas on a gondola-centrifuge both the horizontal and vertical semicircular canals will be stimulated. Furthermore during repositioning tilts inside the gondola the semicircular canals will be stimulated by Coriolis coupling forces (Young 1984). Any roll-tilt stimulus will stimulate the otolith receptors of each utricle and saccule as well as somatosensory receptors distributed over the body. Evidence from numerous previous investigators shows that if the roll-tilt stimulus angle (0) is less than about 40 degrees the subject perceives this angle accurately even without visual cues or a visual frame of reference (Sch6ne 1964; Howard 1982). Roll-tilt perception may be measured by the subject indicating the perceived roll-tilt angle verbally or adjusting a visual or kinaesthetic indicator. One task which has been studied extensively is requiring the subject to set a small, illuminated bar, in an otherwise darkened laboratory, to the gravitational horizontal or vertical. Normal subjects on an ordinary tilt-chair, roll-tilted up to 40 degrees in a 1 g force environment, set such a bar to within about 10 degrees of gravitational horizontal (Sch6ne 1964). These perceptual errors, although small in absolute size, are consistent and have been intensively studied (see Howard 1982 for a review). Rotating in darkness at constant velocity on a fixed-chair centrifuge, a normal subject seated erect with his coronal plane aligned parallel to the radial linear acceleration, will feel himself roll-tilted away from the centrifuge rotation axis and in the otherwise darkened environment, a small visual stimulus (actually fixed relative to the subject) will appear to roll, in the same direction and through the same angle as the apparent roll-tilt of the subject. The subject can indicate the perceived roll-tilt by maintaining the alignment of such a small luminous bar with the gravitational horizontal or vertical. This apparent rolltilt of a small visual stimulus has been called the "oculogravic illusion" (Graybiel 1952) and the angle

3 187 Table 1. Values of forces acting on the otolith associated with different stimulation paradigms. The explanation of the symbols given in the text and shown in Fig. 1 Fixed-chair Tilt-chair in Tilt-chair in centrifuge 1 g environment 2 g environment R = V(co2rg)2 + g2 = 1.4 g Fixed at 1.0 g ~ = 2.0 g 0 = tan- 1 (Fy) = 45 ~ Independent Independent variable (e.g. 45 ~ variable (e.g. 45 ~ Fy = R sin 0 = 1.0 g R sin 0 = 0.7 g R sin 0 = 1.4 g = R cos0 = 1.0 g R cos 0 = 0.7 g R cos 0 = 1.4 g Fp = sin 30-: 0.5 g sin 30 -= 0.35 g F= sin 30 = 0.7 g Fixed-choir Tilt-choir in Tilt-choir in centrifuge lg environment 2g environment ~ Fp X' Fy R Y ~ Fy ~ Fp (.~)~ & ~ Fy X' 0 (." -" Fy y, i... Fp "-" < ~ ify y,,. <I>.. ;p,(~, ; Fy ii Y' "Fp. 0" Fig. 1. Comparison of forces generated in three different roll-tilt stimulus paradigms and the corresponding predicted displacement pattern of utricular otoconia. Top row shows a view from behind of the forces generated at the subject's head; the lower three rows show schematically the pattern of otoconial displacement with the idealized utricular plane viewed from behind (upper row), from the left (middle row) and from above (bottom row). Note that whereas the force directed along the head long axis (F,) and therefore its component in the mean antero-posterior utricular plane, pitch-shear (Fp), decreases during tilting in a 1 g force environment and increases during tilting in a 2 g environment, it remains constant during stimulation in a fixed-chair centrifuge. Changing roll-shear (F~), by altering body orientation with respect to the resultant force (R) necessarily changes the pitch-shear. 0 = angle of resultant force with respect to the head Z-axis; r = effective radius of centrifuge arm; ~0 = angular velocity of centrifuge; X'= antero-posterior axis through utriele, in the sagittal plane; Y'=right-left axis through the utricle, parallel to the Y or interaural axis (refer to Table 1 for precise values)

4 188 through which the bar appears to have rolled from gravitational vertical indicates the perceived roll-tilt angle. It is necessary to distinguish carefully between rolltilt stimulation and roll-tilt perception. Roll-tilt stimulation refers to changes in the physical forces acting on the body, such as changes in 0, the angle between the body Z-axis and the vector R in the roll plane. Roll-tilt perception is the subjective sensation resulting from roll-tilt stimulation. Corresponding to the differences between the two basic methods of roll-tilt stimulation (1. actually tilting the subject on a tilt-chair around his X-axis and 2. tilting the vector R around the subject's X-axis on a fixed-chair centrifuge), there are important differences in the perceptual errors produced by these two methods of stimulation. The model we present below suggests that the perceptual differences occur because the different methods of roll-tilt stimulation produce different patterns of otoconial displacement. The most important difference is that even if the two different methods of roll-tilt stimulation produce the same lateral shear (roll-shear, Fr) force across the utricles, the antero-posterior shear (pitch-shear, Fp) force will be different as shown in Table 1. Considering this with the elastic restoring force of the otolith membrane we propose that these differences between the roll-tilt perceptual errors which occur with different roll-tilt stimuli are due to differences in otoconial displacement pattern. 