Otoliths as biomechanical gravisensors

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Adv. Space Res. Vol. 30, No. 4, pp. 745-750, 2002 © 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved

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OTOLITHS AS BIOMECHANICAL GRAVISENSORS.

A. V. Kondrachuk

Institute of Physics, Natl. Acad. Sci.,46 prospekt Nauki, 03028, Kiev, Ukraine

ABSTRACT

This paper analyzes experimental data related to the reaction of otolith afferents in response to acceleration (Fer- nandez and Goldberg, 1976). It considers the assumptions that were the basis of the interpretation of the stimulus- response characteristics of afferents proposed by Fernandez and Goldberg. Comparing these experimental data with the results of modeling the otolith structures of vertebrates indicates that some peculiarities of the neural responses may be explained by the spatial dependence of the material parameters of the otolithic membrane across its thickness and within the volume of the membrane corresponding to the terminal field. The importance of the spatial dependence of the material parameters of the otolithic membrane for otolith functioning is discussed.

© 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION The otolith functions as a gravisensor through a sequence of different physical and chemical processes that are

difficult or impossible to investigate experimentally. To understand the relationship between the input and output in the otolith organ, certain assumptions have to be used. The goals of the present paper are: 1) to analyze some of the assumptions related to the intermediate stages of transformation of the mechanical stimulus in the neural response used in the study (Fernandez and Goldberg, 1976); and 2) to show by comparison with the results of modeling the otolith structure that some peculiarities of the experiment (Fernandez and Goldberg, 1976) may be related to the spatial in_homogeneity of the otolith membrane (OM).

Otolithic organs of higher animals, especially mammals, are known to be very compliant. The OM of mammals may be described as a thin, soft plate of varying thickness and density lying on a 3-D curved epithelial surface (macular surface (MS)), where the receptor hair cell bundles (HCB) are located. The plate has a complex layered substructure, and its organic material resembles an inhomogeneous gel. The otoconial crystals are located in the upper (denser and heavier) part of the gel plate bordering on the endolymph (otoconial layer (OL)). The lower part of the OM, which is close to the macular surface and surrounds the HCBs, will be called the gel layer (GL). The distribution of otoconia within the OL is inhomogeneous. Therefore, the OM is not a uniform structure, but struc- turally inhomogeneous in directions normal and parallel to the macular surface. The macular area of afferent neurons that innervate several individual hair cells is called the "terminal field" (TF). The TF average size is 40 to80 microns (Goldberg et al., 1990). The neuroelectric activity carried by one afferent usually represents the sensory information provided by several HCBs of the same TF. Thus, there is spatial inhomogeneity related to the distribution of the TFs over the macular surface. Under inertial displacement of the OM with respect to the macula, shear forces deform the HCB, initiating information processing of linear acceleration. It is thought that HCB deformation completes the mechanical stage of the transformation of the external physical stimulus.

MAIN ASSUMPTIONS RELATED TO THE STIMULUS-RESPONSE TRANSFORMATIONS The otolith function assumes a sequence of stages in transforming the external otolith acceleration via

mechano-electrical transduction by the HCBs to changes in rate of afferent pulses. The classic work of Fernandez and Goldberg (1978) was devoted to measuring the neural responses of the units recorded from the otoliths of squirrel monkeys to static forces (gravity and centrifugal force). Therefore, the goal of that study was to link the mechanical input and neural output of the otolith organ. To analyze the afferent response of the individual neuron to the given acceleration, Fernandez and Goldberg (1978) had to formulate special additional assumptions, corresponding to the intermediate stages of the mechanical input transformation, although some of them were not de-

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746 A.V. Kondrachuk

fined explicitly. There are five assumptions. First, the directional sensitivity of the afferent response can be char- acterized by an individual vector of polarization of a terminal field (Vt'TF), which reflects a cumulative reaction of the HCBs belonging to the given terminal field. Second, the VPTF is parallel to the local tangent of the macular surface in the region of a terminal field since the macular surface is curved. Third, the VPTF is a function of the given terminal field and does not depend on the type of the mechanical stimulation of otolith. Fourth, the afferent response is determined by a projection of a vector of acceleration on the VPTF. Fifth, the relationship between the afferent response (expressed as the rate of the discharge) and the acceleration can be determined by the differential equation of a one-dimensional damped oscillator.

