Visco-Elastic Properties of the Tunica Externa of the Swimbladder in Cyprinidae

The anterior sac of the swimbladder in the Cyprinidae is composed of two layers, the tunica externa and the tunica interna, which are connected to each other only weakly by a layer of loose connective tissue. A slit runs in the anterior dorsal mid-line of the tunica externa. The most posterior of the Weberian ossicles, the tripodes, are attached to the edges of this slit. This arrangement, which was demonstrated, apparently independently, by Evans (1925) (with some errors) and Chranilov (1929), is illustrated in Fig. 1.

Chranilov (1929) suggested that as the tissue connexion between tunica externa and tunica interna is so slight, small sliding movements of the tunicae relative to each other should occur readily. Hence, an increase in the volume of the anterior sac will result in outward movement of the edges of the slit, rotating the tripodes forward. On a subsequent decrease in volume, the edges of the slit and the tripodes will be returned to their original positions by the elastic recoil of the ligaments labelled 1 and 2 in Fig. 1. Further, if one or both of these ligaments is of such a length as to maintain tension in ligaments 3 and 4, movements of each tripus will be transmitted via the intercalarium to the scaphium, which forms one wall of the atrium sinus impar. Changes in volume of the anterior sac will thus result in displacement of the contents of the sinus impar. It has been shown that the Weberian apparatus is of value to Cyprinidae in detecting changes of anterior sac volume due both to sound waves (von Frisch & Stetter, 1932) and to slow changes of ambient pressure, such as the fish will experience if its depth below the water surface changes (Dijkgraaf, 1941). The extent to which the tripodes move for a given change of anterior sac volume will depend on the relationship between the elastic properties of the tunica externa and of the ligaments 1 and 2.

Progressive decreases of anterior sac volume will cease to cause movement of the Weberian ossicles as the ligaments 1 and 2 become slack, while progressive increases will cease to cause movement of the scaphia as the ligaments 3 and 4 become slack. It would thus appear that the ears receive information only of those changes of anterior sac volume which lie within a certain range.

A very small change of depth will produce a change of anterior sac volume as great as the amplitude of volume changes resulting from an extremely loud sound. There is a possibility that a quite small change of depth might result in a change of anterior sac volume to a value beyond the range within which the Weberian ossicles operate. Such a change of depth would thus produce partial deafness until the quantity of gas in the swimbladder was adjusted. This would plainly be undesirable. It might be avoided, however, if an appropriate high-pass frequency filter was built into the Weberian apparatus.

The tunica externa consists (Fauré-Fremiet & Garrault, 1937) of a trellis of elastic fibres, and needles of ichthyocol, which is a form of collagen consisting of short needles (length up to ca. 0·3 mm.) instead of long fibres. Ichthyocol slowly becomes fibrous after removal from the animal, and does so rapidly in 70% alcohol. It can therefore be examined only in fresh preparations, after teasing or after digesting the elastic fibres in pancreatin.

The only continuous elements in the tunica externa are thus elastic fibres, which are highly extensible (Burton, 1954). The ichthyocol, while unable to contribute to the elasticity of the tunica externa, might give it high viscosity. If this were so, the tunica externa would be rather inextensible to oscillating forces, such as it would be subject to when the swimbladder vibrated at audio frequencies, but highly extensible to forces applied over relatively long periods, such as those resulting from a change of swimbladder volume due to a change of depth. Provided that ligaments 1 and 2 were less viscous than the tunica externa, slow changes of swimbladder volume would result in smaller movements of the tripodes than rapid movements of the same amplitude. The Weberian apparatus would then incorporate a high-pass frequency filter, such as was suggested above. This paper is mainly concerned with the visco-elastic properties of the tunica externa.

Experiments on the tunica interna will also be reported. It appears to consist entirely of smooth muscle and ordinary collagen, without ichthyocol or elastic fibres.

The position of the slit makes it impossible to cut a ring of tunica externa (whose visco-elastic properties might be determined by stretching between hooks) such that elastic fibres run parallel to the cut edges, and so continuously round it. A method was therefore devised, based on the following principle.