2 Perceptual Effects of Linear Acceleration in Roll When dealing with the effects of linear acceleration stimulation in the roll plane, the terms "A effect" (Aubert 1861) and "E effect" (Miiller 1916) have been used to describe the systematic visual perceptual errors which occur. The A effect describes the perceptual error that occurs when a subject tilts his head to one side from a head erect position: an illuminated gravitationally vertical line viewed in an otherwise darkened room will be apparently rotated in an opposite direction to the head tilt. The A effect also occurs when the whole body is tilted and the error can be substantial and consistent in both cases (Fig. 4). The E effect is the opposite phenomenon, i.e. a gravitationally vertical line will appear to tilt in the same direction as the head tilt. These errors are apparently specific to an individual (Howard 1982) but also depend on the speed of roll-tilt (Stockwell and Guedry 1970). It seems that the E effect is mere likely to occur when the force field is greater than 1 g. In centrifugation studies the A and E effects are present but are smaller than obtained in tilting experiments (Noble 1949; Graybiel 1952; Dai et al. 1988). Typical A and E effects are shown in Fig Models of Otolithic Function Accounting for Perceptual Results The A and E effects have been of interest to psychologists, engineers and mathematicians for over 100 years, and recently various theories and models have been proposed to explain these effects. Schrne (1964) described a simple utricular shear theory to account for tilt perception, expressed in mathematical form as Fr=R.sinO, where F r is the magnitude of lateral shear, R is the magnitude of the resultant force and 0 is the roll-tilt stimulation angle. R. sin 0 simply represents the magnitude of the lateral shear force (the roll-shear of Fr) upon the utricle in the case of roll-tilt. The model is very useful for explaining the otolithic involvement in roll-tilt perception but the predictions from this model do not account for the full range of experimental data. Correia et al. (1968) conducted a careful theoretical analysis based on data from tilting experiments in force fields greater than 1 g and put forward a predictive equation which accounted for most available data, but there was no obvious physiological basis for their equation. They suggested that if the force had already bent the otolith hair cells, then further increases in compressive forces should further bend the receptor hair cells. However Fernfindez and Goldberg (1976) experimentally tested the predictions of this theory by recording primary afferent neurons in the squirrel monkey in varying force fields but could not confirm them. Nevertheless Correia's predictive equation provides a better fit to the data than predictions from Schrne's utricular shear theory. Ormsby and Young (1976) classified the force stimulation of the otoliths according to different experimental procedures and suggested that nonlinearities in tilt perception were the results of saccular stimulation. When the magnitude of shear on the saccular hair cells is either greater than or less than that exerted in the normal head erect position, there will, according to Ormsby and Young, be an "E like" or an "A like" perceptual error respectively. When the saccular shear component is equal to that in the head erect position, there will be no perceptual error. This model essentially states that the utricle and the saccule function as orthogonal linear accelerometers. Nonlinearities in perception are accounted for by arbitrarily altering the saccular shear value in the model. This model fits the perceptual data better than the other models do, although there are no precise details of exactly how to adjust the saccular shear term independently of the data in order to fit the experimental results. Mittelstaedt (1983, 1985) developed a rather different theory, the principal idea of which was that the

