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A piezoelectric theory of fish auditory perception Marine Zoology Research Report Michael Chew
Introduction Despite the fervent interest and research into otoliths for age growth studies, their functionality and specific role in auditory perception remains less clear; current auditory theories are still contested and often lack conclusive evidence. This paper suggests that a theory of otolith piezoelectricity may fill some of the existing theoretical gaps in understanding. It concludes with some sketches of experimental methodologies.
Fish Hearing: An Outline Fish perceive sound through their inner ear, which shares some typical vertebrate features namely three semicircular canals and three otolith organs, the utricle, lagena, and saccule. The semicircular canals detect angular accelerations, while the otoliths themselves appear to share both auditory and vestibule functions.1 Each otolithic organ contains a single calcareous otolith, developed from steady deposition of calcium carbonate and other mineral salts.2 Otoliths are approximately three times denser than the rest of the fish body, whose density is similar to water. Therefore sound waves propagating through water pass straight through the fish body with their phase and amplitude unchanged, while the denser otolith vibrates with differing phase and amplitudes relative to the body. Sensory hairs, similar to those in other vertebrate ears, transduce this motion into nerve firings. The hairs’ apical end, covered with cilia, projects into the lumen of the otolithal chamber; where the cilia produce an electric potential when bent by the vibrating otolith. This stimulus propagates through to the central nervous system via the eighth neuronal nerve where sound is then perceived. Fish possessing a swim bladder may pick up sound via a different ‘indirect’ method. Like the otolith, the hollow swim bladder is of a different density to the fish body and the surrounding water and hence will vibrate with different amplitude and phase. This produces re-radiated acoustic energy which can reinforce otolith motion and thus improve auditory sensitivity. However this effect is only apparent in fish where the swim bladder is physically close to the
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Tavolga 1981:3-4. The otoliths are secreted through daily deposition and form concentric rings or ‘increments’ as they grow, the width of which depends on environmental conditions (Dean 1983:355). 2
2 otolith – else attenuation of the re-radiated energy is excessive and no enhancements to sensitivity are observed.3 Alternatively, if acoustic coupling is present – in cases where there is some special connection between the otolith and the swim bladder4 – re-radiation, and hence sound perception, can be greatly enhanced.
Limitations of the theory Although the hearing mechanisms outlined above appear straightforward, in reality there are many gaps and limitations to our understanding. Underwater acoustics is an area where we are still relatively ignorant. A fundamental fact is that a sound source will produce both a far field propagated pressure wave, and a near field displacement wave. This can be illustrated with the simplest ideal case of an expanding sphere as a sound source.5 If it is sinosoidally pulsing with minimum volume A, maximum volume A+D, then the sphere at its maxima will project radially D volume of water in a spherical shell, which continually to expand radially. Thus the originally displaced volume D will be spread over a larger and larger surface area and the radial displacement wave diminishes as 1/r2. If water is completely incompressible, this near field would be the only wave phenomena - however the slight compressibility of water allows an elastic compression wave, just as sound propagates through air. This obeys the usual wave equations and decreases with 1/r. Therefore, compared with the displacement wave (1/r2) the pressure wave is small at close range6, to take over at longer ranges. The otolith organs of fish are capable of responding ‘directly’ to displacement waves through the otoliths vibratory response, and ‘indirectly’ through the swim bladder’s elastic volume responding to pressure waves. Since particle motion cannot simply be predicted from the near-field, both motion and pressure must be independently measured in behavioural experiments. Conversely, many species react mainly to either pressure or sound; some (otophysans) are especially sensitive to pressure, while others (flatfish, sculpin), are more displacement sensitive. Many experiments have assumed the untested assumption that their subject species were pressure sensitive.7