A piece of the swimbladder layer under investigation was clamped as a membrane over a circular aperture. A pressure difference was applied across the membrane and stretched it into a dome-like shape. The extent of this bulging was determined at a series of measured times after the application of the pressure difference.

Most of the experiments described in this paper were carried out on tench (Tinea tinca (L.)). A few experiments on mirror carp (Cyprinus carpio L.) and rudd (Scardinius erythrophthalmus (L.)) are also reported. Most of the fish used weighed between 100 and 250 g.

The principal part of the apparatus is shown in section in Fig. 2. It is a hollow cylinder of Perspex of diameter 3 in., entered axially above and below by Perspex tubes, and obliquely by another tube from above. A brass plate with a central hole is held by three bolts, symmetrically placed, of which only one appears in the section; it is used to clamp a membrane (either tunica externa or tunica interna) between rubber washers so as to separate cavity A from cavity B. The washers are cut from a toy balloon, and are lightly greased. Access to the interior of the apparatus is provided by the removable bottom, which is held in position by three bolts, symmetrically placed, of which only one appears in the section.

The complete apparatus is represented in Fig. 3. It is filled with Ringer solution (Young, 1933; formula recommended for freshwater teleosts other than eels) whose surfaces are shown in the funnels, and which forms a meniscus in the thick-walled capillary. The position of this meniscus can be adjusted by means of the funnel opening through the oblique tube into cavity A.

The other two funnels are held by retort stands, and their heights can be adjusted. Either may be used to provide a head of water to give a pressure difference between A and B. The provision of two funnels makes possible instantaneous changing of the pressure by simultaneously turning one tap off and the other on. The pressure difference between A and B is given by the height above the capillary of the Ringer surface in the funnel whose tap is open. It stretches the membrane separating the cavities, which bulges into cavity A. This results in movement of the meniscus along the capillary. As the bore of the capillary has been determined by weighing the mercury which filled a measured length of it, this movement gives a measure of the extent to which the membrane has been stretched. The time course of an extension can be followed.

The diameter of cavity A is 0·97 cm. Capillaries of capacity about 0·01 ml./cm. have been found convenient: they are fine enough to give reasonable sensitivity, and coarse enough to give a response which is, for practical purposes, instantaneous.

All experiments were started with a pressure difference of 4 cm. water to hold the membrane taut. The rate of stretching under this low load was negligible by the time the apparatus had been set up. Care was taken to avoid subjecting the membrane to higher pressure difference while the apparatus was being set up (this was necessary as extension of the tunica externa was found to be partially irreversible). As far as possible, air bubbles were eliminated from the apparatus, but their presence could not affect the accuracy of experiments, since the recording side of the apparatus (cavity A) remained at constant pressure. The pressure was increased to 20, and sometimes thence to 36, cm. water.

Sometimes a leak developed in the membrane. As a check against this possibility, the pressure was briefly reversed before and after each experiment, and the consequent meniscus movement noted. This meniscus movement represented double the volume under the domed membrane. This procedure gave a measure of the total stretch that occurred in the course of the experiment, and could be compared with the value, subject to errors due to leaks, obtained by observing the movement of the meniscus through the main part of the experiment. When a leak was found to have occurred no quantitative use was made of the results of the experiment. In each of the experiments from which the data of Table 1 are derived the values for extension obtained by these two methods differed by less than 4%.

Extensions of the tunica externa were found to be partially irreversible, and it was thought necessary to consider the possibility that this result might be an artifact due to slipping of the membrane between the washers. This possibility was rejected for the following reasons :

• The effect was invariably found with tunicae extemae, but in only one experiment with a tunica interna. After this experiment the tunica interna was found, as would be expected, to be wrinkled round the edges. No such wrinkling was observed in experiments on tunicae extemae.

• The pressure of the washers left marks on the tunicae extemae which persisted for many hours after they were removed from the apparatus. The sharpness of the edges of these marks denied the possibility of the membranes having slipped between the washers.