5 189 subjective vertical "is thought to be the result of a compromise between a tendency to perceive it in the direction indicated by the gravity systems and a tendency-probably of central nervous system originto perceive it in or close to the direction of a person's own longitudinal axis" (Mittelstaedt 1985). The mathematical form of this theory is complicated, but the prediction for roll-tilt data in a 1 g force environment is excellent. However the predictions of Mittelstaedt's theory in force environments of greater than 1 g do not show close agreement with the experimental results. In summary, previous models have had serious limitations in accounting for the perceptual data in physiological terms. In those models where the data is close to prediction, the model itself is either not tied to physiological processes or incorporates arbitrary changes to model parameters. All the theories described above deal with both roll-tilt and pitch-tilt but none provides specific predictions for centrifugation studies. In the following we consider only roll-tilt stimulation and develop specific predictions for centrifugation studies as well as for tilting experiments. 4 A New Model of Otolith Function 4.10toconial Displacement A schematic section of an otolith is presented in Fig. 2. The otolith consists of three layers: the otoconial membrane, the cupular membrane and a layer of sensory epithelium and connective tissue (Igarashi 1966). The otoconial membrane is composed of calcium carbonate crystals with a density of 2.7 gml (CarlstrSm et al. 1953) and forms the outermost layer of the otolith. The cupular membrane, composed of a gelatinous muccopolysaccharide material with a density of 1.0 gml, surrounds the hair bundles of the sensory cells. The sensory epithelium is firmly attached to the skull by connective tissue. The surrounding endolymph has a density similar to that of the cupular membrane. I a ~ OTOCONIA CUPULAR MEMBRANE HAIR CELLS Fig. 2. A schematic representation of a section of an otolith organ. When the otolith is subject to a linear acceleration (a), the hair cells are displaced as a result of the inertia of the otoconia Because of the relatively high density of the otoconial membrane, the otoconia will tend to lag behind any imposed linear acceleration and so will deform the jelly-like cupular membrane, which will in turn bend the receptor hair bundles. This bending will be sensed by the cell body and will be transmitted to the brain as nerve impulses via primary afferents within the vestibular nerve. Recordings from otolith primary afferent neurons indicate that individual neurons have a polarization axis along which hair cells can be most effectively stimulated (Lowenstein and Roberts 1949; Milsum and Jones 1967; Fernfindez and Goldberg 1976). A linear acceleration stimulus directed along this axis produces the maximum response in the afferent neuron. As the direction of the linear acceleration vector is altered the neuronal response decreases in a cosine fashion (Shotwell et al. 1981). If it is assumed that the cupular membrane is homogeneous in all directions and that cupular membrane deformation is elastically linear without volume change (DeVries 1950), then hair cell displacement follows otoconial displacement. Therefore a translational displacement of the otoconia would most effectively stimulate only those hair ceils whose polarization axes in the utricular plane are exactly aligned with the direction of otoconial displacement. If the motion of the otoconia in the utricular plane is non-linear, then the output signal from single hair cells should also be non-linear. That this is so has been shown by stimulating and recording from single receptor hair cells (Shotwell et al. 1981). At present there is no evidence that the overall signal from all the individual hair cells or even from all the hair cells with a single polarization vector is linearized, perhaps by some kind of neural computation, even though the stimulus is non-linear. Consequently non-linear motion of the otoconia might quite directly lead to non-linear roll-tilt perception. In the following, it is proposed during simple roll-tilt stimulation the displacement pattern of the utricular otoconia is not unidirectional. Here we are only concerned with the steady state displacement of the otoconia, so that the effect of the endolymph viscosity is nil, and displacement of the utricular otoconia is directly proportional to the imposed shear force. For simplicity, we assume that the utricular macula is a flat plane although anatomical evidence shows that such an assumption is not correct (Corvera et al. 1958). With the head in its normal erect position the average angle of the plane of the utricular macula relative to Reid's base line is about 30 degrees, open anterior (Corvera et al. 1958). Since the utricular macula is not in the gravitationally horizontal plane when the head is erect, there must be a constant pitch-

