The Viscosity of the Pike’s Endolymph

The mechanical sensitivity of the semicircular canals of the vertebrates is determined by the dimensions and the absolute viscosity η of the fluid inside the vestibular organ (ten Kate, 1969). As Table 1 shows, η diverges widely in different species and measurements. These different values reveal the necessity of viscosity determination for comparative labyrinthology. According to Table 1 the viscosity values of the endolymph and of the perilymph are not the same. This is due to the different concentrations of the organic and inorganic compounds (Rauch, 1964; Silverstein, 1966; Fernandèz, 1967).

Evidence exists that there are certain cells that regulate the chemical composition of the endolymph (Bélanger, 1953; Dolman et al. 1959,1964). On account of the un-certainty of η and the need felt for an accurate value of η, the viscosity of the endolymph of the pike was studied in detail. The development of a microviscometer, based on Stoke’s law, has been undertaken. The effect that coagulation of proteins and globulins of the endolymph has on the measurement of η will be reduced compared with most capillary viscometers.

A sphere is allowed to fall in a tube filled with endolymph (method A). The amount of endolymph which can be extracted from one pike is limited (about 30 μl for a pike of 50 cm body length). Therefore the dimensions of the tube and the sphere have to be small. The capillaries used had a length of 6–10 cm and a (circular) inner diameter of 500 μ. The amount of liquid needed to fill one capillary was maximally 19 μl.

In Fig. 1 the specially shaped capillary is depicted.

The dimensions s_t and d of the capillary and the radius r_k of the metal alloy sphere (1% deviations from a perfect sphere) can be measured accurately. The densities ρ_k and ρ_L are found by determination of mass and volume.

Thus in our experiments we have measured the time t which the sphere takes to fall in a capillary filled with liquid over a distance s_t marked by two slits S₁ and S₂.

When the sphere passes the first slit S_o a photomultiplier produces an electric pulse, which triggers an oscilloscope. The second and third slits S₁ and S₂ subsequently cause vertical deflexions on the oscilloscope screen. In this way the time t could be measured (see Fig. 2).

In the actual experiment the capillary tube could be turned through 180°, its position deviating maximally 0·12 degrees from vertical (ten Kate, 1969).

A sphere is produced by pushing a melt metal alloy through a glass pipette with a tip diameter of 1·2 ρ. Then to overcome the surface tension this sphere, still attached to the tip of the pipette, is brought into the liquid of the capillary and is then dislodged (Fig. 1). At the end of the experiment with a microscope the exact diameter 2r_k is determined. In order to get the endolymph out of the semicircular canal, the sharp tip T of the capillary (Fig. 1) has been run through the thin wall of the osdum tubulare into the anterior ampulla with the aid of a micromanipulator (sometimes also into the ampulla lateralis). After sucking up the endolymph (with or without a seal of paraffin oil) T is removed from the nearly deflated labyrinth. Then each end of the capillary is closed with a rubber cover. Subsequently the above described procedure of viscosity determination begins.

Though we have carried out preliminary experiments with distilled water to confirm the correctness of the correction factor for Stoke’s law in the case f and R_e ⩽ 3, we have preferred also to check the effect of the adjacent walls on the absolute viscosity of the endolymph. Another method (method B) resembling the rolling sphere viscometer of Flowers (1914) was used in order to test method A and to avoid the effect of surface tension on the sphere. A ‘large’ sphere of 450 μ diameter falls in a straight tube of 500 μ width.

In. all cases the endolymph has been taken from preparations of decapitated pike 20 min after death.

The calculated values of η in Table 2 contain absolute errors calculated from estimated errors in the measurements. The errors in r_k and _st are one-fifth of a scale division in the microscopical measurements. Δt is one-tenth of the time scale on the screen of the oscilloscope. The relative error Δη/η can be calculated easily from the individual relative errors (see ten Kate, 1969).

The resulting values of the viscosity of the endolymph obtained by method B are similar to the values of method A. This conclusion can be drawn from Table 3.

This conclusion appears to be also in agreement with simultaneous measurement of the endolymph viscosity by methods A and B, using endolymph from both labyrinths of one pike; with method A η = 1·24 ± 0·08 cP and with method B η = 1·20 ± 0·07 cP. The measured values are within the range of possible errors of both methods.

The example of pike 8 demonstrates the change in viscosity after death. The pike’s head was thawed after 60 h in the refrigerator. The increase in viscosity of the post-mortem endolymph was also observed by ten Doesschate (1914). All measurements of the pike’s endolymph are performed 20–60 min after death and in this period no change of viscosity was noticed.

When the temperature is raised from 8 to 37 °C. the sensitivity of the pike’s semicircular canal would be doubled at a result of the change in the viscosity of the endolymph. If we compare the size of the semicircular canals of a pike and a mammal with the same body mass, the mammalian semicircular canal appears to be much smaller. Despite this difference in magnitude the semicircular canals of mammals and pike do have nearly the same sensitivity (ten Kate, 1969), if all parameters of the semicircular canal (including its dimensions) and the temperature are taken into account. In actual fact this aspect is related to the question of how the sensitivity and the dimensions of the pike’s semicircular canal change during growth. This is described in a second paper.

d inner radius of the capillary.

g acceleration of gravity.

h₀ height of the cupula.

l_l length of the narrow duct of the semicircular canal.

r_c radius of the narrow duct.

r_k radius of sphere.

s_t distance in a capillary between S₁ and S₂.

t time.

T_e temperature in °C.

A area enclosed by the average semicircular canal.

O_a area of cross-section of ampulla.

R_c radius of curvature of the deflected cupula.

R_e Reynolds number.

η, η_r absolute and relative viscosity of the endolymph, respectively.

η_w absolute viscosity of water.

ρ, ρ_k specific density of endolymph and of the sphere, respectively.