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Tavolga 2000:18. These coupling mechanisms include Weberian ossicles in Otophysans, and rostral projections in soldierfish. Fay 1993:26-27. 5 Tavolga 1964:282. This example represents only the simplest case - the single monopole source - but is helpful to bring up issues pertaining to more complicated sounds. 6 ‘Close range’ is around wavelength/2π. Fay 1993:16-17. 7 An exception is van de Berg and Schiuijf 1985. See Fay 1988 for a review. 4
3 Another gap in understanding concerns frequency analysis. Studies have shown that the ability to discriminate frequencies is widespread amongst fish.8 However, the specific mechanism underlying this analysis remains elusive, given that the structure enabling frequency discrimination in mammals, the cochlea, is absent from fish. Temporal analysis is seen as one possible explanation – where sound information is encoded in neuronal spiking rates that is related to the temporal nature of the stimulus. 9 Another explanation describes how the fish ear is imbued with a frequency-to-spatial mapping, where different regions of the saccular macula may respond to different frequencies. 10 However, both these theories have problems and the issue of frequency discrimination is still uncertain. 11
Piezoelectricity and otolith structure Piezoelectricity is an effect seen in certain classes of crystals where compression or torsion creates a proportional electric potential. This arises from these crystals possessing a structure with an asymmetric charge distribution; when it is distorted, the positive and negative ions are slightly separated and thus this charge separation creates an electric potential which causes a subsequent flow of current. It has been experimentally shown that the otoliths of several fish species are piezoelectric.12 The specific process of otolith growth is not totally understood, however from what is known piezoelectric qualities in the microstructure are plausible. Ultra-high resolution electron microscope studies of otoliths have shown that they are comprised of composite crystallites, arranged in micro-domains - not the single crystals they can resemble under lower magnification.13 The growth and arrangement of these asymmetric crystallites are thought to be organised by organic material which forms the matrix-substrate for the crystals.14 It is this asymmetry which may give rise to piezoelectricity. The main minerals involved in otolith growth are carbonate polymorphs - in fish the mineral is usually deposited in the form of aragonite or calcite crystals. Piezoelectricity could not exist if the organic ‘seeds’ were not present - calcite and argonite are symmetric and hence are not piezoelectric. The selective organic deposition, mediating the forming of crystal domains, therefore suggests that piezoelectricity is not simply a chance byproduct of the natural otolith structure, but rather that it is a planned or selected for effect. The fact that for many fish, otoliths possess an outward morphology that mimics that of 8
Popper 2000:22, Fay 1993:20. Rogers 1988:341. 10 Fay 1984:952-3. 11 Tavolga 1976:27, Fay 1993:21. The results of Sand 1978:89 refute the frequency/spatial hypothesis. 12 See Morris 1967. The two species examined were Parophrys vetulus, and Tremeatomus bernacchii. 13 Mann 1983:417-418. 14 Ross 1984:447. 9
4 single crystals of calcite or aragonite, while their bones and teeth assume shapes totally unrelated to the mineral crystallites of which they are composed15 reinforces the contention that the piezoelectric effect is planned for.
Piezoelectricity - Implications Having established that piezoelectricity is not only is present in some fish otoliths, but that it appears as if is it is selected for, we move on to postulating its possible functions. Although there has been demonstrated a correlation between hearing ‘specialists’ – fish possessing swim bladders and Weberian apparatus - and hearing sensitivity 16, there are still inconsistencies between some species of fish lacking swim bladders but which still exhibit sensitivity to pressure waves.17 Namely the presence or absence of a swim bladder has be found experimentally to be ineffective in altering the auditory perception in some species. 18 Clearly another mechanism is at work, and piezoelectricity offers one possible explanation for such an alternative pressure transducing mechanism. By this hypothesis, the pressure waves impacting on the otolith create a miniscule distortions in its crystal structure. These distortions give rise to charge separation and a proportional current flow (and hence nerve firing) due to the otolith’s piezoelectric properties. The possibility of deformation of a calcareous otolith may appear small, however it has been shown that the otolith’s collagenous matrix gives it some pliability19, allowing for the deformations that piezoelectricity requires. Taking the piezoelectric hypothesis to the extreme would change profoundly how we view sound perception in fish; instead of the actual movement of the otolith and the bending of the cilia to generate action potentials, the potentials are generated inside the otolith while the hair cells propagate the signals. It has been clearly demonstrated that hair cells do excite specifically when bent20, therefore it is likely that the piezoelectric transduction occurs in conjunction with the currently accepted theories discussed above, possibly acting to enhance sensitivity. Given