6 190 g 2.0 F X" 9,,, o.. ~ h ~ t " ~ I 2.0 " y, 9.,,,...,. _i.o I Fig. 3. Schematic view from above of the utricular otoconia for a tilt-chair in a ] g environment (solid ellipse), in a 2 g environment (dotted ellipse) and for a fixed-chair centrifuge (thick straight line under abscissa)9 During roll-tilt stimulation the utricular otoconia will be displaced as shown by the elliptical paths. During fixed-chair centrifugation on the other hand the utricular otoconia will be displaced in a simple linear fashion. The equation for the hypothesized displacement pattern is given by the equation for an ellipse: Y' = R- K. sin 0 and X'=R.K.cosO.sine. In this equation Y' is the otoconial displacement in coronal plane in arbitrary units; X' is the otoconial displacement in the sagittal plane in arbitrary units; R is the magnitude of resultant force; 0 is the angle between the resultant force and the subject's Z-axis; c~ is the angle between the average utricular plane and Reid's baseline (30~ K is a constant of proportionality (the ratio of displacement, in arbitrary units, to the imposed force)9 Assuming that the deformation of the utricular macula is directly proportional to the imposed force, K equals 1. The X' Y' plane is coincident with the average utricular plane. Displacement of otoconia is symbolically shown with springs representing restoring forces. The inset in the centre indicates what would be the case if there was no shearing force acting on the otolith. All insets represent the right utricle. M = medial; P = posterior; L= lateral; A -- anterior shear force acting upon the receptor hair cells and in a 1 g force field the magnitude of this force is -0.5 g pointed backwards (1 g. sin330~ Since the otoconia are in a state of equilibrium the constant pitch-shear must be balanced by an elastic restoring force. During increasing roll-tilts to 90 degrees from gravitational vertical, this constant pitch-shear will progressively diminish, so that the elastic restoring force will progressively displace the receptor hair cells further anteriorly. Whilst this release from pitch-shear is occurring, the lateral displacement of the otoconia in a coronal plane (i.e. "roll-shear") will be increasing to a maximum. During further roll-tilts to the head upsidedown position, the pitch-shear will gradually reach +0.5 g pointed forwards (1 g-sin30 ~ and roll-shear will be zero (Fig. 3). From this analysis we conclude that during simple roll-tilt stimulation in a 1 g force L field the utricular otoconia are displaced not in a purely linear, lateral trajectory but rather an elliptical pattern. The proposed displacement pattern of the utricular otoconia for roll-tilt stimulation of 360 degrees from a head erect start position is shown in Fig. 3. For this analysis the displacement of the utricular otoconia in a 1 g force field is arbitrarily defined as zero at the start position, i.e. head erect. When the force field is 2 g, the utricular otoconia are additionally displaced in a posterior direction by 0.5 arbitrary units. The otoconial displacement patterns for 1 g and 2 g rolltilts are ellipses, whereas in contrast the otoconial displacement pattern for centrifugal stimulation is a straight line. Clearly there is a major difference in otoconial displacement patterns produced by simple roll-tilt and by centrifugation, and these different otoconial stimulation patterns may explain some of the differences in perceptual results obtained in these paradigms. The average saccular plane is parallel to the sagittal plane and the saccular pitch angle, the angle of the striola relative to the X Y plane, is approximately the same as that of the average utricular plane relative to the XY plane (Corvera et al. 1958; Rosenhall 1972). Therefore during roll-tilts a similar displacement pattern of the saccular otoconia should also occur in the saccular plane as occurs for the utricular otoconia in the utricular plane. This elliptical motion of the otoconia will change the population of the hair cells stimulated. During roll-tilt stimulation by centrifugation, the magnitude of roll-shear increases, but the magnitude of pitch-shear remains unchanged and therefore there should be no perceptual errors during centrifugation. In tilting experiments, however, there will be a change in pitch-shear which will cause an elliptical displacement pattern of both utricular otoconia and saccular otoconia, so perceptual errors (A and E effects) will occur. In accordance with these predictions, there is a corresponding tendency to overestimate roll-tilt angles (E effect) when the change in pitch-shear is less than 0.0 g and to underestimate roll-tilt angles (A effect) when the change in pitch-shear is greater than 0.0 g (Sch6ne 1964; Miller and Graybiel 1966; Correia 1968; Colenbrander 1964). Furthermore, only small underand overestimates have been reported in fixed-chair centrifugation studies (Noble 1949; Graybiel 1952; Dai et al. 1988). The effect of the change in pitch-shear will be further discussed in the next section. In the following, we develop predictive equations using Hixson's conventions for body axes (Hixson et al. 1966; Guedry 1974). All forces are expressed as specific force and rendered dimensionless by division throughout by g (where g=9.81 ms2).