Thus, the analysis of the stimulus-response characteristics of the otolith afferent proposed by Fernandez and C-oldberg (1978) dealt with two subjects: the vector of acceleration and the vector of polarization of the terminal field. The listed assumptions define the presumed properties of these objects (Figure 1).

The analysis of the OM morphology (Lindeman, 1969; Ross et al., 1987; Takumida et al., 1992; Kachar B. et al., 1990), the experimental data related to the afferent responses (Goldberg et al., 1990; Fernandez and Goldberg, 1976) and modeling results (Kondrachuk and Ross, 1997; Kondrachuk and Ross, 1996, Kondrachuk, 2000a, Kon- drachuk, 2000b, Kondrachuk, 2001) show that the listed assumptions are not obvious and need to be discussed.

1. The acceleration of the upper (heavy) pan of the OM deforms the OM gel layer. Because the OM is a spatially distributed system, local displacements of the every point of the OM volume under inertial acceleration are 3- D vectors. These vectors depend on the locations of the points in the OM volume and the spatial distribution of the material parameters of the OM. Thus, their directions may differ from the direction of the inertial acceleration even within the volume corresponding to the terminal field (VTF). This may be illustrated by the following estimates. The size of a terminal field (40 to 80 p~m) (Goldberg et al., 1990) exceeds the effective thickness of the GL (10 to 20 ~tm) (Lindeman, 1969). The widths of the specific spatial inhomogenious regions of the OM (striola region and the border regions) are 50 to 70 ~m and 30 to 50 ~m respectively. Therefore, the OM displacements within a terminal field may vary.

The existence of otoconia of different sizes may also affect the difference of the local displacements within the TF. Data from guinea pig (Lindeman, 1969) show that there is a significant diversity of otoconia size distribu- tions in the peripheral region (largest otoconia) and central (striola) region (smallest otoconia) of the OM. The average distance between receptor cells in the first region is about 7.6 ~ and 8.6 ~tm in striola region, while the otoconia sizes are l0 to 20 ~m and less than 1 ~tm in these regions. The displacement of otoconia in the peripheral region of the OM may thus overlaps a few underlying receptor cells whose displacements will be strongly synchro- nized, in contrast with more independent behavior of the receptor cells in the striola region.

In summary, we suggest that the acceleration results in a set of vectors of the displacements of the GL micro- volumes corresponding to the HCBs of the same TF. The vectors of displacements of these volumes may differ from each other and from the direction of the applied acceleration depending on the local inhomogeneities of the OM within the TF and the location of the TF on the macular surface. Therefore, we have to assume that there are certain peculiarities of the OM structure that decrease the diversity of local vectors of displacements.

2. According to the modeling results (Kondrachuk and Ross, 1996, 1997; Kondrachuk, 2000b, Kondrachuk, 2001), the displacements of the GL are functions of the distance from the macular surface. Therefore, the information about the displacement of the GL is not sufficient to predict the deformation of the 3-D structure of the HCBs because it also depends on the details of the attachment of the HCB to the GL and may differ for hair cells of different heights and configurations. (It may also depend on the location of the hair cells on the macular surface.) The selection of the possible movements of the HCB may be conditioned by the structure of the attachment and the parameters of the HCB itself.

Thus, the displacement of the HCB is a function of the material parameters of the corresponding microvolume of the GL and depends on the HCB 3-D structure and its attachment to the GL.