Experiments were carried out on both tunica externa and tunica interna of each fish, usually but not always in that order. The ventral thickening of the tunica interna was avoided. The fish was killed immediately before the first experiment, and the specimen for the second was kept in Ringer until it was required. Experiments ended between and 12 hr. after the death of the fish. There was no evidence of the deterioration of material in this period. In one case (tench D 15) experiments were carried out on two pieces of tunica externa, one immediately after the fish had been killed and the other 7 hr. later. The second piece stretched rather more rapidly than the first, but in a qualitatively similar manner.

At the large deflexions occurring in these experiments, the shape of the membrane is determined almost entirely by pure stretching, and its flexural rigidity contributes little. The standard formula for small deflexions of a uniformly loaded plate (Love, 1893, p. 199) is, therefore, quite inapplicable. An exact mathematical treatment of the relation between strain of the membrane and movement of the meniscus in the capillary would necessarily be extremely complex. As the outer margin of the membrane is fixed, less extension in the circular direction occurs peripherally than centrally. In satisfying the well-known relationship between pressure difference, tension and radii of curvature, the membrane assumes the form of a dome which rises sharply at the edges but is more flattened centrally.

On this account the extending membrane may be considered as forming approximately the surface of a low cylinder open at one end. The radius of the cylinder, r, is constant and equal to the radius of the hole across which the membrane is clamped. Its height will be zero when there is no pressure difference across the membrane : let it be h after equifibration at a pressure difference p, and (h+Δh_t) a period of time, t, after the changing of the pressure difference to (p + Δp).

It was thus possible to calculate values for J_t.

An entirely different approximation in which the stretched membrane is assumed to take a spherical form gives values for J_t differing from those calculated from the above formula by only 20%. This gives added confidence that the values of compliance derived from the simple approximation here used will be accurate within a factor of two.

Pieces of tunica interna of tench, rudd and mirror carp showed, in this apparatus, no appreciable viscosity. Meniscus movements were practically complete within i sec. of any change of pressure. Extensions were found to be completely reversible. Compliances of about 2×10⁻⁷ cm.²/dyne were found.

In these experiments the tunicae internae were at much lower tensions than those to which they are subject in life, due to the excess internal pressure of the swimbladder (Alexander, 1959). The results obtained for them are thus of interest only as a contrast with those for tunicae externae, and in showing that the apparatus was capable of registering rapid extensions.

The behaviour of pieces of tunica externa was found to be considerably more complex. Fig. 4 shows the results of a typical experiment with a tench. The arrows mark the occasions when the pressure was briefly reversed, to check against the possibility of leakage through the membrane. The total strains observed were much larger than sfor tunica interna, but they were by no means instantaneous. The rate of stretching of tunica externa is clearly limited by a very high viscosity. The extensions were by no means completely reversible. The final rates of extension observed in each experiment were much too low to permit explanation of this irreversibility in terms of series viscous components. The course of extension can most simply be interpreted in terms of Voigt elements (i.e. of viscous components arranged in parallel with elastic ones). The partial irreversibility is behaviour of the type known in ‘frozen rubbers’ as described by Pryor (1950).

In Figs. 5 and 6 radial strain per unit stress, J_t, is plotted against the time t (shown On a logarithmic scale) after the initial increase of pressure from 4 to 20 cm. water in the successful experiments on the tunicae externae of tench. The values of may be compared with the compliances of about 3×10⁻⁷ cm.²/dyne which have been found for elastin (Burton, 1954). Only a small proportion, of course, of the volume of the tunica externa consists of elastin.

The distribution of gradient along such curves approximates closely to the distribution of elastic compliance with respect to retardation time, except in its tendency to suppress sharp discontinuities (Alfrey & Doty, 1945). The gradients are seen to be low for small values of t, but rise rapidly to steady values which are maintained, except in the case of D16, to the highest value of t for which measurements were made. The gradients and intercepts on the time axis of these straight parts of the curves are given in Table 1. It appears that compliance of about 8 × 10⁻⁷ cm.^a/dyne is associated with each increase by a factor of 10 of retardation time from about 4 to 2000 sec. or more.