7 Modelling In developing the equations for roll-tilt perception, we consider the whole otolithic system only, although the effect for the individual receptor organs, the utricle and saccule, may be different. If the otolith organs were perfect linear accelerometers and if there were no other signals to modify the otolith signals, the direction of the resultant force would be accurately perceived. This can be expressed by a simple trigonometrical equation as: P = 0 = tan- I(FrF~), (1) where P = the perceived roll-tilt angle, 0--the roll-tilt stimulus angle, Fy - the component of R in the body interaural (Y) axis (it is identical to roll shear), F~ = the component of the resultant force in the body longitudinal (Z) axis, R = the magnitude of the resultant and when R is in the Y-Z plane it is given by V(Fy)2 + () z. The obtained data from various kinds of experiments, i.e. 1 g tilt, 2 g tilt and centrifugation, is plotted in Fig. 4 together with the prediction from (1) as the diagonally dashed line. The 1 g roll-tilt data were reported by Sch6ne (1964) and Udo de Haes (1970); the 2 g roll-tilt data were reported by Colenbrander (1964), Sch6ne (1964), Miller and Graybiel (1966), and Correia t80 P toes) t20 60 O o A., TZLT ZN lg FORCE FZELD [3.. TZLT ZN 2g FORCE FZELO 9 " CENTRZFUBATZON (HEAD ERECT) D D A a ~ A A a Elefl,, i 8o, a D ft i o A, A a B 0 (OEG) Fig. 4. Prediction of roll-tilt perception (P) as a function of roll-tilt stimulation angle (0) shown by dashed line from (1) (see text). The 2 g data (squares) are from Colenbrander (1964), Sch6ne (1964), Miller (1966) and Correia (1968); the 1 g data (triangles) are from Sch6ne (1964) and Udo de Haes (1970); the fixed-chair centrifugation data (filled circles) are from Dai et al. (1988) I et al. (1968); the centrifugation data were reported by Dai et al. (1988). For any data point the particular distance between the perceived roll-tilt angle and dashed line shows the size of the roll-tilt perceptual error. From Fig. 4 one can see that the response from a perfect accelerometer deviates from the experimental data, increasingly as the roll-tilt angle increases, except for 2 g tilt at about 60 ~ roll-tilt stimulus angle where the perceived roll-tilt is close to the dashed line. The perceptual error appears to be associated, as described previously, with the change in pitch-shear, which can be expressed as Fps = Fp- Fp(o), where Fps = the change in pitch-shear, Fp = pitch-shear, given by R. cos 0. sin a, a = Reid's angle, Fps = the change in pitch-shear, vertical in 1 g force field (= -0.5 g). The following analysis of the results shows that perceptual error is related to Fps. When a subject is roll-tilted from an upright position (0 ~ to upside down (180 ~ in a 1 g force field, Fps is always equal or greater than 0.0 g and an A effect occurs (triangles in Fig. 4). When the subject is roll-tilted in a 2 g force field, Fps is less than 0.0 g for roll-tilt angles less than 60 ~ and in this situation an E effect occurs shown by the experimental data (Fig. 4). When the roll-tilt angle equals 60 ~ Fp~ is 0.0 g and there is small perceptual error: the experimental data are close to 60 ~. When the roll-tilt angle is greater than 60 ~ Fps is greater than 0.0 g and an A effect occurs (squares in Fig. 4). When the subject is roll-tilted by means of centrifugation alone, Fps is always zero, the experimental data is close to the dashed line although there are small A and E effects (filled circle in Figs. 4 and 7). Therefore it seems that in all these situations of rolltilt stimulation whenever Fp, is less than 0.0 g, the E effect occurs and whenever Fps is greater than 0.0 g, the A effect occurs and whenever Fps equals 0.0 g, the E and A effects should be zero. However the experimental data from 2 g tilt and centrifugation show that there is a small E effect when Fps is zero. This small discrepancy between the experimental data and predictions based on Fp~ alone will be discussed later. The ratio of and R determines the roll-tilt stimulus and from Fig. 4 one can see the error is roll-tilt stimulus dependent. Since the error may be also dependent on the change in pitch-shear, as described above, the ratio of F~ and R is scaled by this change in pitch-shear in the error function. Mathematically the magnitude of the error is derived from the sine transformation of the product of the ratio and the