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Ross 1984:446. Popper 2000:19. 17 Fay 1993:27. It has been shown for some species that the resonance frequency of the swim bladder is considerably above the frequency of best hearing and so its role as indirect resonator or reflector is far from clear. 18 Offutt 1970:226. 19 Maisey 1987:496 20 Fay 1993:16, Tavolga 2000:17. However this does not rule out the possibility that piezoelectricity is primarily the auditory response mechanism, and gross otolith movement exciting hairs cells primarily for the gravity and linear acceleration response. 16
5 there are three otoliths, it is possible that one or more specialize in piezoelectric transduction, with remainder devoted to vibratory response. 21 A piezoelectric otolith may also provide an alternative to the frequency analysis theories described above. Any structure that has acoustic asymmetry will respond differently to sound waves of different frequencies.22 Analogously, asymmetric piezoelectric crystals may resonate differently at different frequencies.23 Therefore the piezoelectric otolith may act to discriminate frequencies as the cochlea does in mammals. This view has unexpected support from an evolutionary perspective. It is known that primitive fish exhibited the amorphous otolith microstructure, while more advanced fish developed crystalline structures which have enabled piezoelectricity. What is telling is that mammals and birds, which have developed the cochlea - a highly effective hearing and frequency processing mechanism - have lost this crystal structure as well.24 Therefore a reasonable conjecture is that the frequency-discriminating role of the piezoelectric crystals have passed onto the cochlea.
Problems The piezoelectric hypothesis presents a number of problems. One is charge leakage; the charge built up on the otolith due to its compression is likely to drain away via unintended charge carriers, such as extraneous ions. So far no mechanism preventing this is known. Another problem is variation in auditory sensitivity with age. As the fish ages the surface area of the otolith is enlarged through deposition of calcareous material - if a certain charge density is invokes on the otolith surface due to compression, then consequently an older fish with a larger otolith would store more charge, and have a possibly different piezoelectric response. The exact mechanism for determining the piezoelectric response is also unknown. If the surface of the otolith is an equipotential, then there must exist some means of completing the circuit to its interior. The distinct radial spokes, emanating from the otolith’s core, may serve this function, though no studies have been conducted on this to date.
Experimental Methods Experimental verification of the piezoelectric hypothesis may be difficult on several counts. Determining the actual potential generated by the otoliths is complicated since the crystal 21
The theory that the sacculus functions specifically using a piezoelectric mechanism while the lagena and utriculus use vibratory means is found in Offutt 1970:227. 22 See van Bergeijk’s ‘Bongo drum theory’ in van Bergeijk 1967. 23 Cady 1964:469-483. 24 Tetrapods exhibit mono-crystalline calite or aragonite otoliths, which are symmetric and hence nonpiezoelectric.
6 micro-domains have complex, varied orientations which could produce localised, highly specific piezoelectric activity (which could be picked up by single hair cells), or the larger type of global piezoelectric effects as measured by (Morris 1967). The very act of removing the otolith from the fish and the subsequent dehydration suffered 25 may destroy the natural domain orientation of the crystals26 and hence eliminate any potential local piezoelectric activity, which may be providing the fish with frequency-specific neuronal signals (assuming some frequency/spatial mapping). Behavioural responses are of little use alone since we are trying to determine the method of transduction at the otolith site; the fishes’ response to sound could be due to piezoelectric effects or vibratory and we would have no way of determining through just behavioural responses. Thirdly, the piezoelectric effect may provide only a small measure of enhancement to the vibratory transduction, at specific frequencies perhaps, and thus to experimentally separate out this subtle effect past experimental error may be difficult.