A large part of the compliance of tench tunica externa is thus associated with retardation times greater than 1 sec., and this compliance is distributed uniformly with respect to the logarithm of retardation time over a wide range of retardation times. Distributions of this type occur in rubbers and certain synthetic polymers (see, for instance, Tobolsky, Dunnell & Andrews, 1951). However, only a small part of this compliance is reversible.

In experiments D15 (both specimens of tunica externa) and D16 the pressure difference across the tunica externa was returned to 4 cm. water after a period at 20 cm. water. The course of the consequent incomplete elastic recoil was followed. The results are presented in Fig. 7, which is a graph of the same type as Figs. 5 and 6 except that meniscus movement is plotted instead of radial strain per unit stress. The latter cannot be calculated, since extension at the higher pressure was not complete when the pressure was reduced again. The restoring force is therefore not known. The meniscus movements are small, and more sensitive apparatus would be required to record them accurately. However, the data appear to show that the reversible part of the compliance of tunica externa is almost entirely associated with retardation times between 5 and 1000 sec. The mean total meniscus return, of 13 cm., indicates a reversible compliance of not less than 2·5×10⁻⁷ cm.²/dyne between the stresses involved in the experiment.

Experiments on the tunicae externae of two mirror carp and four rudd gave results qualitatively similar to those reported for tench, but these could not be used for quantitative analysis owing to leakage of fluid through the specimens.

Most tunicae externae used withstood pressure differences of 36 cm. water, but those of a 97 g. and a 282 g. tench tested to destruction, ruptured at 60 and 100 cm. water, respectively. Tunicae internae are much stronger.

The point was made in the introduction to this paper that the extent to which the tripodes move for a given change of anterior sac volume will depend on the relationship between the elastic properties of the tunica externa and of ligaments 1 and 2 of Fig. 1. It has been shown in this paper that the tunica externa is markedly viscous. A large part of its compliance (both of the reversible and of the irreversible components) is associated with retardation times greater than 1 sec. It will thus yield much less to forces oscillating at audio frequencies than it will over a period of many seconds to a steady force. If ligaments 1 and 2 are more normal tissues with less viscous properties, slow changes of anterior sac volume will result in smaller movements of the tripodes than oscillatory changes of the same amplitude at audio frequencies. The possibility that a change of depth will move the Weberian ossicles to the limits of their working range, and so produce temporary partial deafness, is thus reduced, without reducing the sensitivity of the system to sound.

This hypothesis depends on the viscosities of ligaments 1 and 2 being reasonably small. The viscous properties of the tunica externa are probably due to the presence of a large proportion of ichthyocol in this tissue. In sections of goldfish (Carassius auratus (L.)) stained with Mallory’s triple stain, ligaments 1 and 2 stain (as does the tunica externa) as collagen. However, I have been unable to find ichthyocol in teased ligaments 1 and 2 of tench and crucian carp (C. carassius (L)). It therefore appears that this collagen is of the normal fibrous type, and there is no reason to suppose that these ligaments share the peculiar visco-elastic properties of tunica externa.

The hypothesis meets a difficulty, however, in the partial irreversibility of tunica externa extensions. One is tempted to suppose that complete reversibility may obtain in life, perhaps owing to the presence of a plasticizer. If this is not the case, the behaviour of the tunica externa will still be viscous (as shown by the results displayed in Fig. 7) but only the smaller reversible part of the compliance will be effective. The tunica externa will become permanently slack, and the Weberian apparatus will cease to function, if the anterior sac is ever allowed temporarily to exceed a certain size. However, the ‘Gasspuckreflex’ may be sufficient protection against this. Further investigation is required.

I find that ligaments 3 and 4 (see Fig. 1) of tench and crucian carp are rich in ichthyocol. It therefore seems likely that their visco-elastic properties may resemble those of the tunica externa. They may transmit rapid vibrations of the tripodes to the scaphia more strongly than slow movements. If so they will constitute a high-pass frequency filter supplementary to the one involving the tunica externa. An investigation of the properties of these ligaments is planned.

I wish to thank Dr K. E. Machin for valuable advice on the physics of this problem.