8 192 change in pitch-shear, expressed mathematically as below: El =sin- x [Fy(Fv~ Fv'~ ]. (2) Therefore the perceptual roll-tilt angle now can be presented by: P=O-Ex. (3) p (OEO) o,,a PRED'rCT1rOHs FOR t0 Tt'LT (E2 - O) ~.....~..~'""..~.."~ 'Z'""" 9 O- El! 8o.~9149 i 9 A.'A b.4 0 (DEe) t Fig. 5. Prediction of roll-tilt perception in a i g force field (dotted line) in relation to relevant data from Sch6ne (1964) and Udo de Haes (1970). The effects of Ex is shown. E2 equals zero since the resultant force equals 1 g I Equation (3) closely fits the experimental data from 1 g roll-tilt experiments (Fig. 5). However when the force field is 2 g, (3) provides a reasonable fit to the data for roll-tilt angles only up to about 55 degrees (Fig. 6). For the roll-tilt angles greater than 55 degrees the prediction from (3) deviates from the data. For centrifugation experiments, there is no change in pitchshear with increasing roll-tilt angle so E 1 = 0 and the prediction for centrifugation experiments from (3) is the same as from (1), i.e. there is a small deviation between the predictions and experimental data9 These discrepancies between the predictions from (3) and experimental data may be due to the effect of the increased force field on sensory inputs other than otolithic ones: e.g. tactile and proprioceptive inputs. Another possibility is that the errors could be due to the non-planar characteristics of the receptor structures becoming a more dominant factor when the force field is greater than 1 g. In any case, to account for this discrepancy, another error term (E2) must be introduced to (3): E2=sin- i I(1-- R)(ff~--F~)F, 1 +sin- I [(R-1)(1- F~)(R-F~)Fv(o)Frl R5, (4) where the variables are as defined above. This second error term was obtained by computer curve fitting 2 g roll-tilt data, using a arbitrary combination of trigonometrical functions, and we can give it p (DES) PI:I~-II)ZCTZONS FOR 211 TI"LT.~ ~..."'" ~i" 9 " f o9 9 9 r f 'P (OEG) ~, PFIEDZCTZONS FOil CENTRZFI.~ATZON ~ IEI - o) ~ O- ~ 120.;,,.~.':..",~.'o.." 9 " ~...". ~ "... el....." a..~,.t~'" [] o ~;.!! 0 O0 t20! 10o Fig. 6. Prediction of roll-tilt perception in 2 g force field (dotted lines) for the 3 different predictive equations. The individual effects of E1 and E 2 as well as their combined effects are shown o (,Ab,.... 0,(DEG), Fig. 7. Prediction of roll-tilt perception for centrifugation (solid line). The fit is an improvement over the fit for a simple tan function. E1 equals zero since there is no change in pitch-shear during centrifugation

9 193 t o P (DEE) Am TZLT ZN to FORCE FZELD 1:3,, TZLT ZN 2g FORCE FZELD e,, CENTRZFUeATION (HEAD ERECT) ta..g"..~ a... tt"" A..'"".13"'.'" A..'~." B.. ".~a.t0 -','A A.:: 00:mG) O I,! O 80 t20 t80 Fig. 8. Summarized predictions for experimental data under different conditions as well as for head upside down centrifugation no reasonable physiological interpretation at this time. The magnitude of this error then can be seen in Fig. 6 which shows the different contribution ofe 1 and E 2 to roll-tilt perception in a 2 g force field. The term E 2 was constructed to fit the 2 g roll-tilt data, but E 2 was then included in a prediction of the centrifugation data. It is of great interest that when E2 was included the predicted curve for the