With these limitations in hand, we will tentatively sketch some possible experimental procedures. One way would be to compare the piezoelectric frequency response range of the otolith to the frequency response range for the fish. Since our hypothesis relies on piezoelectricity as the transductor for frequency, a strong correlation between the two would suggest that piezoelectricity plays a definite role in hearing. The piezoelectric frequency response can be determined in a way analogous to (Morris 1967); that is, otoliths are mounted between two plates - a frequency generator for exciting the crystal and a microphone for listening to its response. Vibration from the otolith indicates that it would respond piezoelectrically to sound waves of that frequency, this would be picked up by the microphone.27 The frequency response of the fish could be measured behaviourally through prior conditioning of the fish to sound.28 There is the possibility that the piezoelectric effect only enhances or provides transduction over a certain range of frequencies, with vibratory transduction filling in for the remainder of the fishes total range – in this case a large discrepancy between the two ranges could be observed without invalidating the hypothesis. Further investigation would be required in this case. Another procedure could be based on piezoelectricity’s temperature dependant relation.29 If the otoliths are slowly heated while undergoing sonic stimulus, while the neuronal traffic of the eighth nerve is monitored, some measure of the piezoelectric component to overall auditory 25
Maisey 1987:495. Ross 1984:448. 27 This indicates the converse effect for piezoelectrics, namely that the crystal will deform if applied with an electric potential. It is symmetric in frequency with the ‘direct’ effect of excitation (namely deformations producing the potential) Cady 1964:175-6. 28 Atypical example of this technique is found in Tavolga 1976:116-140. 29 Cady 1964:136-140. 26
7 transduction could be determined by the deviation of the nerve firings as proportional to otolith temperature, since the piezoelectric component would alter while the vibratory response would stay constant. This relies on the vibratory component having less temperature sensitivity than the piezoelectric component, which needs to be investigated further. This heating of the otolith could be produced by a highly focused laser, while the nerve measurement could be carried out analogously to (Tavolga 1976:298-308). A similar experiment could be conducted with the otolith being exposed to a variable electric field, instead of heat. The piezoelectric effect, through relying on a mechanism of charge separation, is altered by the presence of an electric field.30 The vibratory response would be unchanged by such as field, as the proportion of free charges in the otolith are a negligible contribution to its total mass and center of gravity. The electric field could be supplied by charged plates on either side of the fish. The orientation of the plates and hence the electric field could be altered to compare along the otolith’s specific axes of vibration. In addition to these experiments, the procedure of testing the hair cells for their conduction of potentials would vital – for if they react only to mechanical stimulus then this would obviously invalid the piezoelectric theory. It may be revealing to compare the results of the experiments between fish possessing swim bladders and those not – the former already have the means of pressure wave transduction, while the latter do not, and thus we may expect piezoelectric activity to be more active in the nonbladder fish if it is operating as a primary mechanism. Another approach would be to run the experiments using sound stimuli from both the near field and the far field; the former comprising of both pressure and displacement waves, the latter just pressure waves. We thus expect piezoelectricity to take a distinct role in the far field. In conducting the near field experiments it is vital to be aware of small tank acoustic effects – ‘ideally’ the procedures would take place in the open ocean.31 While we have been so far focusing on fish otoliths, some statocysts are also quite likely to exhibit piezoelectricity, as many have similar microstructures, and the above experiments could be equally applied to them. Beside the discrete statoconia, we may expect strong piezoelectric behaviour as statocysts operate independently of swim bladders and hence are the only pressure sensitive tranductors in cephalopods and gastropods.
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Cady 1964:177-200. Poggendorf’s seminal psychophysical paper on fish hearing (as reproduced in Tavolga 1976:147-181) outlines much of the problems (standing waves, reflective interference) in dealing with smalls tanks. Fay 1984 also sketches these problems. 31
8 Conclusion There exist sufficiently large gaps in our understanding of fish hearing to suggest that there exists alternate mechanisms at work. It has been established previously that otoliths exhibit piezoelectric qualities, and in this paper I have outlined a hypothesis concerning their application to auditory perception. While there exists non-trivial problems with the physics of a piezoelectric otolith, research has been very limited to date and further experimentation is necessary to uncover the underlying mechanisms. There is a strong possibility that piezoelectric effects may work in conjunction with vibratory effects to produce an overall auditory response. Further directions for research may aim to determine whether similar piezoelectric effects are present in statocysts or cochleas.
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