Hence, the set of assumptions listed above has to include two additional ones. First, the HCB displacement can be described by a single vector. Second, this vector has to be proportional to the vector of the local displacement of the OM. This may mean that the HCB displacements are tightly bound to the GL displacements and that their possible modes are restricted by some structural peculiarities of the GL and/or the HCB attachment to the GL.

3. The same problems are related to the assumptions concerning the polarization vectors. The experiments carried out by mechanical stimulation of the isolated HCBs (Hudspeth and Corey, 1977) demonstrated the existence of the effective vector of the morphological polarization of the individual HCB (VP). (These experiments were the basis of the statement that the HCB response to stimulation is determined by the projection of the vector of displacement on the VI'.)

Otoliths as Biomechanical Gravisensors 747

We should note that the TF includes a few type I and II hair cells. These hair cells are interconnected by effer- ent and afferent endings that form the complex, spatially distributed structure. Therefore, the vector of morphological polarization that corresponds to this unit and can be determined by precise tilt experiments represents a coupled function of the group of spatially distributed and interconnected hair cells. The orientations of the VI ) of each of the cells from this group and the structure of their bundles (location of the kinocilium with respect to the distribution and locations of stereocilia) are not identical and/or symmetrical, as can be seen from morphological studies (Ross et al., 1990). Thus, we have to introduce an additional assumption. Specifically, the possibility of representing the function of this complex structure by a unique and stable vector of the polarization with well-defined orientation and a single transformation function may indicate that the outputs from the individual HCBs corresponding to the unit are preprocessed before or during the formation of its neural response (Ross et al., 1990).

The validity of the assumptions proposed in (Fernandez and Goldberg, 1976;Goldberg et al., 1990) was based on the consistency of the interpretation of the experimental data obtained. We suggest that these assumptions reflect some unknown specific peculiarities of the OM structure and function and will focus on two of them related to the mechanical properties of the OM.

THE INHOMOGENEITY OF THE OTOLITH STRUCTURE A) The first of the assumed peculiarities of the mechanical and structural properties of the OM may be the in-

homogeneity of the OM gel layer across its thickness which corresponds to the smallest value of Young s modulus near the macular surface. The thickness of this sublayer is probably comparable to the HCBs heights.

This hypothesis may be explained as follows. When the GM sublayer has a much lower Young s modulus than the rest of the otolithic membrane, almost all deformation of the GM caused by the inertial displacement of the overlying otoconial mass takes place within the thickness of the sublayer. This will result in the most effective transfer of the inertial displacement of the otoconia to deforming the receptor cells. In this case, the vectors of the sublayer displacements will be almost parallel to the macular surface, and their magnitude will be chiefly determined by the projection of the inertial acceleration on this surface. We should note that the macular surface is curved and the local displacements will reflect the local curvature of the MS. The following modeling results based on experiments (Fernandez and Goldberg, 1976; Benser et al., 1993) appear to support this hypothesis. Benser and colleagues (1993) have reported the only direct mechanical measurements of an otolith organ, that of the bullfrog s sacculus. In this study, shear forces were applied at the center of the surface of the gel layer (compact otolithic gel membrane (GM)) with the otoconial mass removed, and the resultant motion of the layer in this plane was measured. The results of computer stimulation (Kondrachuk, 2000a) of the experiment (Benser et al., 1993) show that the measured displacements of markers located on the GM surface that were caused by the movement of the probe s tip can be explained only with the supposition of the GM inhomogeneity across its thickness, when the lower part (sublayer) bordering the epithelial surface has much a more lower Young s modulus than the upper part attached to the otoconial mass (2.5 102 N/m: and 6.6 103 N/m 2 respectively). The known morphological findings (Lindeman, 1969; Ross et al., 1987; Takumida et al., 1992; Kachar B. et al., 1990) also indicate the existence of a weak gel layer near the macular surface. The thickness of this sublayer was found to be close to the height of the kinocilium of the HCBs. Since the studies (Lindeman, 1969; Ross et al., 1987; Takumida et al., 1992; Kachar B. et al., 1990) used the otoliths from different animals such as rat (Lindeman, 1969) and bullfrog (Kachar B. et al., 1990), the existence of sublayer with lower Young's modulus appears to be a general property of otolith organs.