centrifugation data was an even better fit than the simple Eq. (1) above (see Fig. 7). Moreover, the new term did not impair the fit to the 1 g roll-tilt data (Fig. 5) since the resultant force equals 1 g [see (4)]. The complete predictive equation for tilting experiments and for fixed-chair centrifugation experiments, therefore, can be expressed as: P = O- (E 1 + Ez). (5) The predictive curves for various roll-tilt experiments as well as the predictions for head upside down centrifugation are summarized in Fig Model Predictions and Discussion The model prediction and the actual experimental data are shown in Fig. 8. The model fits most of the data available from roll-tilts in 1 g and 2 g force environments as well as from fixed-chair centrifugation studies. No data are available for centrifugation studies in the head upside-down position, the so called otolithic blind spot (Miller and Graybiel 1966). The model predicts that whenever the change in pitch-shear is less than 0.0 g, there will be a tendency to overestimate the roll-tilt angle in simple tilting experiments, whereas whenever the change in pitch-shear is greater than 0.0 g there will be a tendency to underestimate it. If the magnitude of the resultant force is greater than 1 g, apart from the factors mentioned above, an enhanced asymmetry of sensory signals other than otolith signals will also contribute to the overestimate. It is noteworthy that as 0 approaches 90 degrees, the centrifugal force must approach infinity. In Fig. 8 we show predictions for fixed-chair centrifugation studies in which the resultant force exceeds 2 g, but this prediction would probably fail because the resultant force is outside the physiological range of human subjects. Our model cannot predict the small perceptual underestimates, obtained in fixed-chair centrifugation experiments (Noble 1949; Graybiel and Clark 1"965; Dai et al. 1988). A better knowledge of utricular and saccular geometry and the effect of ocular counterrolling on perception is necessary to modify the error terms and so to improve the model predictions. If a subject is not only tilted in the coronal plane but also in the sagittal plane, the perception of roll-tilt will be complicated as the unusual viewing position may interfere with the subject's concept of gravitational vertical or horizontal. For this reason, the model cannot predict the situation in which the illuminated bar deviates from eye level. Although the model can predict roll-tilt in a 2 g force environment quite well, we do not know the role of the induced elevator effect (Cohen 1973) on the perception of rolltilt. In a microgravity environment the elastic restoring force will cause the utricular otoconia to slide forward and the saccular otoconia to slide upward in comparison with their position in an upright subject on earth. However in microgravity the lateral shear on the utricle (Fv) will be zero. Such a displacement pattern of otoconia in microgravity resembles the displacement pattern when the head is upside-down on earth. The hair cell receptors cannot distinguish the displacement induced by linear acceleration from the displacement induced by elastic restoring forces. Consequently the interpretation of visual vertical by astronauts in a microgravity environment may be inverted as reported by some astronauts (Mittelstaedt 1985). This sustained displacement of the otoliths due to the release from the tonically acting pitch-shear may be a cause of space motion sickness. In conclusion, accurate perception of roll-tilt can be achieved in the fixed chair centrifuge studies and in tilting experiments in a 1 g environment with small roll-tilt angles. The perceptual errors which occur (A and E effects) may be associated with pitch-shear modulation of otolith roll-shear.

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