Distribution of Oxygen Tension in the Blood and Water Along the Secondary Lamella of the Icefish Gill

Although the terminal water and blood tensions have been measured for a number of fish (Stevens & Randall, 1967; Piiper & Baumgarten-Schumann, 1967, 1968; Holeton, 1970; Garey, 1967), investigation of this aspect of gill function is extremely difficult. Measurements of the tension at different points along the lamellar surfaces have been made only for the crab gill (Hughes, Knights & Scammell, 1969). A knowledge of the distribution of O₂ tensions along the exchange surface is important theoretically and also for practical use in relation to diffusing capacity etc. In many recent studies the term ΔP_G (Randall, Holeton & Stevens, 1967; Holeton, 1970; Jones et al. 1970) has been used as a measure of the effective O₂ tension difference. It assumes a linear relationship between gas tension and content, and that the difference between water and blood O₂ tensions is constant along the exchange surface. Piiper & Baumgarten-Schumann (1968) recognized this deficiency and applied a Bohr integration method to the dogfish gill.

In a recent analysis (Hughes & Hills, 1971) the distribution of O₂ tensions in the dogfish gill was calculated and plotted by a method which took into account the particular shape of the secondary lamellae and also the blood O₂ dissociation curve. The dogfish was convenient because CO₂ has relatively little effect on the O₂ dissociation curve. In many ways the antarctic fish which lack haemoglobin are even more ideal since complications due to the form of the O₂ dissociation curve are absent, which makes them suitable material for theoretical analyses on the influence of secondary lamellar shape. Gas tensions in the water and blood have been measured for the icefish (Holeton, 1970), and are combined with recent measurements of the secondary gill lamellae in this analysis.

= volume of water passing across gills in unit time.

= volume of blood passing through gills in unit time.

S_w = solubility coefficient of O₂ in water.

S_b = solubility coefficient of O₂ in blood (= S_w in icefish).

P_wi= O₂ tension of water entering the gill.

P_wo = O₂ tension of water leaving the gill.

P_aff = O₂ tension in afferent blood, entering the gill.

P_eff= O₂ tension in efferent blood, leaving the gill.

p_w = O_a tension of water at a particular point, x, along a secondary lamella.

P_w = O₂ tension in blood at x, along a secondary lamella.

C_a = O₂. content of afferent blood.

C_e = O₂ content of efferent blood.

Specimens of Chaenocephalus aceratus were caught near the Signy Island laboratory of the British Antarctic Survey. They were used in laboratory experiments which included the measurement of O₂ tensions in the inspired and expired water, and in afferent and efferent blood under the conditions described by Holeton (1970). Gills of some of the fish used were brought to Bristol and their surface areas were measured using a method of weighted averages. It was shown that these areas were smaller than those previously measured (Hughes in Hughes & Shelton, 1962; Steen & Kruysse, 1966) and further investigation has suggested that the earlier specimens were not Chaenocephalus aceratus but another species of icefish, possibly Pseudochaenichthys georgianas. Profiles of individual secondary lamellae were taken and measurements were made of the cumulative surface area as described by Hughes (1970) (Figs. 1–3).

The surface areas of the gills and their component parameters are shown in Table 1, together with corresponding data from earlier measurements.

The most obvious differences are in the number of secondary lamellae per milli-metre and the area of an average secondary lamella. Such marked differences strongly support the view that the earlier measurements were on a different species.

From Figs. 1 and 2,a it is clear that although the bilateral surface area may not differ for secondary lamellae from the tip or middle of a filament, there are marked differences in their form, as shown by plotting cumulative area against water-path length. However, the same data plotted so as to cancel out differences in absolute dimensions (Fig. 2,b), shows that secondary lamellae from the tip and middle of a filament have very similar relationships between cumulative area and fractional path length. Secondary lamellae from the base of the filament, however, are somewhat different in that their cumulative area increases more rapidly from the point of water entry and is added to at a constant rate over more than 95 % of the remaining path length. Cumulative area can also be plotted in the direction of blood flow as is done below (figs. 3 and 5) because this will not change from co-current to counter flow.

The method adopted is the same as that developed by Hughes & Hills (1971) for the dogfish. Essentially this consists in dividing the known overall change in blood O₂ tension into a convenient number of sections, in this case 11 (column A, Table 2). The corresponding percentage saturation of the blood is calculated assuming a linear relationship between tension and content (column B). From the available data and the mass-balance equation

(Note that in this particular case the capacity rate ratio (Hughes, 1964), wbuld have been the appropriate constant.) Inserting data based on that summarized by Holeton (1970), i.e. P_wi = 150 mm; P_wo = 120 mm; P_aff = 25 mm; P_eff = 120 mm this ratio is 0·474. This constant can now be inserted in equations for co-current and counter-current flow, enabling (P_wi – p_w) to be calculated and hence the water O₂ tensions (p_w) which correspond to the chosen blood O₂ tensions at different positions along the secondary lamella. From this data and a plot (Fig. 4) of 1/(P_w – p₀) against O₂ tensions between p_wb and p_wi it is possible to obtain values for the function F, by graphical integration:

This fractional change is effectively a measure of the area necessary for O₂ transfer assuming either co-current or counter-current flow, i.e. the greater the area beneath this curve (Fig. 4) the greater the area required for gas exchange. In Fig. 4 it is shown that the total area under the curve for co-current is 91·58 as against 52-96 for counter-current flow and from which the fractional areas may be derived (I in Table 3) at

different values of p_w between p_wo and p_wi. Having obtained values for F from both morphological and functional plots, it is possible to read off the corresponding fractional path length (x/L) along the secondary lamella for p_w and hence p_b (Fig. 5). When plotted out these values give the final graph showing the distribution of O₂ tensions in the water and blood for co-current and counter-current flows across the chosen secondary lamella profile.