This fact is also supported by the analysis of the experimental data (Fernandez and Goldberg, 1976). The following combinations of the gravity and centrifugal force were used in this study: the gravitational force (G) normal to the macular plane and the vector of morphological polarization of the unit (VPTF) + the centrifugal force (F) parallel to this vector; the G-force parallel to the VPTF + the force F normal to the macular plane and the VPTF; and the G-force normal to the macular plane and the VP + the force F normal to the VP, but parallel to the macular plane. The centrifugal forces normal to the macular plane and the VP were called orthogonal-compression forces; forces normal to the VP but parallel to the macular plane were called orthogonal-shearing forces (Figure 2). The study (Fernandez and Goldberg, 1976) indicated the absence or very small effect of the orthogonal-compression forces on the unit response.

The computer modeling of Fernandez and Goldberg experiments (Fernandez and Goldberg, 1976) devoted to orthogonal-compression forces was carried out (Kondrachuk and Ross, 1996; Kondrachuk and Ross, 1997; Kon- drachuk, 2001) using the 3-D model of the OM. The modeling results indicate that the relatively small displacements of the inner points of the OM for experimental conditions corresponding to the orthogonal-compression forces correspond to the existence of a thin GL (10 to 20gm) with the lowest Young s modulus (10 N/me). The average difference of the displacements of the inner points of the OM corresponding to the opposite directions of the orthogonal-compression forces in the experiments (Fernandez and Goldberg, 1976) was 0.04 and 0.043 microns or

748 A.V. Kondrachuk

4 and 4.5% of the average X displacements in these cases. The average difference of the calculated di~lacements corresponding to 135 ° and 45 ° angles of the G-vectors relative to the macular plane was 0.024 microns or 5.5% of the average X displacements (Kondrachuk, 2001). (These estimates were carried out using a finite-element computer model of the OM.) Therefore, we may assume that the ratio of the magnitudes of the elastic parameters of the upper and lower (gel) layers of the OM as well as the thinness of the gel layer are mainly responsible for the weak dependence of the displacements on the orthogonal-compression forces.

A thin GL sublayer with a very low Young s modulus is thus an effective way of Uansforming the applied acceleration into the displacements parallel to the macular surface. However, the modulus has to be sufficiently high to provide the coupled HCB+gel displacement.

We may also assume that the material parameters of this sublayer have to be homogeneous within the TF in order to ensure the best possible unidirectionality of corresponding HCBs displacements. Taking into account the complex structure of the system, this condition may be practicable only if the local inhomogeneities of the sublayer within the TF and the values of the acceleration are small enough.

What happens if the inhomogeneities of the material parameters of the gel sublayer are not small or if a high acceleration is applied7 We may expect that different parts of the TF will undergo different (nonlinear) displacements. The relation of the magnitudes of acceleration and inhomogeneity will determine the effect, and would vio- late the assumption of linear dependence of the displacement vector on the acceleration vector or the assumption of the unidirectionality of vectors of displacements over the TF.

The following experimental data appear to indicate this effect. B) The experimental results (Fernandez and Goldberg, 1976) related to the neural response caused by the or-

thogonal-shearing forces (OSF) demonstrate the following peculiarities, a) The average response to the OSF was found to be 10-15% of the average response corresponding to the parallel excitatory and inhibitory forces, but for some units this was about 33%. b) This response had the same sign for the centrifugal forces 180 degrees apart.

It can be shown (Kondrachuk, 2001) that the magnitude of the displacement, which is normal to the OSF and has the same sign for the OSFs 180 apart, cannot be explained in the framework of the homogeneous (along the surface) elastic model of the gel sublayer. We suggest that the OSF effect may be explained by the inhomogeneity of the elastic properties of the gel layer within the VTF. The explanation is as follows.

For inhomogeneous elasticity of the gel within the VTF, the displacements of the different parts of the TF volume will be different and will not be parallel to the inertial acceleration vector. The maximal displacements will be in the regions of the lower Young s modulus. In this case, a single vector of displacement can not describe the displacement of the TF volume. Let s assume that there is a gradient of the elastic modulus of the gel along the VPTF and that the opposite parts of the TF (A and B) have the lowest and the highest Young s modulus. Let the acceleration vector be initially normal to the VPTF. When acceleration is applied, the displacements of the VTF will not be parallel to the acceleration. The effective projection of the acceleration vector on the VPTF of the dis- placed "IF volume may be represented by the projection of acceleration on the turned vector of polarization. (We assume that true VPTF remains the same.) In this case, there will be a nonzero projection of the acceleration vector on the effectively turned VPTF. (Figure 3). To compensate this projection, the angle between the acceleration and initial VPTF has to be decreased. This angle will also be decreased for accelerations applied 180 ° apart. This hypothesis explains the observed experimental data (Fernandez and Goldberg, 1976).

There are some indirect morphological confirmations of this hypothesis. For example, the structure and likely material parameters (including the parameters of the otoconial layer) of striola region differ from those of the other parts of the OM (Lindeman, 1969; Ross et al., 1987; Takumida et al., 1992; Kachar B. et al., 1990). The orientations of polarization vectors of afferents that are mostly normal to the striola line are grouped in stripes that roughly reproduce the topography of the striola. If we assume that the material parameters of the OM (and in par- ticular, the gel layer) gradually vary normally to the striola line, it may provide the necessary correlation between the TF polarizations and the gradient of OM inhomogeneity.

We should note two points. First, the observed OSF effects are rather small. The angle of assumed turn of the VPTF averages 5°to 8 ° but reaches 15 ° for some units. Since the TF is 50 to 80 ttm in diameter, the inhomogeneity of the gel may be a few percent to provide the difference of displacements corresponding to this angle. Sec- ond, the OSF effect was observed for a rather high magnitude of acceleration (1.23g) that exceeds the physiologi- cally normal range of the steady-state acceleration. The effect may be negligibly small for lower accelerations.

Therefore, this hypothesis may be formulated as follows. There is a small inhomogeneity of the gel within some TF volume the gradient of which is parallel to the vector of TF polarization. This inhomogeneity may show up when a high acceleration is applied.

Otoliths as Biomechanical Gravisensors 749

Acceleration

I Projection ofgel displacement on the VP

Projection of acceleration on the MP =* displacement of gel sublayer

L Orthogonal- [ compression force

Orthogonal- shearing force

[Otolithic membrane [

Fig. 1. The relationship between the acceleration and the projection of weak gel sublayer displacement on the VP.

Fig. 2. The scheme of centrifugal forces that were used in Fernandez and Goldberg experiments (1976).

I Terminal field

Gradient of gel elasticity Projection of acceleration on the VP

/ Acceleration I Acceleration

Vectors of displacements

Fig. 3. Gradient of material parameters of otolith within the TF may result in the turn of terminal field.

750 A.V. Kondrachuk

FUTURE PERSPECTIVES The stimulus-response relationship in the otolith organ remains a most important but unresolved problem of

otolith functioning and interpretation of experiment results, Mathematical modeling can be helpful tool for solving this problem. The modeling results presented in this study suggest the following future work related to modeling the stimulus-response properties of the otolith. 1. Modeling of the dynamics of the 3-D otolith membrane taking into account its viscoelastic properties. 2.Analyzing the possible role of the striola region inhomogeneities in dy- namic responses of the otolithic membrane. 3. Simulating otolith behavior for a curved macular surface. 4.Analyzing the deformation of the hair cell bundle spatial structure caused by the displacement of the surrounding gel. The results of the present work also suggest the necessity of conducting experiments devoted to estimating the material parameters of the otolithic membrane.