From this plot (Fig. 6) it is clear that for co-current flow the gas tensions approach one another asymptotically so that the difference in O₂ tension between water and blood is very great to begin with but finally becomes zero. Correspondingly 1/(P_w – p_b) approaches infinity (Fig. 4). With counter-current flow, however, there is always a significant difference between the water and blood O₂ tensions. The usual method of calculation:

Because the blood O₂ dissociation curve is not a complicating factor, the icefish provides a suitable model for investigating the effects of different shapes of secondary lamellae on the O₂ tension distribution. The profiles shown in Fig. 7 have been used to plot out cumulative areas along the fractional path length. These morphological plots of F against x/L were used together with data for the terminal water and blood O₂ tensions in the same way as described for counter-current flow across an actual secondary lamella and are shown in fig. 8.

For the simple rectangular profile (1), the blood and water tensions are slightly greater than those obtained by connecting directly P_wi with and P_wo with P_aff. For a profile in which the major part of the area comes early in the water path length (2), p_w falls more rapidly than in the other cases and correspondingly p_b increases less rapidly at the afferent end because this particular model has the least exchange area in this region of the path length.

Calculations based on secondary lamellae from the tip or middle of a filament show tension changes which lie somewhat between profiles 2 and 3 as would be expected from their geometry. The advantages of a shape such as that in profile 2 is that it ensures that the maximum exchange area is in the region where the difference in O₂ tensions of water and blood is smaller and vice versa. Hence this particular arrangement maintains the greatest tension differential between water and blood throughout their passage across the gill.

The measurements made on the gills of Chaenocephalus aceratus confirm the generalization made from the previous specimens of icefish that the sieve will provide relatively little resistance to water flow (Hughes, 1966). The smaller gill area of these specimens is presumably an interspecific difference. From the data reported here and other specimens (G. F. Holeton, personal communication), it seems that the weight-specific gill area remains constant at all body sizes.

Because of its lack of haemoglobin the icefish is useful in several theoretical calculations. It illustrates, for example, the value of the concept of effectiveness as against utilization as a measure of the performance of a gill gas exchanger. This is especially so if one remembers that from a homeostatic point of view it is the condition of the blood leaving the gill which is so important (Hughes, 1964).

The same is also true of a rainbow trout when the haemoglobin has been combined with carbon monoxide (Table 4).

Thus the gill is very effectively carrying out its function of oxygenating the blood, although it does not seem very efficient as measured by its utilization of O₂ in the water. The analysis presented in this paper indicates that an important factor in maintaining this performance is not only the area of the gas-exchange surface but also its particular shape. The shape most commonly found and used here seems to be designed to maintain a high difference in gas tension between the water and blood throughout their passage over the exchange surface.

From the measurements available, it seems almost certain that counter-current flow is normally present, and these calculations have been based on this assumption.

Hence, a greater total amount of O₂ will be transferred for a given area of exchange surface if a larger proportion (a) of the total secondary lamellar area (A) is in contact with water of the highest O₂ tensions. Further analysis of gas transfer across secondary lamellae must take into account the differences in path length of the water flowing at different levels of the secondary lamella rather than assume that all the water remains within the profile boundary, as is true for the blood.

A further limitation of this type of analysis relates to the basic experimental data used in the calculations (i.e. values of P_wi, P_wo, P_aff and P_eff). Although it wbuld be extremely difficult to obtain true values for P_aff and P_eff of individual secondary lamellae, this should be possible for P_wi and P_wo and hence some of the dilution effects of water shunted between the filament tips could be assessed. Before such analyses can be expanded to the whole of the gill system a great deal needs to be learned about different degrees of recruitment on both sides of the exchanger and consequent ventilation/perfusion inequalities (Hughes, 1972).

1. Measurements of the gill area of two specimens of Chaenocephalus aceratus indicate that the resistance to water flow and overall exchange area are even less than had been supposed from work with other icefish.

2. Measurements of the oxygen tensions in the water and in blood entering and leaving the gills are used to determine the expected distribution of O₂ tensions along a typical secondary lamella profile. The advantage of counter-current over co-current flow is clearly indicated by such analyses.

3. The absence of complications due to the O₂ dissociation curve of the blood facilitates an extension of the analysis to different theoretical secondary lamellar profiles. It is shown that profiles similar to those usually found in fish gills are more efficient in maintaining O₂ transfer.

4. Although the percentage utilization of O₂ in the water passing through the gills is relatively low, the effectiveness of oxygenating the blood is very high in the icefish gill.

This work was supported by a grant from the Natural Environment Research Council. I wish to thank Dr. G. F. Holeton for carrying out the O₂ measurements and bringing back the gill material from Signy Island. I also enjoyed valuable discussion with Dr Brian Hills.