CONCLUSIONS The analysis of the assumptions posited in the interpretation of Fernandez and Goldberg (1976) experiments

shows that these assumptions have to be extended. One of the main additional hypotheses relates to the existence of certain mechanisms that integrate (preprocess) the directionally sensitive responses of individual HCBs in an after- ent fiber so as to foam a stable end unique direction of the VPTF.

These assumptions reflect the specific peculiarities of the OM structure that promote the transformation of the mechanical stimulus (acceleration) in the neural unit response. Comparison of modeling with experimental data suggests that some of these peculiarities are related to the spatial dependence of the material parameters of the OM structure. For example, the OM gel near the maeular surface has the lowest Young s modulus, and this gel sublayer is homogeneous within the terminal field.

REFERENCES Benser, M. E., N. P. Issa, and A. J. Hudspeth, Hair-bundle stiffness dominates the elastic reactance to otolithic-

membrane shear, Hearing Res., 68, pp. 243-252, 1993. Fernandez, C., and J. M. Goldberg, Physiology of peripheral neurons innervating otolith organs of the squirrel

monkey. II. Directional selectivity and force-response relations, J. Neurophysiol., 39, pp. 985-996, 1976. Goldberg, J. M., G. l)esmadryl, R. A. Baird, and C. Fernandez, The vestibular nerve of the chinchilla. V. Relation

between afferent discharge properties and peripheral innervation patterns in the utricular macula, J. Neuro- physiol., 63, pp. 791-802, 1990.

Hudspeth, J., and D. P. Corey, Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli, Proc. Natl. Acad.Sci. USA, 74, pp. 2407-2411, 1977.

Kachar, B., M. Parakkal, and J.Fex, Slruetural basis for mechanical transduction in the frog vestibular sensory apparatus. 1. The otolithic membrane, Hear. Res., 45, pp. 179-90, 1990.

Kondrachuk, A. V., Computer simulation of the mechanical stimulation of the saccular membrane of the bullfrog, HearRes., 143, pp. 130-138, 2000a.

Kondrachuk, A.V., Modeling of the struclme and mechanics of the otolith membrane, Aviakosmicheskaya and ek- ologieheskaya meditsina, 34, pp.45-51,2000b.

Kondrachuk, A. V., Finite-element modeling of the 3-D otolith structure, J. Vest. Res. 11 (1), 2001 (in press). Kondrachuk, A. V., and M. D. Ross, The 3-D model of otolith structure under static loads, Abstracts of the Twelfth

American Society for Gravitational and Space Biology, Charlotte, NC, USA, 1996. Kondrachuk, A. V., and M. D. Ross, Modeling of the otolith structure behavior under static loads (inertial forces

and endolymphatic pressure), Abstracts of the Twentieth Annual Midwinter Meeting, Association for Research in Otolaryngology, St-Petersburg, Florida, USA, p. 154, 1997.

Lindeman, H. M., Studies on the morphology of the sensory organs of the vestibular apparatus. Ergebn. Anat. Entw. Gesch., 42, pp. 1-113, 1969.

Ross, M.D, T. E. Komorovski, K. M. Donovan, and K. G. Pore, The suprastructure of the saccular macula. Acta Otolaryng. (Stockh.), 103, pp. 56-63, 1987.

Ross, M. D., G. Meyer, T. Lain, L. Cutler, and P. Vaziri, 3-D components of a biological neural network visualized in computer generated imagery, Acta-Otolaring.(Stockh.), 109, pp. 235-239, 1990.

Takumida, M., Y. Harada, and D. Bagger-Sjoback, The statoconial membrane of guinea pig utricular macula. Acta Otolaryng. (Stockh.), 112, pp. 643-648, 1992.

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Otoliths as biomechanical gravisensors